diff --git a/ProcessLib/SmallDeformation/Tests.cmake b/ProcessLib/SmallDeformation/Tests.cmake
index 49192fb4fc37f39e2f59176dfd48eab2a56dd7a5..285c4bfaebc8846300a6f042fb8f551781f01f69 100644
--- a/ProcessLib/SmallDeformation/Tests.cmake
+++ b/ProcessLib/SmallDeformation/Tests.cmake
@@ -18,6 +18,8 @@ if (NOT OGS_USE_MPI)
     OgsTest(PROJECTFILE Mechanics/Linear/Orthotropy/square_1e0_orthotropic_xyz.prj)
     OgsTest(PROJECTFILE Mechanics/Linear/Orthotropy/square_1e0_orthotropic_yzx.prj)
     OgsTest(PROJECTFILE Mechanics/Linear/Orthotropy/square_1e0_orthotropic_zxy.prj)
+    OgsTest(PROJECTFILE Mechanics/Linear/Orthotropy/square_1e0_orthotropic_45xy_z.prj)
+    OgsTest(PROJECTFILE Mechanics/Linear/Orthotropy/square_1e0_orthotropic_y-xz.prj)
     OgsTest(PROJECTFILE Mechanics/Burgers/cube_1e0.prj)
     OgsTest(PROJECTFILE Mechanics/Burgers/cube_1e3.prj LARGE)
     OgsTest(PROJECTFILE Mechanics/Ehlers/cube_1e0.prj)
@@ -51,7 +53,12 @@ if (OGS_USE_MFRONT)
     OgsTest(PROJECTFILE Mechanics/MohrCoulombAbboSloan/load_test_mc.prj)
     #TODO (naumov) enable when output file format can be specified
     #OgsTest(PROJECTFILE Mechanics/MohrCoulombAbboSloan/oedometer.prj RUNTIME 80)
-
+    OgsTest(PROJECTFILE Mechanics/Linear/MFront/cube_1e0_orthotropic_xyz.prj)
+    OgsTest(PROJECTFILE Mechanics/Linear/MFront/cube_1e0_orthotropic_yzx.prj)
+    OgsTest(PROJECTFILE Mechanics/Linear/MFront/cube_1e0_orthotropic_zxy.prj)
+    OgsTest(PROJECTFILE Mechanics/Linear/MFront/square_1e0_orthotropic_xyz.prj)
+    OgsTest(PROJECTFILE Mechanics/Linear/MFront/square_1e0_orthotropic_45xy_z.prj)
+    OgsTest(PROJECTFILE Mechanics/Linear/MFront/square_1e0_orthotropic_y-xz.prj)
 # Linear elastic, no internal state variables, no external state variables.
 AddTest(
     NAME Mechanics_SDL_disc_with_hole_mfront
diff --git a/Tests/Data/Mechanics/Linear/MFront/cube_1e0_orthotropic_xyz.prj b/Tests/Data/Mechanics/Linear/MFront/cube_1e0_orthotropic_xyz.prj
new file mode 100644
index 0000000000000000000000000000000000000000..b362795d02bf4506a062ee211dfc26ec0d4d90fc
--- /dev/null
+++ b/Tests/Data/Mechanics/Linear/MFront/cube_1e0_orthotropic_xyz.prj
@@ -0,0 +1,253 @@
+<?xml version="1.0" encoding="ISO-8859-1"?>
+<OpenGeoSysProject>
+    <mesh>cube_1x1x1_hex_1e0.vtu</mesh>
+    <geometry>cube_1x1x1.gml</geometry>
+    <processes>
+        <process>
+            <name>SD</name>
+            <type>SMALL_DEFORMATION</type>
+            <integration_order>2</integration_order>
+            <constitutive_relation>
+                <type>MFront</type>
+                <behaviour>StandardElasticityBrickOrtho</behaviour>
+                <material_properties>
+                    <material_property name="YoungModulus1" parameter="E1"/>
+                    <material_property name="YoungModulus2" parameter="E2"/>
+                    <material_property name="YoungModulus3" parameter="E3"/>
+                    <material_property name="PoissonRatio12" parameter="nu12"/>
+                    <material_property name="PoissonRatio23" parameter="nu23"/>
+                    <material_property name="PoissonRatio13" parameter="nu13"/>
+                    <material_property name="ShearModulus12" parameter="G12"/>
+                    <material_property name="ShearModulus23" parameter="G23"/>
+                    <material_property name="ShearModulus13" parameter="G13"/>
+                </material_properties>
+            </constitutive_relation>
+            <solid_density>rho_sr</solid_density>
+            <specific_body_force>0 0 0</specific_body_force>
+            <reference_temperature>293.15</reference_temperature>
+            <process_variables>
+                <process_variable>displacement</process_variable>
+            </process_variables>
+            <secondary_variables>
+                <secondary_variable internal_name="sigma" output_name="sigma"/>
+                <secondary_variable internal_name="epsilon" output_name="epsilon"/>
+            </secondary_variables>
+        </process>
+    </processes>
+    <time_loop>
+        <processes>
+            <process ref="SD">
+                <nonlinear_solver>basic_newton</nonlinear_solver>
+                <convergence_criterion>
+                    <type>DeltaX</type>
+                    <norm_type>NORM2</norm_type>
+                    <abstol>1e-15</abstol>
+                </convergence_criterion>
+                <time_discretization>
+                    <type>BackwardEuler</type>
+                </time_discretization>
+                <time_stepping>
+                    <type>FixedTimeStepping</type>
+                    <t_initial>0</t_initial>
+                    <t_end>1</t_end>
+                    <timesteps>
+                        <pair>
+                            <repeat>4</repeat>
+                            <delta_t>0.25</delta_t>
+                        </pair>
+                    </timesteps>
+                </time_stepping>
+            </process>
+        </processes>
+        <output>
+            <type>VTK</type>
+            <prefix>cube_1e0_xyz_orthotropic</prefix>
+            <timesteps>
+                <pair>
+                    <repeat>1</repeat>
+                    <each_steps>10000000</each_steps>
+                </pair>
+            </timesteps>
+            <variables>
+                <variable>displacement</variable>
+                <variable>sigma</variable>
+                <variable>epsilon</variable>
+            </variables>
+        </output>
+    </time_loop>
+    <local_coordinate_system>
+        <basis_vector_0>e0</basis_vector_0>
+        <basis_vector_1>e1</basis_vector_1>
+        <basis_vector_2>e2</basis_vector_2>
+    </local_coordinate_system>
+    <parameters>
+        <parameter>
+            <name>e0</name>
+            <type>Constant</type>
+            <values>1 0 0</values>
+        </parameter>
+        <parameter>
+            <name>e1</name>
+            <type>Constant</type>
+            <values>0 1 0</values>
+        </parameter>
+        <parameter>
+            <name>e2</name>
+            <type>Constant</type>
+            <values>0 0 1</values>
+        </parameter>
+        <parameter>
+            <name>E1</name>
+            <type>Constant</type>
+            <values>1</values>
+        </parameter>
+        <parameter>
+            <name>E2</name>
+            <type>Constant</type>
+            <values>1</values>
+        </parameter>
+        <parameter>
+            <name>E3</name>
+            <type>Constant</type>
+            <values>0.5</values>
+        </parameter>
+        <parameter>
+            <name>nu12</name>
+            <type>Constant</type>
+            <values>.2</values>
+        </parameter>
+        <parameter>
+            <name>nu23</name>
+            <type>Constant</type>
+            <values>.3</values>
+        </parameter>
+        <parameter>
+            <name>nu13</name>
+            <type>Constant</type>
+            <values>.4</values>
+        </parameter>
+        <parameter>
+            <name>G12</name>
+            <type>Constant</type>
+            <values>1</values>
+        </parameter>
+        <parameter>
+            <name>G23</name>
+            <type>Constant</type>
+            <values>1</values>
+        </parameter>
+        <parameter>
+            <name>G13</name>
+            <type>Constant</type>
+            <values>1</values>
+        </parameter>
+
+        <parameter>
+            <name>rho_sr</name>
+            <type>Constant</type>
+            <value>1</value>
+        </parameter>
+        <parameter>
+            <name>displacement0</name>
+            <type>Constant</type>
+            <values>0 0 0</values>
+        </parameter>
+        <parameter>
+            <name>dirichlet0</name>
+            <type>Constant</type>
+            <value>0</value>
+        </parameter>
+        <parameter>
+            <name>Neumann_force_top</name>
+            <type>Constant</type>
+            <value>0.01</value>
+        </parameter>
+    </parameters>
+    <process_variables>
+        <process_variable>
+            <name>displacement</name>
+            <components>3</components>
+            <order>1</order>
+            <initial_condition>displacement0</initial_condition>
+            <boundary_conditions>
+                <!-- fixed boundaries -->
+                <boundary_condition>
+                    <geometrical_set>cube_1x1x1_geometry</geometrical_set>
+                    <geometry>left</geometry>
+                    <type>Dirichlet</type>
+                    <component>0</component>
+                    <parameter>dirichlet0</parameter>
+                </boundary_condition>
+                <boundary_condition>
+                    <geometrical_set>cube_1x1x1_geometry</geometrical_set>
+                    <geometry>front</geometry>
+                    <type>Dirichlet</type>
+                    <component>1</component>
+                    <parameter>dirichlet0</parameter>
+                </boundary_condition>
+                <boundary_condition>
+                    <geometrical_set>cube_1x1x1_geometry</geometrical_set>
+                    <geometry>bottom</geometry>
+                    <type>Dirichlet</type>
+                    <component>2</component>
+                    <parameter>dirichlet0</parameter>
+                </boundary_condition>
+                <boundary_condition>
+                    <geometrical_set>cube_1x1x1_geometry</geometrical_set>
+                    <geometry>top</geometry>
+                    <type>Neumann</type>
+                    <component>2</component>
+                    <parameter>Neumann_force_top</parameter>
+                </boundary_condition>
+            </boundary_conditions>
+        </process_variable>
+    </process_variables>
+    <nonlinear_solvers>
+        <nonlinear_solver>
+            <name>basic_newton</name>
+            <type>Newton</type>
+            <max_iter>4</max_iter>
+            <linear_solver>general_linear_solver</linear_solver>
+        </nonlinear_solver>
+    </nonlinear_solvers>
+    <linear_solvers>
+        <linear_solver>
+            <name>general_linear_solver</name>
+            <lis>-i cg -p jacobi -tol 1e-16 -maxiter 10000</lis>
+            <eigen>
+                <solver_type>SparseLU</solver_type>
+                <scaling>true</scaling>
+            </eigen>
+            <petsc>
+                <prefix>sd</prefix>
+                <parameters>-sd_ksp_type cg -sd_pc_type bjacobi -sd_ksp_rtol 1e-16 -sd_ksp_max_it 10000</parameters>
+            </petsc>
+        </linear_solver>
+    </linear_solvers>
+    <test_definition>
+        <vtkdiff>
+            <file>cube_1e0_xyz_orthotropic_pcs_0_ts_4_t_1.000000.vtu</file>
+            <field>displacement</field>
+            <absolute_tolerance>1e-14</absolute_tolerance>
+            <relative_tolerance>1e-15</relative_tolerance>
+        </vtkdiff>
+        <vtkdiff>
+            <file>cube_1e0_xyz_orthotropic_pcs_0_ts_4_t_1.000000.vtu</file>
+            <field>NodalForces</field>
+            <absolute_tolerance>1e-14</absolute_tolerance>
+            <relative_tolerance>1e-15</relative_tolerance>
+        </vtkdiff>
+        <vtkdiff>
+            <file>cube_1e0_xyz_orthotropic_pcs_0_ts_4_t_1.000000.vtu</file>
+            <field>sigma</field>
+            <absolute_tolerance>1e-14</absolute_tolerance>
+            <relative_tolerance>1e-15</relative_tolerance>
+        </vtkdiff>
+        <vtkdiff>
+            <file>cube_1e0_xyz_orthotropic_pcs_0_ts_4_t_1.000000.vtu</file>
+            <field>epsilon</field>
+            <absolute_tolerance>1e-14</absolute_tolerance>
+            <relative_tolerance>1e-15</relative_tolerance>
+        </vtkdiff>
+    </test_definition>
+</OpenGeoSysProject>
diff --git a/Tests/Data/Mechanics/Linear/MFront/cube_1e0_orthotropic_yzx.prj b/Tests/Data/Mechanics/Linear/MFront/cube_1e0_orthotropic_yzx.prj
new file mode 100644
index 0000000000000000000000000000000000000000..4f6ea6387446ca0c122203f310d0baa4dfb0b44d
--- /dev/null
+++ b/Tests/Data/Mechanics/Linear/MFront/cube_1e0_orthotropic_yzx.prj
@@ -0,0 +1,253 @@
+<?xml version="1.0" encoding="ISO-8859-1"?>
+<OpenGeoSysProject>
+    <mesh>cube_1x1x1_hex_1e0.vtu</mesh>
+    <geometry>cube_1x1x1.gml</geometry>
+    <processes>
+        <process>
+            <name>SD</name>
+            <type>SMALL_DEFORMATION</type>
+            <integration_order>2</integration_order>
+            <constitutive_relation>
+                <type>MFront</type>
+                <behaviour>StandardElasticityBrickOrtho</behaviour>
+                <material_properties>
+                    <material_property name="YoungModulus1" parameter="E1"/>
+                    <material_property name="YoungModulus2" parameter="E2"/>
+                    <material_property name="YoungModulus3" parameter="E3"/>
+                    <material_property name="PoissonRatio12" parameter="nu12"/>
+                    <material_property name="PoissonRatio23" parameter="nu23"/>
+                    <material_property name="PoissonRatio13" parameter="nu13"/>
+                    <material_property name="ShearModulus12" parameter="G12"/>
+                    <material_property name="ShearModulus23" parameter="G23"/>
+                    <material_property name="ShearModulus13" parameter="G13"/>
+                </material_properties>
+            </constitutive_relation>
+            <solid_density>rho_sr</solid_density>
+            <specific_body_force>0 0 0</specific_body_force>
+            <reference_temperature>293.15</reference_temperature>
+            <process_variables>
+                <process_variable>displacement</process_variable>
+            </process_variables>
+            <secondary_variables>
+                <secondary_variable internal_name="sigma" output_name="sigma"/>
+                <secondary_variable internal_name="epsilon" output_name="epsilon"/>
+            </secondary_variables>
+        </process>
+    </processes>
+    <time_loop>
+        <processes>
+            <process ref="SD">
+                <nonlinear_solver>basic_newton</nonlinear_solver>
+                <convergence_criterion>
+                    <type>DeltaX</type>
+                    <norm_type>NORM2</norm_type>
+                    <abstol>1e-15</abstol>
+                </convergence_criterion>
+                <time_discretization>
+                    <type>BackwardEuler</type>
+                </time_discretization>
+                <time_stepping>
+                    <type>FixedTimeStepping</type>
+                    <t_initial>0</t_initial>
+                    <t_end>1</t_end>
+                    <timesteps>
+                        <pair>
+                            <repeat>4</repeat>
+                            <delta_t>0.25</delta_t>
+                        </pair>
+                    </timesteps>
+                </time_stepping>
+            </process>
+        </processes>
+        <output>
+            <type>VTK</type>
+            <prefix>cube_1e0_yzx_orthotropic</prefix>
+            <timesteps>
+                <pair>
+                    <repeat>1</repeat>
+                    <each_steps>10000000</each_steps>
+                </pair>
+            </timesteps>
+            <variables>
+                <variable>displacement</variable>
+                <variable>sigma</variable>
+                <variable>epsilon</variable>
+            </variables>
+        </output>
+    </time_loop>
+    <local_coordinate_system>
+        <basis_vector_0>e1</basis_vector_0>
+        <basis_vector_1>e2</basis_vector_1>
+        <basis_vector_2>e0</basis_vector_2>
+    </local_coordinate_system>
+    <parameters>
+        <parameter>
+            <name>e0</name>
+            <type>Constant</type>
+            <values>1 0 0</values>
+        </parameter>
+        <parameter>
+            <name>e1</name>
+            <type>Constant</type>
+            <values>0 1 0</values>
+        </parameter>
+        <parameter>
+            <name>e2</name>
+            <type>Constant</type>
+            <values>0 0 1</values>
+        </parameter>
+        <parameter>
+            <name>E1</name>
+            <type>Constant</type>
+            <values>1</values>
+        </parameter>
+        <parameter>
+            <name>E2</name>
+            <type>Constant</type>
+            <values>0.5</values>
+        </parameter>
+        <parameter>
+            <name>E3</name>
+            <type>Constant</type>
+            <values>1</values>
+        </parameter>
+        <parameter>
+            <name>nu12</name>
+            <type>Constant</type>
+            <values>.3</values>
+        </parameter>
+        <parameter>
+            <name>nu23</name>
+            <type>Constant</type>
+            <values>.2</values>
+        </parameter>
+        <parameter>
+            <name>nu13</name>
+            <type>Constant</type>
+            <values>.2</values>
+        </parameter>
+        <parameter>
+            <name>G12</name>
+            <type>Constant</type>
+            <values>1</values>
+        </parameter>
+        <parameter>
+            <name>G23</name>
+            <type>Constant</type>
+            <values>1</values>
+        </parameter>
+        <parameter>
+            <name>G13</name>
+            <type>Constant</type>
+            <values>1</values>
+        </parameter>
+
+        <parameter>
+            <name>rho_sr</name>
+            <type>Constant</type>
+            <value>1</value>
+        </parameter>
+        <parameter>
+            <name>displacement0</name>
+            <type>Constant</type>
+            <values>0 0 0</values>
+        </parameter>
+        <parameter>
+            <name>dirichlet0</name>
+            <type>Constant</type>
+            <value>0</value>
+        </parameter>
+        <parameter>
+            <name>Neumann_force_top</name>
+            <type>Constant</type>
+            <value>0.01</value>
+        </parameter>
+    </parameters>
+    <process_variables>
+        <process_variable>
+            <name>displacement</name>
+            <components>3</components>
+            <order>1</order>
+            <initial_condition>displacement0</initial_condition>
+            <boundary_conditions>
+                <!-- fixed boundaries -->
+                <boundary_condition>
+                    <geometrical_set>cube_1x1x1_geometry</geometrical_set>
+                    <geometry>left</geometry>
+                    <type>Dirichlet</type>
+                    <component>0</component>
+                    <parameter>dirichlet0</parameter>
+                </boundary_condition>
+                <boundary_condition>
+                    <geometrical_set>cube_1x1x1_geometry</geometrical_set>
+                    <geometry>front</geometry>
+                    <type>Dirichlet</type>
+                    <component>1</component>
+                    <parameter>dirichlet0</parameter>
+                </boundary_condition>
+                <boundary_condition>
+                    <geometrical_set>cube_1x1x1_geometry</geometrical_set>
+                    <geometry>bottom</geometry>
+                    <type>Dirichlet</type>
+                    <component>2</component>
+                    <parameter>dirichlet0</parameter>
+                </boundary_condition>
+                <boundary_condition>
+                    <geometrical_set>cube_1x1x1_geometry</geometrical_set>
+                    <geometry>top</geometry>
+                    <type>Neumann</type>
+                    <component>2</component>
+                    <parameter>Neumann_force_top</parameter>
+                </boundary_condition>
+            </boundary_conditions>
+        </process_variable>
+    </process_variables>
+    <nonlinear_solvers>
+        <nonlinear_solver>
+            <name>basic_newton</name>
+            <type>Newton</type>
+            <max_iter>4</max_iter>
+            <linear_solver>general_linear_solver</linear_solver>
+        </nonlinear_solver>
+    </nonlinear_solvers>
+    <linear_solvers>
+        <linear_solver>
+            <name>general_linear_solver</name>
+            <lis>-i cg -p jacobi -tol 1e-16 -maxiter 10000</lis>
+            <eigen>
+                <solver_type>SparseLU</solver_type>
+                <scaling>true</scaling>
+            </eigen>
+            <petsc>
+                <prefix>sd</prefix>
+                <parameters>-sd_ksp_type cg -sd_pc_type bjacobi -sd_ksp_rtol 1e-16 -sd_ksp_max_it 10000</parameters>
+            </petsc>
+        </linear_solver>
+    </linear_solvers>
+    <test_definition>
+        <vtkdiff>
+            <file>cube_1e0_yzx_orthotropic_pcs_0_ts_4_t_1.000000.vtu</file>
+            <field>displacement</field>
+            <absolute_tolerance>1e-14</absolute_tolerance>
+            <relative_tolerance>1e-15</relative_tolerance>
+        </vtkdiff>
+        <vtkdiff>
+            <file>cube_1e0_yzx_orthotropic_pcs_0_ts_4_t_1.000000.vtu</file>
+            <field>NodalForces</field>
+            <absolute_tolerance>1e-14</absolute_tolerance>
+            <relative_tolerance>1e-15</relative_tolerance>
+        </vtkdiff>
+        <vtkdiff>
+            <file>cube_1e0_yzx_orthotropic_pcs_0_ts_4_t_1.000000.vtu</file>
+            <field>sigma</field>
+            <absolute_tolerance>1e-14</absolute_tolerance>
+            <relative_tolerance>1e-15</relative_tolerance>
+        </vtkdiff>
+        <vtkdiff>
+            <file>cube_1e0_yzx_orthotropic_pcs_0_ts_4_t_1.000000.vtu</file>
+            <field>epsilon</field>
+            <absolute_tolerance>1e-14</absolute_tolerance>
+            <relative_tolerance>1e-15</relative_tolerance>
+        </vtkdiff>
+    </test_definition>
+</OpenGeoSysProject>
diff --git a/Tests/Data/Mechanics/Linear/MFront/cube_1e0_orthotropic_zxy.prj b/Tests/Data/Mechanics/Linear/MFront/cube_1e0_orthotropic_zxy.prj
new file mode 100644
index 0000000000000000000000000000000000000000..ce292c8d7a38238e6f994c5440580495303501bc
--- /dev/null
+++ b/Tests/Data/Mechanics/Linear/MFront/cube_1e0_orthotropic_zxy.prj
@@ -0,0 +1,253 @@
+<?xml version="1.0" encoding="ISO-8859-1"?>
+<OpenGeoSysProject>
+    <mesh>cube_1x1x1_hex_1e0.vtu</mesh>
+    <geometry>cube_1x1x1.gml</geometry>
+    <processes>
+        <process>
+            <name>SD</name>
+            <type>SMALL_DEFORMATION</type>
+            <integration_order>2</integration_order>
+            <constitutive_relation>
+                <type>MFront</type>
+                <behaviour>StandardElasticityBrickOrtho</behaviour>
+                <material_properties>
+                    <material_property name="YoungModulus1" parameter="E1"/>
+                    <material_property name="YoungModulus2" parameter="E2"/>
+                    <material_property name="YoungModulus3" parameter="E3"/>
+                    <material_property name="PoissonRatio12" parameter="nu12"/>
+                    <material_property name="PoissonRatio23" parameter="nu23"/>
+                    <material_property name="PoissonRatio13" parameter="nu13"/>
+                    <material_property name="ShearModulus12" parameter="G12"/>
+                    <material_property name="ShearModulus23" parameter="G23"/>
+                    <material_property name="ShearModulus13" parameter="G13"/>
+                </material_properties>
+            </constitutive_relation>
+            <solid_density>rho_sr</solid_density>
+            <specific_body_force>0 0 0</specific_body_force>
+            <reference_temperature>293.15</reference_temperature>
+            <process_variables>
+                <process_variable>displacement</process_variable>
+            </process_variables>
+            <secondary_variables>
+                <secondary_variable internal_name="sigma" output_name="sigma"/>
+                <secondary_variable internal_name="epsilon" output_name="epsilon"/>
+            </secondary_variables>
+        </process>
+    </processes>
+    <time_loop>
+        <processes>
+            <process ref="SD">
+                <nonlinear_solver>basic_newton</nonlinear_solver>
+                <convergence_criterion>
+                    <type>DeltaX</type>
+                    <norm_type>NORM2</norm_type>
+                    <abstol>1e-15</abstol>
+                </convergence_criterion>
+                <time_discretization>
+                    <type>BackwardEuler</type>
+                </time_discretization>
+                <time_stepping>
+                    <type>FixedTimeStepping</type>
+                    <t_initial>0</t_initial>
+                    <t_end>1</t_end>
+                    <timesteps>
+                        <pair>
+                            <repeat>4</repeat>
+                            <delta_t>0.25</delta_t>
+                        </pair>
+                    </timesteps>
+                </time_stepping>
+            </process>
+        </processes>
+        <output>
+            <type>VTK</type>
+            <prefix>cube_1e0_zxy_orthotropic</prefix>
+            <timesteps>
+                <pair>
+                    <repeat>1</repeat>
+                    <each_steps>10000000</each_steps>
+                </pair>
+            </timesteps>
+            <variables>
+                <variable>displacement</variable>
+                <variable>sigma</variable>
+                <variable>epsilon</variable>
+            </variables>
+        </output>
+    </time_loop>
+    <local_coordinate_system>
+        <basis_vector_0>e2</basis_vector_0>
+        <basis_vector_1>e0</basis_vector_1>
+        <basis_vector_2>e1</basis_vector_2>
+    </local_coordinate_system>
+    <parameters>
+        <parameter>
+            <name>e0</name>
+            <type>Constant</type>
+            <values>1 0 0</values>
+        </parameter>
+        <parameter>
+            <name>e1</name>
+            <type>Constant</type>
+            <values>0 1 0</values>
+        </parameter>
+        <parameter>
+            <name>e2</name>
+            <type>Constant</type>
+            <values>0 0 1</values>
+        </parameter>
+        <parameter>
+            <name>E1</name>
+            <type>Constant</type>
+            <values>0.5</values>
+        </parameter>
+        <parameter>
+            <name>E2</name>
+            <type>Constant</type>
+            <values>1</values>
+        </parameter>
+        <parameter>
+            <name>E3</name>
+            <type>Constant</type>
+            <values>1</values>
+        </parameter>
+        <parameter>
+            <name>nu12</name>
+            <type>Constant</type>
+            <values>.2</values>
+        </parameter>
+        <parameter>
+            <name>nu23</name>
+            <type>Constant</type>
+            <values>.2</values>
+        </parameter>
+        <parameter>
+            <name>nu13</name>
+            <type>Constant</type>
+            <values>.15</values>
+        </parameter>
+        <parameter>
+            <name>G12</name>
+            <type>Constant</type>
+            <values>1</values>
+        </parameter>
+        <parameter>
+            <name>G23</name>
+            <type>Constant</type>
+            <values>1</values>
+        </parameter>
+        <parameter>
+            <name>G13</name>
+            <type>Constant</type>
+            <values>1</values>
+        </parameter>
+
+        <parameter>
+            <name>rho_sr</name>
+            <type>Constant</type>
+            <value>1</value>
+        </parameter>
+        <parameter>
+            <name>displacement0</name>
+            <type>Constant</type>
+            <values>0 0 0</values>
+        </parameter>
+        <parameter>
+            <name>dirichlet0</name>
+            <type>Constant</type>
+            <value>0</value>
+        </parameter>
+        <parameter>
+            <name>Neumann_force_top</name>
+            <type>Constant</type>
+            <value>0.01</value>
+        </parameter>
+    </parameters>
+    <process_variables>
+        <process_variable>
+            <name>displacement</name>
+            <components>3</components>
+            <order>1</order>
+            <initial_condition>displacement0</initial_condition>
+            <boundary_conditions>
+                <!-- fixed boundaries -->
+                <boundary_condition>
+                    <geometrical_set>cube_1x1x1_geometry</geometrical_set>
+                    <geometry>left</geometry>
+                    <type>Dirichlet</type>
+                    <component>0</component>
+                    <parameter>dirichlet0</parameter>
+                </boundary_condition>
+                <boundary_condition>
+                    <geometrical_set>cube_1x1x1_geometry</geometrical_set>
+                    <geometry>front</geometry>
+                    <type>Dirichlet</type>
+                    <component>1</component>
+                    <parameter>dirichlet0</parameter>
+                </boundary_condition>
+                <boundary_condition>
+                    <geometrical_set>cube_1x1x1_geometry</geometrical_set>
+                    <geometry>bottom</geometry>
+                    <type>Dirichlet</type>
+                    <component>2</component>
+                    <parameter>dirichlet0</parameter>
+                </boundary_condition>
+                <boundary_condition>
+                    <geometrical_set>cube_1x1x1_geometry</geometrical_set>
+                    <geometry>top</geometry>
+                    <type>Neumann</type>
+                    <component>2</component>
+                    <parameter>Neumann_force_top</parameter>
+                </boundary_condition>
+            </boundary_conditions>
+        </process_variable>
+    </process_variables>
+    <nonlinear_solvers>
+        <nonlinear_solver>
+            <name>basic_newton</name>
+            <type>Newton</type>
+            <max_iter>4</max_iter>
+            <linear_solver>general_linear_solver</linear_solver>
+        </nonlinear_solver>
+    </nonlinear_solvers>
+    <linear_solvers>
+        <linear_solver>
+            <name>general_linear_solver</name>
+            <lis>-i cg -p jacobi -tol 1e-16 -maxiter 10000</lis>
+            <eigen>
+                <solver_type>SparseLU</solver_type>
+                <scaling>true</scaling>
+            </eigen>
+            <petsc>
+                <prefix>sd</prefix>
+                <parameters>-sd_ksp_type cg -sd_pc_type bjacobi -sd_ksp_rtol 1e-16 -sd_ksp_max_it 10000</parameters>
+            </petsc>
+        </linear_solver>
+    </linear_solvers>
+    <test_definition>
+        <vtkdiff>
+            <file>cube_1e0_zxy_orthotropic_pcs_0_ts_4_t_1.000000.vtu</file>
+            <field>displacement</field>
+            <absolute_tolerance>1e-14</absolute_tolerance>
+            <relative_tolerance>1e-15</relative_tolerance>
+        </vtkdiff>
+        <vtkdiff>
+            <file>cube_1e0_zxy_orthotropic_pcs_0_ts_4_t_1.000000.vtu</file>
+            <field>NodalForces</field>
+            <absolute_tolerance>1e-14</absolute_tolerance>
+            <relative_tolerance>1e-15</relative_tolerance>
+        </vtkdiff>
+        <vtkdiff>
+            <file>cube_1e0_zxy_orthotropic_pcs_0_ts_4_t_1.000000.vtu</file>
+            <field>sigma</field>
+            <absolute_tolerance>1e-14</absolute_tolerance>
+            <relative_tolerance>1e-15</relative_tolerance>
+        </vtkdiff>
+        <vtkdiff>
+            <file>cube_1e0_zxy_orthotropic_pcs_0_ts_4_t_1.000000.vtu</file>
+            <field>epsilon</field>
+            <absolute_tolerance>1e-14</absolute_tolerance>
+            <relative_tolerance>1e-15</relative_tolerance>
+        </vtkdiff>
+    </test_definition>
+</OpenGeoSysProject>
diff --git a/Tests/Data/Mechanics/Linear/MFront/cube_1e0_xyz_orthotropic_pcs_0_ts_4_t_1.000000.vtu b/Tests/Data/Mechanics/Linear/MFront/cube_1e0_xyz_orthotropic_pcs_0_ts_4_t_1.000000.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..cd43c6d65152a7a836ea225cfb3efbd0d688ccc7
--- /dev/null
+++ b/Tests/Data/Mechanics/Linear/MFront/cube_1e0_xyz_orthotropic_pcs_0_ts_4_t_1.000000.vtu
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9c9f570002f569b42e7b1520f5122e3e818e49198cd9c0db39fb909bb65392d9
+size 6166
diff --git a/Tests/Data/Mechanics/Linear/MFront/cube_1e0_yzx_orthotropic_pcs_0_ts_4_t_1.000000.vtu b/Tests/Data/Mechanics/Linear/MFront/cube_1e0_yzx_orthotropic_pcs_0_ts_4_t_1.000000.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..cd43c6d65152a7a836ea225cfb3efbd0d688ccc7
--- /dev/null
+++ b/Tests/Data/Mechanics/Linear/MFront/cube_1e0_yzx_orthotropic_pcs_0_ts_4_t_1.000000.vtu
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9c9f570002f569b42e7b1520f5122e3e818e49198cd9c0db39fb909bb65392d9
+size 6166
diff --git a/Tests/Data/Mechanics/Linear/MFront/cube_1e0_zxy_orthotropic_pcs_0_ts_4_t_1.000000.vtu b/Tests/Data/Mechanics/Linear/MFront/cube_1e0_zxy_orthotropic_pcs_0_ts_4_t_1.000000.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..cd43c6d65152a7a836ea225cfb3efbd0d688ccc7
--- /dev/null
+++ b/Tests/Data/Mechanics/Linear/MFront/cube_1e0_zxy_orthotropic_pcs_0_ts_4_t_1.000000.vtu
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9c9f570002f569b42e7b1520f5122e3e818e49198cd9c0db39fb909bb65392d9
+size 6166
diff --git a/Tests/Data/Mechanics/Linear/MFront/square_1e0_orthotropic_45xy_z.prj b/Tests/Data/Mechanics/Linear/MFront/square_1e0_orthotropic_45xy_z.prj
new file mode 100644
index 0000000000000000000000000000000000000000..b6c95f3f70612ff3ae76cea90003bbdb6fe7e85e
--- /dev/null
+++ b/Tests/Data/Mechanics/Linear/MFront/square_1e0_orthotropic_45xy_z.prj
@@ -0,0 +1,228 @@
+<?xml version="1.0" encoding="ISO-8859-1"?>
+<OpenGeoSysProject>
+    <mesh>square_1x1_quad_1e0.vtu</mesh>
+    <geometry>square_1x1.gml</geometry>
+    <processes>
+        <process>
+            <name>SD</name>
+            <type>SMALL_DEFORMATION</type>
+            <integration_order>2</integration_order>
+            <constitutive_relation>
+                <type>MFront</type>
+                <behaviour>StandardElasticityBrickOrtho</behaviour>
+                <material_properties>
+                    <material_property name="YoungModulus1" parameter="E1"/>
+                    <material_property name="YoungModulus2" parameter="E2"/>
+                    <material_property name="YoungModulus3" parameter="E3"/>
+                    <material_property name="PoissonRatio12" parameter="nu12"/>
+                    <material_property name="PoissonRatio23" parameter="nu23"/>
+                    <material_property name="PoissonRatio13" parameter="nu13"/>
+                    <material_property name="ShearModulus12" parameter="G12"/>
+                </material_properties>
+            </constitutive_relation>
+            <solid_density>rho_sr</solid_density>
+            <specific_body_force>0 0</specific_body_force>
+            <reference_temperature>293.15</reference_temperature>
+            <process_variables>
+                <process_variable>displacement</process_variable>
+            </process_variables>
+            <secondary_variables>
+                <secondary_variable internal_name="sigma" output_name="sigma"/>
+                <secondary_variable internal_name="epsilon" output_name="epsilon"/>
+            </secondary_variables>
+        </process>
+    </processes>
+    <time_loop>
+        <processes>
+            <process ref="SD">
+                <nonlinear_solver>basic_newton</nonlinear_solver>
+                <convergence_criterion>
+                    <type>DeltaX</type>
+                    <norm_type>NORM2</norm_type>
+                    <abstol>1e-15</abstol>
+                </convergence_criterion>
+                <time_discretization>
+                    <type>BackwardEuler</type>
+                </time_discretization>
+                <time_stepping>
+                    <type>FixedTimeStepping</type>
+                    <t_initial>0</t_initial>
+                    <t_end>1</t_end>
+                    <timesteps>
+                        <pair>
+                            <repeat>4</repeat>
+                            <delta_t>0.25</delta_t>
+                        </pair>
+                    </timesteps>
+                </time_stepping>
+            </process>
+        </processes>
+        <output>
+            <type>VTK</type>
+            <prefix>square_1e0_orthotropic_45xy_z</prefix>
+            <timesteps>
+                <pair>
+                    <repeat>1</repeat>
+                    <each_steps>10000000</each_steps>
+                </pair>
+            </timesteps>
+            <variables>
+                <variable>displacement</variable>
+                <variable>sigma</variable>
+                <variable>epsilon</variable>
+            </variables>
+        </output>
+    </time_loop>
+    <local_coordinate_system>
+        <basis_vector_0>e0</basis_vector_0>
+        <basis_vector_1>e1</basis_vector_1>
+    </local_coordinate_system>
+    <parameters>
+        <parameter>
+            <name>e0</name>
+            <type>Constant</type>
+            <values>0.7071067811865475244 0.7071067811865475244</values>
+        </parameter>
+        <parameter>
+            <name>e1</name>
+            <type>Constant</type>
+            <values>-0.7071067811865475244 0.7071067811865475244</values>
+        </parameter>
+        <parameter>
+            <name>E1</name>
+            <type>Constant</type>
+            <values>1</values>
+        </parameter>
+        <parameter>
+            <name>E2</name>
+            <type>Constant</type>
+            <values>0.75</values>
+        </parameter>
+        <parameter>
+            <name>E3</name>
+            <type>Constant</type>
+            <values>0.5</values>
+        </parameter>
+        <parameter>
+            <name>nu12</name>
+            <type>Constant</type>
+            <values>.2</values>
+        </parameter>
+        <parameter>
+            <name>nu23</name>
+            <type>Constant</type>
+            <values>.3</values>
+        </parameter>
+        <parameter>
+            <name>nu13</name>
+            <type>Constant</type>
+            <values>.4</values>
+        </parameter>
+        <parameter>
+            <name>G12</name>
+            <type>Constant</type>
+            <values>1</values>
+        </parameter>
+
+        <parameter>
+            <name>rho_sr</name>
+            <type>Constant</type>
+            <value>1</value>
+        </parameter>
+        <parameter>
+            <name>displacement0</name>
+            <type>Constant</type>
+            <values>0 0</values>
+        </parameter>
+        <parameter>
+            <name>dirichlet0</name>
+            <type>Constant</type>
+            <value>0</value>
+        </parameter>
+        <parameter>
+            <name>Neumann_force_top</name>
+            <type>Constant</type>
+            <value>0.01</value>
+        </parameter>
+    </parameters>
+    <process_variables>
+        <process_variable>
+            <name>displacement</name>
+            <components>2</components>
+            <order>1</order>
+            <initial_condition>displacement0</initial_condition>
+            <boundary_conditions>
+                <!-- fixed boundaries -->
+                <boundary_condition>
+                    <geometrical_set>square_1x1_geometry</geometrical_set>
+                    <geometry>left</geometry>
+                    <type>Dirichlet</type>
+                    <component>0</component>
+                    <parameter>dirichlet0</parameter>
+                </boundary_condition>
+                <boundary_condition>
+                    <geometrical_set>square_1x1_geometry</geometrical_set>
+                    <geometry>bottom</geometry>
+                    <type>Dirichlet</type>
+                    <component>1</component>
+                    <parameter>dirichlet0</parameter>
+                </boundary_condition>
+                <boundary_condition>
+                    <geometrical_set>square_1x1_geometry</geometrical_set>
+                    <geometry>top</geometry>
+                    <type>Neumann</type>
+                    <component>1</component>
+                    <parameter>Neumann_force_top</parameter>
+                </boundary_condition>
+            </boundary_conditions>
+        </process_variable>
+    </process_variables>
+    <nonlinear_solvers>
+        <nonlinear_solver>
+            <name>basic_newton</name>
+            <type>Newton</type>
+            <max_iter>4</max_iter>
+            <linear_solver>general_linear_solver</linear_solver>
+        </nonlinear_solver>
+    </nonlinear_solvers>
+    <linear_solvers>
+        <linear_solver>
+            <name>general_linear_solver</name>
+            <lis>-i cg -p jacobi -tol 1e-16 -maxiter 10000</lis>
+            <eigen>
+                <solver_type>SparseLU</solver_type>
+                <scaling>true</scaling>
+            </eigen>
+            <petsc>
+                <prefix>sd</prefix>
+                <parameters>-sd_ksp_type cg -sd_pc_type bjacobi -sd_ksp_rtol 1e-16 -sd_ksp_max_it 10000</parameters>
+            </petsc>
+        </linear_solver>
+    </linear_solvers>
+    <test_definition>
+        <vtkdiff>
+            <file>square_1e0_orthotropic_45xy_z_pcs_0_ts_4_t_1.000000.vtu</file>
+            <field>displacement</field>
+            <absolute_tolerance>1e-16</absolute_tolerance>
+            <relative_tolerance>1e-16</relative_tolerance>
+        </vtkdiff>
+        <vtkdiff>
+            <file>square_1e0_orthotropic_45xy_z_pcs_0_ts_4_t_1.000000.vtu</file>
+            <field>NodalForces</field>
+            <absolute_tolerance>1e-14</absolute_tolerance>
+            <relative_tolerance>1e-15</relative_tolerance>
+        </vtkdiff>
+        <vtkdiff>
+            <file>square_1e0_orthotropic_45xy_z_pcs_0_ts_4_t_1.000000.vtu</file>
+            <field>sigma</field>
+            <absolute_tolerance>1e-16</absolute_tolerance>
+            <relative_tolerance>1e-16</relative_tolerance>
+        </vtkdiff>
+        <vtkdiff>
+            <file>square_1e0_orthotropic_45xy_z_pcs_0_ts_4_t_1.000000.vtu</file>
+            <field>epsilon</field>
+            <absolute_tolerance>1e-14</absolute_tolerance>
+            <relative_tolerance>1e-15</relative_tolerance>
+        </vtkdiff>
+    </test_definition>
+</OpenGeoSysProject>
diff --git a/Tests/Data/Mechanics/Linear/MFront/square_1e0_orthotropic_45xy_z_pcs_0_ts_4_t_1.000000.vtu b/Tests/Data/Mechanics/Linear/MFront/square_1e0_orthotropic_45xy_z_pcs_0_ts_4_t_1.000000.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..67d608b2c22879b390feb909aebac3373b516cfd
--- /dev/null
+++ b/Tests/Data/Mechanics/Linear/MFront/square_1e0_orthotropic_45xy_z_pcs_0_ts_4_t_1.000000.vtu
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:87cfbbff946ac3ac208009b526aec18f04ec6f330726e6c0c2de6091c5e029f0
+size 4118
diff --git a/Tests/Data/Mechanics/Linear/MFront/square_1e0_orthotropic_xyz.prj b/Tests/Data/Mechanics/Linear/MFront/square_1e0_orthotropic_xyz.prj
new file mode 100644
index 0000000000000000000000000000000000000000..b5b23f3caee06eb785dffa69301c42bcf063d69c
--- /dev/null
+++ b/Tests/Data/Mechanics/Linear/MFront/square_1e0_orthotropic_xyz.prj
@@ -0,0 +1,228 @@
+<?xml version="1.0" encoding="ISO-8859-1"?>
+<OpenGeoSysProject>
+    <mesh>square_1x1_quad_1e0.vtu</mesh>
+    <geometry>square_1x1.gml</geometry>
+    <processes>
+        <process>
+            <name>SD</name>
+            <type>SMALL_DEFORMATION</type>
+            <integration_order>2</integration_order>
+            <constitutive_relation>
+                <type>MFront</type>
+                <behaviour>StandardElasticityBrickOrtho</behaviour>
+                <material_properties>
+                    <material_property name="YoungModulus1" parameter="E1"/>
+                    <material_property name="YoungModulus2" parameter="E2"/>
+                    <material_property name="YoungModulus3" parameter="E3"/>
+                    <material_property name="PoissonRatio12" parameter="nu12"/>
+                    <material_property name="PoissonRatio23" parameter="nu23"/>
+                    <material_property name="PoissonRatio13" parameter="nu13"/>
+                    <material_property name="ShearModulus12" parameter="G12"/>
+                </material_properties>
+            </constitutive_relation>
+            <solid_density>rho_sr</solid_density>
+            <specific_body_force>0 0</specific_body_force>
+            <reference_temperature>293.15</reference_temperature>
+            <process_variables>
+                <process_variable>displacement</process_variable>
+            </process_variables>
+            <secondary_variables>
+                <secondary_variable internal_name="sigma" output_name="sigma"/>
+                <secondary_variable internal_name="epsilon" output_name="epsilon"/>
+            </secondary_variables>
+        </process>
+    </processes>
+    <time_loop>
+        <processes>
+            <process ref="SD">
+                <nonlinear_solver>basic_newton</nonlinear_solver>
+                <convergence_criterion>
+                    <type>DeltaX</type>
+                    <norm_type>NORM2</norm_type>
+                    <abstol>1e-15</abstol>
+                </convergence_criterion>
+                <time_discretization>
+                    <type>BackwardEuler</type>
+                </time_discretization>
+                <time_stepping>
+                    <type>FixedTimeStepping</type>
+                    <t_initial>0</t_initial>
+                    <t_end>1</t_end>
+                    <timesteps>
+                        <pair>
+                            <repeat>4</repeat>
+                            <delta_t>0.25</delta_t>
+                        </pair>
+                    </timesteps>
+                </time_stepping>
+            </process>
+        </processes>
+        <output>
+            <type>VTK</type>
+            <prefix>square_1e0_orthotropic_xyz</prefix>
+            <timesteps>
+                <pair>
+                    <repeat>1</repeat>
+                    <each_steps>10000000</each_steps>
+                </pair>
+            </timesteps>
+            <variables>
+                <variable>displacement</variable>
+                <variable>sigma</variable>
+                <variable>epsilon</variable>
+            </variables>
+        </output>
+    </time_loop>
+    <local_coordinate_system>
+        <basis_vector_0>e0</basis_vector_0>
+        <basis_vector_1>e1</basis_vector_1>
+    </local_coordinate_system>
+    <parameters>
+        <parameter>
+            <name>e0</name>
+            <type>Constant</type>
+            <values>1 0</values>
+        </parameter>
+        <parameter>
+            <name>e1</name>
+            <type>Constant</type>
+            <values>0 1</values>
+        </parameter>
+        <parameter>
+            <name>E1</name>
+            <type>Constant</type>
+            <values>1</values>
+        </parameter>
+        <parameter>
+            <name>E2</name>
+            <type>Constant</type>
+            <values>1</values>
+        </parameter>
+        <parameter>
+            <name>E3</name>
+            <type>Constant</type>
+            <values>0.5</values>
+        </parameter>
+        <parameter>
+            <name>nu12</name>
+            <type>Constant</type>
+            <values>.2</values>
+        </parameter>
+        <parameter>
+            <name>nu23</name>
+            <type>Constant</type>
+            <values>.3</values>
+        </parameter>
+        <parameter>
+            <name>nu13</name>
+            <type>Constant</type>
+            <values>.4</values>
+        </parameter>
+        <parameter>
+            <name>G12</name>
+            <type>Constant</type>
+            <values>1</values>
+        </parameter>
+
+        <parameter>
+            <name>rho_sr</name>
+            <type>Constant</type>
+            <value>1</value>
+        </parameter>
+        <parameter>
+            <name>displacement0</name>
+            <type>Constant</type>
+            <values>0 0</values>
+        </parameter>
+        <parameter>
+            <name>dirichlet0</name>
+            <type>Constant</type>
+            <value>0</value>
+        </parameter>
+        <parameter>
+            <name>Neumann_force_top</name>
+            <type>Constant</type>
+            <value>0.01</value>
+        </parameter>
+    </parameters>
+    <process_variables>
+        <process_variable>
+            <name>displacement</name>
+            <components>2</components>
+            <order>1</order>
+            <initial_condition>displacement0</initial_condition>
+            <boundary_conditions>
+                <!-- fixed boundaries -->
+                <boundary_condition>
+                    <geometrical_set>square_1x1_geometry</geometrical_set>
+                    <geometry>left</geometry>
+                    <type>Dirichlet</type>
+                    <component>0</component>
+                    <parameter>dirichlet0</parameter>
+                </boundary_condition>
+                <boundary_condition>
+                    <geometrical_set>square_1x1_geometry</geometrical_set>
+                    <geometry>bottom</geometry>
+                    <type>Dirichlet</type>
+                    <component>1</component>
+                    <parameter>dirichlet0</parameter>
+                </boundary_condition>
+                <boundary_condition>
+                    <geometrical_set>square_1x1_geometry</geometrical_set>
+                    <geometry>top</geometry>
+                    <type>Neumann</type>
+                    <component>1</component>
+                    <parameter>Neumann_force_top</parameter>
+                </boundary_condition>
+            </boundary_conditions>
+        </process_variable>
+    </process_variables>
+    <nonlinear_solvers>
+        <nonlinear_solver>
+            <name>basic_newton</name>
+            <type>Newton</type>
+            <max_iter>4</max_iter>
+            <linear_solver>general_linear_solver</linear_solver>
+        </nonlinear_solver>
+    </nonlinear_solvers>
+    <linear_solvers>
+        <linear_solver>
+            <name>general_linear_solver</name>
+            <lis>-i cg -p jacobi -tol 1e-16 -maxiter 10000</lis>
+            <eigen>
+                <solver_type>SparseLU</solver_type>
+                <scaling>true</scaling>
+            </eigen>
+            <petsc>
+                <prefix>sd</prefix>
+                <parameters>-sd_ksp_type cg -sd_pc_type bjacobi -sd_ksp_rtol 1e-16 -sd_ksp_max_it 10000</parameters>
+            </petsc>
+        </linear_solver>
+    </linear_solvers>
+    <test_definition>
+        <vtkdiff>
+            <file>square_1e0_orthotropic_xyz_pcs_0_ts_4_t_1.000000.vtu</file>
+            <field>displacement</field>
+            <absolute_tolerance>1e-16</absolute_tolerance>
+            <relative_tolerance>1e-16</relative_tolerance>
+        </vtkdiff>
+        <vtkdiff>
+            <file>square_1e0_orthotropic_xyz_pcs_0_ts_4_t_1.000000.vtu</file>
+            <field>NodalForces</field>
+            <absolute_tolerance>1e-14</absolute_tolerance>
+            <relative_tolerance>1e-15</relative_tolerance>
+        </vtkdiff>
+        <vtkdiff>
+            <file>square_1e0_orthotropic_xyz_pcs_0_ts_4_t_1.000000.vtu</file>
+            <field>sigma</field>
+            <absolute_tolerance>1e-16</absolute_tolerance>
+            <relative_tolerance>1e-16</relative_tolerance>
+        </vtkdiff>
+        <vtkdiff>
+            <file>square_1e0_orthotropic_xyz_pcs_0_ts_4_t_1.000000.vtu</file>
+            <field>epsilon</field>
+            <absolute_tolerance>1e-14</absolute_tolerance>
+            <relative_tolerance>1e-15</relative_tolerance>
+        </vtkdiff>
+    </test_definition>
+</OpenGeoSysProject>
diff --git a/Tests/Data/Mechanics/Linear/MFront/square_1e0_orthotropic_xyz_pcs_0_ts_4_t_1.000000.vtu b/Tests/Data/Mechanics/Linear/MFront/square_1e0_orthotropic_xyz_pcs_0_ts_4_t_1.000000.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..4146c074c23a5c3e4a9450a788e73ef2faa8a6b5
--- /dev/null
+++ b/Tests/Data/Mechanics/Linear/MFront/square_1e0_orthotropic_xyz_pcs_0_ts_4_t_1.000000.vtu
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a8db2c386c022dc0822d1914a14f9352a3d8a8fb838951973a110caef79f2aac
+size 5365
diff --git a/Tests/Data/Mechanics/Linear/MFront/square_1e0_orthotropic_y-xz.prj b/Tests/Data/Mechanics/Linear/MFront/square_1e0_orthotropic_y-xz.prj
new file mode 100644
index 0000000000000000000000000000000000000000..62d27c424dec386233f9c45b7ed5442f6e1007cd
--- /dev/null
+++ b/Tests/Data/Mechanics/Linear/MFront/square_1e0_orthotropic_y-xz.prj
@@ -0,0 +1,228 @@
+<?xml version="1.0" encoding="ISO-8859-1"?>
+<OpenGeoSysProject>
+    <mesh>square_1x1_quad_1e0.vtu</mesh>
+    <geometry>square_1x1.gml</geometry>
+    <processes>
+        <process>
+            <name>SD</name>
+            <type>SMALL_DEFORMATION</type>
+            <integration_order>2</integration_order>
+            <constitutive_relation>
+                <type>MFront</type>
+                <behaviour>StandardElasticityBrickOrtho</behaviour>
+                <material_properties>
+                    <material_property name="YoungModulus1" parameter="E1"/>
+                    <material_property name="YoungModulus2" parameter="E2"/>
+                    <material_property name="YoungModulus3" parameter="E3"/>
+                    <material_property name="PoissonRatio12" parameter="nu12"/>
+                    <material_property name="PoissonRatio23" parameter="nu23"/>
+                    <material_property name="PoissonRatio13" parameter="nu13"/>
+                    <material_property name="ShearModulus12" parameter="G12"/>
+                </material_properties>
+            </constitutive_relation>
+            <solid_density>rho_sr</solid_density>
+            <specific_body_force>0 0</specific_body_force>
+            <reference_temperature>293.15</reference_temperature>
+            <process_variables>
+                <process_variable>displacement</process_variable>
+            </process_variables>
+            <secondary_variables>
+                <secondary_variable internal_name="sigma" output_name="sigma"/>
+                <secondary_variable internal_name="epsilon" output_name="epsilon"/>
+            </secondary_variables>
+        </process>
+    </processes>
+    <time_loop>
+        <processes>
+            <process ref="SD">
+                <nonlinear_solver>basic_newton</nonlinear_solver>
+                <convergence_criterion>
+                    <type>DeltaX</type>
+                    <norm_type>NORM2</norm_type>
+                    <abstol>1e-15</abstol>
+                </convergence_criterion>
+                <time_discretization>
+                    <type>BackwardEuler</type>
+                </time_discretization>
+                <time_stepping>
+                    <type>FixedTimeStepping</type>
+                    <t_initial>0</t_initial>
+                    <t_end>1</t_end>
+                    <timesteps>
+                        <pair>
+                            <repeat>4</repeat>
+                            <delta_t>0.25</delta_t>
+                        </pair>
+                    </timesteps>
+                </time_stepping>
+            </process>
+        </processes>
+        <output>
+            <type>VTK</type>
+            <prefix>square_1e0_orthotropic_y-xz</prefix>
+            <timesteps>
+                <pair>
+                    <repeat>1</repeat>
+                    <each_steps>10000000</each_steps>
+                </pair>
+            </timesteps>
+            <variables>
+                <variable>displacement</variable>
+                <variable>sigma</variable>
+                <variable>epsilon</variable>
+            </variables>
+        </output>
+    </time_loop>
+    <local_coordinate_system>
+        <basis_vector_0>e1</basis_vector_0>
+        <basis_vector_1>e0_negative</basis_vector_1>
+    </local_coordinate_system>
+    <parameters>
+        <parameter>
+            <name>e0_negative</name>
+            <type>Constant</type>
+            <values>-1 0</values>
+        </parameter>
+        <parameter>
+            <name>e1</name>
+            <type>Constant</type>
+            <values>0 1</values>
+        </parameter>
+        <parameter>
+            <name>E1</name>
+            <type>Constant</type>
+            <values>1</values>
+        </parameter>
+        <parameter>
+            <name>E2</name>
+            <type>Constant</type>
+            <values>0.75</values>
+        </parameter>
+        <parameter>
+            <name>E3</name>
+            <type>Constant</type>
+            <values>0.5</values>
+        </parameter>
+        <parameter>
+            <name>nu12</name>
+            <type>Constant</type>
+            <values>.2</values>
+        </parameter>
+        <parameter>
+            <name>nu23</name>
+            <type>Constant</type>
+            <values>.3</values>
+        </parameter>
+        <parameter>
+            <name>nu13</name>
+            <type>Constant</type>
+            <values>.4</values>
+        </parameter>
+        <parameter>
+            <name>G12</name>
+            <type>Constant</type>
+            <values>1</values>
+        </parameter>
+
+        <parameter>
+            <name>rho_sr</name>
+            <type>Constant</type>
+            <value>1</value>
+        </parameter>
+        <parameter>
+            <name>displacement0</name>
+            <type>Constant</type>
+            <values>0 0</values>
+        </parameter>
+        <parameter>
+            <name>dirichlet0</name>
+            <type>Constant</type>
+            <value>0</value>
+        </parameter>
+        <parameter>
+            <name>Neumann_force_top</name>
+            <type>Constant</type>
+            <value>0.01</value>
+        </parameter>
+    </parameters>
+    <process_variables>
+        <process_variable>
+            <name>displacement</name>
+            <components>2</components>
+            <order>1</order>
+            <initial_condition>displacement0</initial_condition>
+            <boundary_conditions>
+                <!-- fixed boundaries -->
+                <boundary_condition>
+                    <geometrical_set>square_1x1_geometry</geometrical_set>
+                    <geometry>left</geometry>
+                    <type>Dirichlet</type>
+                    <component>0</component>
+                    <parameter>dirichlet0</parameter>
+                </boundary_condition>
+                <boundary_condition>
+                    <geometrical_set>square_1x1_geometry</geometrical_set>
+                    <geometry>bottom</geometry>
+                    <type>Dirichlet</type>
+                    <component>1</component>
+                    <parameter>dirichlet0</parameter>
+                </boundary_condition>
+                <boundary_condition>
+                    <geometrical_set>square_1x1_geometry</geometrical_set>
+                    <geometry>top</geometry>
+                    <type>Neumann</type>
+                    <component>1</component>
+                    <parameter>Neumann_force_top</parameter>
+                </boundary_condition>
+            </boundary_conditions>
+        </process_variable>
+    </process_variables>
+    <nonlinear_solvers>
+        <nonlinear_solver>
+            <name>basic_newton</name>
+            <type>Newton</type>
+            <max_iter>4</max_iter>
+            <linear_solver>general_linear_solver</linear_solver>
+        </nonlinear_solver>
+    </nonlinear_solvers>
+    <linear_solvers>
+        <linear_solver>
+            <name>general_linear_solver</name>
+            <lis>-i cg -p jacobi -tol 1e-16 -maxiter 10000</lis>
+            <eigen>
+                <solver_type>SparseLU</solver_type>
+                <scaling>true</scaling>
+            </eigen>
+            <petsc>
+                <prefix>sd</prefix>
+                <parameters>-sd_ksp_type cg -sd_pc_type bjacobi -sd_ksp_rtol 1e-16 -sd_ksp_max_it 10000</parameters>
+            </petsc>
+        </linear_solver>
+    </linear_solvers>
+    <test_definition>
+        <vtkdiff>
+            <file>square_1e0_orthotropic_y-xz_pcs_0_ts_4_t_1.000000.vtu</file>
+            <field>displacement</field>
+            <absolute_tolerance>1e-16</absolute_tolerance>
+            <relative_tolerance>1e-16</relative_tolerance>
+        </vtkdiff>
+        <vtkdiff>
+            <file>square_1e0_orthotropic_y-xz_pcs_0_ts_4_t_1.000000.vtu</file>
+            <field>NodalForces</field>
+            <absolute_tolerance>1e-14</absolute_tolerance>
+            <relative_tolerance>1e-15</relative_tolerance>
+        </vtkdiff>
+        <vtkdiff>
+            <file>square_1e0_orthotropic_y-xz_pcs_0_ts_4_t_1.000000.vtu</file>
+            <field>sigma</field>
+            <absolute_tolerance>1e-16</absolute_tolerance>
+            <relative_tolerance>1e-16</relative_tolerance>
+        </vtkdiff>
+        <vtkdiff>
+            <file>square_1e0_orthotropic_y-xz_pcs_0_ts_4_t_1.000000.vtu</file>
+            <field>epsilon</field>
+            <absolute_tolerance>1e-14</absolute_tolerance>
+            <relative_tolerance>1e-15</relative_tolerance>
+        </vtkdiff>
+    </test_definition>
+</OpenGeoSysProject>
diff --git a/Tests/Data/Mechanics/Linear/MFront/square_1e0_orthotropic_y-xz_pcs_0_ts_4_t_1.000000.vtu b/Tests/Data/Mechanics/Linear/MFront/square_1e0_orthotropic_y-xz_pcs_0_ts_4_t_1.000000.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..45b9bc99cc4d9aa6bf4f71331401c55903963683
--- /dev/null
+++ b/Tests/Data/Mechanics/Linear/MFront/square_1e0_orthotropic_y-xz_pcs_0_ts_4_t_1.000000.vtu
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:78fabdfcaea32720057cee260c0dbd9b267e25cc3a2913c41745f9600a74bf21
+size 3930
diff --git a/Tests/Data/Mechanics/Linear/MFront/square_1x1.gml b/Tests/Data/Mechanics/Linear/MFront/square_1x1.gml
new file mode 100644
index 0000000000000000000000000000000000000000..736c751499be4d6bfa58b9f0697bf0aeaddda6da
--- /dev/null
+++ b/Tests/Data/Mechanics/Linear/MFront/square_1x1.gml
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ae859f36dfbe8ed106090c118ef9d99c553bf763dd926f7eec4e32e0f9729dee
+size 930
diff --git a/Tests/Data/Mechanics/Linear/MFront/square_1x1_quad_1e0.vtu b/Tests/Data/Mechanics/Linear/MFront/square_1x1_quad_1e0.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..2e6fc2e4412db4a41dd4be8bf0f0f0b3f2d94ea2
--- /dev/null
+++ b/Tests/Data/Mechanics/Linear/MFront/square_1x1_quad_1e0.vtu
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:cd87128b2c36d59cff91fd9d072f97be311ecc5119a6e607fd58e318e25b441c
+size 1578
diff --git a/Tests/Data/Mechanics/Linear/Orthotropy/square_1e0_orthotropic_45xy_z.prj b/Tests/Data/Mechanics/Linear/Orthotropy/square_1e0_orthotropic_45xy_z.prj
new file mode 100644
index 0000000000000000000000000000000000000000..6ec7ad537b1f4844eede5ca03c0d3b0c24253de5
--- /dev/null
+++ b/Tests/Data/Mechanics/Linear/Orthotropy/square_1e0_orthotropic_45xy_z.prj
@@ -0,0 +1,207 @@
+<?xml version="1.0" encoding="ISO-8859-1"?>
+<OpenGeoSysProject>
+    <mesh>square_1x1_quad_1e0.vtu</mesh>
+    <geometry>square_1x1.gml</geometry>
+    <processes>
+        <process>
+            <name>SD</name>
+            <type>SMALL_DEFORMATION</type>
+            <integration_order>2</integration_order>
+            <constitutive_relation>
+                <type>LinearElasticOrthotropic</type>
+                <youngs_moduli>E</youngs_moduli>
+                <shear_moduli>G</shear_moduli>
+                <poissons_ratios>nu</poissons_ratios>
+            </constitutive_relation>
+            <solid_density>rho_sr</solid_density>
+            <specific_body_force>0 0</specific_body_force>
+            <process_variables>
+                <process_variable>displacement</process_variable>
+            </process_variables>
+            <secondary_variables>
+                <secondary_variable internal_name="sigma" output_name="sigma"/>
+                <secondary_variable internal_name="epsilon" output_name="epsilon"/>
+            </secondary_variables>
+        </process>
+    </processes>
+    <time_loop>
+        <processes>
+            <process ref="SD">
+                <nonlinear_solver>basic_newton</nonlinear_solver>
+                <convergence_criterion>
+                    <type>DeltaX</type>
+                    <norm_type>NORM2</norm_type>
+                    <abstol>1e-15</abstol>
+                </convergence_criterion>
+                <time_discretization>
+                    <type>BackwardEuler</type>
+                </time_discretization>
+                <time_stepping>
+                    <type>FixedTimeStepping</type>
+                    <t_initial>0</t_initial>
+                    <t_end>1</t_end>
+                    <timesteps>
+                        <pair>
+                            <repeat>4</repeat>
+                            <delta_t>0.25</delta_t>
+                        </pair>
+                    </timesteps>
+                </time_stepping>
+            </process>
+        </processes>
+        <output>
+            <type>VTK</type>
+            <prefix>square_1e0_orthotropic_45xy_z</prefix>
+            <timesteps>
+                <pair>
+                    <repeat>1</repeat>
+                    <each_steps>10000000</each_steps>
+                </pair>
+            </timesteps>
+            <variables>
+                <variable>displacement</variable>
+                <variable>sigma</variable>
+                <variable>epsilon</variable>
+            </variables>
+        </output>
+    </time_loop>
+    <local_coordinate_system>
+        <basis_vector_0>e0</basis_vector_0>
+        <basis_vector_1>e1</basis_vector_1>
+        <basis_vector_2>e2</basis_vector_2>
+    </local_coordinate_system>
+    <parameters>
+        <parameter>
+            <name>e0</name>
+            <type>Constant</type>
+            <values>0.7071067811865475244 0.7071067811865475244 0</values>
+        </parameter>
+        <parameter>
+            <name>e1</name>
+            <type>Constant</type>
+            <values>-0.7071067811865475244 0.7071067811865475244 0</values>
+        </parameter>
+        <parameter>
+            <name>e2</name>
+            <type>Constant</type>
+            <values>0 0 1</values>
+        </parameter>
+        <parameter>
+            <name>E</name>
+            <type>Constant</type>
+            <values>1 0.75 0.5</values>
+        </parameter>
+        <parameter>
+            <name>G</name>
+            <type>Constant</type>
+            <values>1 1 1</values>
+        </parameter>
+        <parameter>
+            <name>nu</name>
+            <type>Constant</type>
+            <values>.2 .3 .4</values>
+        </parameter>
+        <parameter>
+            <name>rho_sr</name>
+            <type>Constant</type>
+            <value>1</value>
+        </parameter>
+        <parameter>
+            <name>displacement0</name>
+            <type>Constant</type>
+            <values>0 0</values>
+        </parameter>
+        <parameter>
+            <name>dirichlet0</name>
+            <type>Constant</type>
+            <value>0</value>
+        </parameter>
+        <parameter>
+            <name>Neumann_force_top</name>
+            <type>Constant</type>
+            <value>0.01</value>
+        </parameter>
+    </parameters>
+    <process_variables>
+        <process_variable>
+            <name>displacement</name>
+            <components>2</components>
+            <order>1</order>
+            <initial_condition>displacement0</initial_condition>
+            <boundary_conditions>
+                <!-- fixed boundaries -->
+                <boundary_condition>
+                    <geometrical_set>square_1x1_geometry</geometrical_set>
+                    <geometry>left</geometry>
+                    <type>Dirichlet</type>
+                    <component>0</component>
+                    <parameter>dirichlet0</parameter>
+                </boundary_condition>
+                <boundary_condition>
+                    <geometrical_set>square_1x1_geometry</geometrical_set>
+                    <geometry>bottom</geometry>
+                    <type>Dirichlet</type>
+                    <component>1</component>
+                    <parameter>dirichlet0</parameter>
+                </boundary_condition>
+                <boundary_condition>
+                    <geometrical_set>square_1x1_geometry</geometrical_set>
+                    <geometry>top</geometry>
+                    <type>Neumann</type>
+                    <component>1</component>
+                    <parameter>Neumann_force_top</parameter>
+                </boundary_condition>
+            </boundary_conditions>
+        </process_variable>
+    </process_variables>
+    <nonlinear_solvers>
+        <nonlinear_solver>
+            <name>basic_newton</name>
+            <type>Newton</type>
+            <max_iter>4</max_iter>
+            <linear_solver>general_linear_solver</linear_solver>
+        </nonlinear_solver>
+    </nonlinear_solvers>
+    <linear_solvers>
+        <linear_solver>
+            <name>general_linear_solver</name>
+            <lis>-i cg -p jacobi -tol 1e-16 -maxiter 10000</lis>
+            <eigen>
+                <solver_type>CG</solver_type>
+                <precon_type>DIAGONAL</precon_type>
+                <max_iteration_step>10000</max_iteration_step>
+                <error_tolerance>1e-16</error_tolerance>
+            </eigen>
+            <petsc>
+                <prefix>sd</prefix>
+                <parameters>-sd_ksp_type cg -sd_pc_type bjacobi -sd_ksp_rtol 1e-16 -sd_ksp_max_it 10000</parameters>
+            </petsc>
+        </linear_solver>
+    </linear_solvers>
+    <test_definition>
+        <vtkdiff>
+            <file>square_1e0_orthotropic_45xy_z_pcs_0_ts_4_t_1.000000.vtu</file>
+            <field>displacement</field>
+            <absolute_tolerance>1e-16</absolute_tolerance>
+            <relative_tolerance>1e-16</relative_tolerance>
+        </vtkdiff>
+        <vtkdiff>
+            <file>square_1e0_orthotropic_45xy_z_pcs_0_ts_4_t_1.000000.vtu</file>
+            <field>NodalForces</field>
+            <absolute_tolerance>1e-14</absolute_tolerance>
+            <relative_tolerance>1e-15</relative_tolerance>
+        </vtkdiff>
+        <vtkdiff>
+            <file>square_1e0_orthotropic_45xy_z_pcs_0_ts_4_t_1.000000.vtu</file>
+            <field>sigma</field>
+            <absolute_tolerance>1e-16</absolute_tolerance>
+            <relative_tolerance>1e-16</relative_tolerance>
+        </vtkdiff>
+        <vtkdiff>
+            <file>square_1e0_orthotropic_45xy_z_pcs_0_ts_4_t_1.000000.vtu</file>
+            <field>epsilon</field>
+            <absolute_tolerance>1e-14</absolute_tolerance>
+            <relative_tolerance>1e-15</relative_tolerance>
+        </vtkdiff>
+    </test_definition>
+</OpenGeoSysProject>
diff --git a/Tests/Data/Mechanics/Linear/Orthotropy/square_1e0_orthotropic_45xy_z_pcs_0_ts_4_t_1.000000.vtu b/Tests/Data/Mechanics/Linear/Orthotropy/square_1e0_orthotropic_45xy_z_pcs_0_ts_4_t_1.000000.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..67d608b2c22879b390feb909aebac3373b516cfd
--- /dev/null
+++ b/Tests/Data/Mechanics/Linear/Orthotropy/square_1e0_orthotropic_45xy_z_pcs_0_ts_4_t_1.000000.vtu
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:87cfbbff946ac3ac208009b526aec18f04ec6f330726e6c0c2de6091c5e029f0
+size 4118
diff --git a/Tests/Data/Mechanics/Linear/Orthotropy/square_1e0_orthotropic_y-xz.prj b/Tests/Data/Mechanics/Linear/Orthotropy/square_1e0_orthotropic_y-xz.prj
new file mode 100644
index 0000000000000000000000000000000000000000..17e04024799286b15dab2c819744f040a4745ffb
--- /dev/null
+++ b/Tests/Data/Mechanics/Linear/Orthotropy/square_1e0_orthotropic_y-xz.prj
@@ -0,0 +1,207 @@
+<?xml version="1.0" encoding="ISO-8859-1"?>
+<OpenGeoSysProject>
+    <mesh>square_1x1_quad_1e0.vtu</mesh>
+    <geometry>square_1x1.gml</geometry>
+    <processes>
+        <process>
+            <name>SD</name>
+            <type>SMALL_DEFORMATION</type>
+            <integration_order>2</integration_order>
+            <constitutive_relation>
+                <type>LinearElasticOrthotropic</type>
+                <youngs_moduli>E</youngs_moduli>
+                <shear_moduli>G</shear_moduli>
+                <poissons_ratios>nu</poissons_ratios>
+            </constitutive_relation>
+            <solid_density>rho_sr</solid_density>
+            <specific_body_force>0 0</specific_body_force>
+            <process_variables>
+                <process_variable>displacement</process_variable>
+            </process_variables>
+            <secondary_variables>
+                <secondary_variable internal_name="sigma" output_name="sigma"/>
+                <secondary_variable internal_name="epsilon" output_name="epsilon"/>
+            </secondary_variables>
+        </process>
+    </processes>
+    <time_loop>
+        <processes>
+            <process ref="SD">
+                <nonlinear_solver>basic_newton</nonlinear_solver>
+                <convergence_criterion>
+                    <type>DeltaX</type>
+                    <norm_type>NORM2</norm_type>
+                    <abstol>1e-15</abstol>
+                </convergence_criterion>
+                <time_discretization>
+                    <type>BackwardEuler</type>
+                </time_discretization>
+                <time_stepping>
+                    <type>FixedTimeStepping</type>
+                    <t_initial>0</t_initial>
+                    <t_end>1</t_end>
+                    <timesteps>
+                        <pair>
+                            <repeat>4</repeat>
+                            <delta_t>0.25</delta_t>
+                        </pair>
+                    </timesteps>
+                </time_stepping>
+            </process>
+        </processes>
+        <output>
+            <type>VTK</type>
+            <prefix>square_1e0_orthotropic_y-xz</prefix>
+            <timesteps>
+                <pair>
+                    <repeat>1</repeat>
+                    <each_steps>10000000</each_steps>
+                </pair>
+            </timesteps>
+            <variables>
+                <variable>displacement</variable>
+                <variable>sigma</variable>
+                <variable>epsilon</variable>
+            </variables>
+        </output>
+    </time_loop>
+    <local_coordinate_system>
+        <basis_vector_0>e1</basis_vector_0>
+        <basis_vector_1>e0_negative</basis_vector_1>
+        <basis_vector_2>e2</basis_vector_2>
+    </local_coordinate_system>
+    <parameters>
+        <parameter>
+            <name>e0_negative</name>
+            <type>Constant</type>
+            <values>-1 0 0</values>
+        </parameter>
+        <parameter>
+            <name>e1</name>
+            <type>Constant</type>
+            <values>0 1 0</values>
+        </parameter>
+        <parameter>
+            <name>e2</name>
+            <type>Constant</type>
+            <values>0 0 1</values>
+        </parameter>
+        <parameter>
+            <name>E</name>
+            <type>Constant</type>
+            <values>1 0.75 0.5</values>
+        </parameter>
+        <parameter>
+            <name>G</name>
+            <type>Constant</type>
+            <values>1 1 1</values>
+        </parameter>
+        <parameter>
+            <name>nu</name>
+            <type>Constant</type>
+            <values>.2 .3 .4</values>
+        </parameter>
+        <parameter>
+            <name>rho_sr</name>
+            <type>Constant</type>
+            <value>1</value>
+        </parameter>
+        <parameter>
+            <name>displacement0</name>
+            <type>Constant</type>
+            <values>0 0</values>
+        </parameter>
+        <parameter>
+            <name>dirichlet0</name>
+            <type>Constant</type>
+            <value>0</value>
+        </parameter>
+        <parameter>
+            <name>Neumann_force_top</name>
+            <type>Constant</type>
+            <value>0.01</value>
+        </parameter>
+    </parameters>
+    <process_variables>
+        <process_variable>
+            <name>displacement</name>
+            <components>2</components>
+            <order>1</order>
+            <initial_condition>displacement0</initial_condition>
+            <boundary_conditions>
+                <!-- fixed boundaries -->
+                <boundary_condition>
+                    <geometrical_set>square_1x1_geometry</geometrical_set>
+                    <geometry>left</geometry>
+                    <type>Dirichlet</type>
+                    <component>0</component>
+                    <parameter>dirichlet0</parameter>
+                </boundary_condition>
+                <boundary_condition>
+                    <geometrical_set>square_1x1_geometry</geometrical_set>
+                    <geometry>bottom</geometry>
+                    <type>Dirichlet</type>
+                    <component>1</component>
+                    <parameter>dirichlet0</parameter>
+                </boundary_condition>
+                <boundary_condition>
+                    <geometrical_set>square_1x1_geometry</geometrical_set>
+                    <geometry>top</geometry>
+                    <type>Neumann</type>
+                    <component>1</component>
+                    <parameter>Neumann_force_top</parameter>
+                </boundary_condition>
+            </boundary_conditions>
+        </process_variable>
+    </process_variables>
+    <nonlinear_solvers>
+        <nonlinear_solver>
+            <name>basic_newton</name>
+            <type>Newton</type>
+            <max_iter>4</max_iter>
+            <linear_solver>general_linear_solver</linear_solver>
+        </nonlinear_solver>
+    </nonlinear_solvers>
+    <linear_solvers>
+        <linear_solver>
+            <name>general_linear_solver</name>
+            <lis>-i cg -p jacobi -tol 1e-16 -maxiter 10000</lis>
+            <eigen>
+                <solver_type>CG</solver_type>
+                <precon_type>DIAGONAL</precon_type>
+                <max_iteration_step>10000</max_iteration_step>
+                <error_tolerance>1e-16</error_tolerance>
+            </eigen>
+            <petsc>
+                <prefix>sd</prefix>
+                <parameters>-sd_ksp_type cg -sd_pc_type bjacobi -sd_ksp_rtol 1e-16 -sd_ksp_max_it 10000</parameters>
+            </petsc>
+        </linear_solver>
+    </linear_solvers>
+    <test_definition>
+        <vtkdiff>
+            <file>square_1e0_orthotropic_y-xz_pcs_0_ts_4_t_1.000000.vtu</file>
+            <field>displacement</field>
+            <absolute_tolerance>1e-16</absolute_tolerance>
+            <relative_tolerance>1e-16</relative_tolerance>
+        </vtkdiff>
+        <vtkdiff>
+            <file>square_1e0_orthotropic_y-xz_pcs_0_ts_4_t_1.000000.vtu</file>
+            <field>NodalForces</field>
+            <absolute_tolerance>1e-14</absolute_tolerance>
+            <relative_tolerance>1e-15</relative_tolerance>
+        </vtkdiff>
+        <vtkdiff>
+            <file>square_1e0_orthotropic_y-xz_pcs_0_ts_4_t_1.000000.vtu</file>
+            <field>sigma</field>
+            <absolute_tolerance>1e-16</absolute_tolerance>
+            <relative_tolerance>1e-16</relative_tolerance>
+        </vtkdiff>
+        <vtkdiff>
+            <file>square_1e0_orthotropic_y-xz_pcs_0_ts_4_t_1.000000.vtu</file>
+            <field>epsilon</field>
+            <absolute_tolerance>1e-14</absolute_tolerance>
+            <relative_tolerance>1e-15</relative_tolerance>
+        </vtkdiff>
+    </test_definition>
+</OpenGeoSysProject>
diff --git a/Tests/Data/Mechanics/Linear/Orthotropy/square_1e0_orthotropic_y-xz_pcs_0_ts_4_t_1.000000.vtu b/Tests/Data/Mechanics/Linear/Orthotropy/square_1e0_orthotropic_y-xz_pcs_0_ts_4_t_1.000000.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..45b9bc99cc4d9aa6bf4f71331401c55903963683
--- /dev/null
+++ b/Tests/Data/Mechanics/Linear/Orthotropy/square_1e0_orthotropic_y-xz_pcs_0_ts_4_t_1.000000.vtu
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:78fabdfcaea32720057cee260c0dbd9b267e25cc3a2913c41745f9600a74bf21
+size 3930