[Bbar#M] Jupyter Notebook benchmark to evaluate the

B-bar method with simple examples

ProcessLib/SmallDeformation/Tests.cmake

@@ -353,6 +353,7 @@ AddTest(
 if(NOT OGS_USE_PETSC)
     NotebookTest(NOTEBOOKFILE Mechanics/CooksMembrane/CooksMembraneBbar.ipynb RUNTIME 1)
     NotebookTest(NOTEBOOKFILE Mechanics/Linear/SimpleMechanics.ipynb RUNTIME 5)
+    NotebookTest(NOTEBOOKFILE Mechanics/EvaluatingBbarWithSimpleExamples/evaluating_bbbar_with_simple_examples.ipynb RUNTIME 5)
     NotebookTest(NOTEBOOKFILE Mechanics/Linear/DiscWithHole/Linear_Disc_with_hole.md RUNTIME 15)
     if(NOT WIN32)
         NotebookTest(NOTEBOOKFILE Mechanics/Linear/DiscWithHole/Linear_Disc_with_hole_convergence_analysis.ipynb RUNTIME 40)

Tests/Data/Mechanics/EvaluatingBbarWithSimpleExamples/quad.gml

+<?xml version="1.0" encoding="utf-8"?>
+<OpenGeoSysGLI>
+    <name>geometry</name>
+    <points>
+         <point id="0"  x="0." y="0."  z="0." name = "origin"/>
+         <point id="1"  x="1.0" y="0.0"  z="0." />
+         <point id="2"  x="1.0" y="1.0"  z="0." />
+         <point id="3"  x="0." y="1.0"  z="0." />
+    </points>
+
+    <polylines>
+        <polyline id="1" name="bottom">
+            <pnt>0</pnt>
+            <pnt>1</pnt>
+        </polyline>
+        <polyline id="2" name="top">
+            <pnt>2</pnt>
+            <pnt>3</pnt>
+        </polyline>
+    </polylines>
+</OpenGeoSysGLI>

Tests/Data/Mechanics/EvaluatingBbarWithSimpleExamples/quad_edge_div_2.vtu

+<?xml version="1.0"?>
+<VTKFile type="UnstructuredGrid" version="1.0" byte_order="LittleEndian" header_type="UInt64">
+  <UnstructuredGrid>
+    <Piece NumberOfPoints="21"                   NumberOfCells="4"                   >
+      <PointData>
+      </PointData>
+      <CellData>
+        <DataArray type="Int32" Name="MaterialIDs" format="appended" RangeMin="0"                    RangeMax="0"                    offset="0"                   />
+      </CellData>
+      <Points>
+        <DataArray type="Float64" Name="Points" NumberOfComponents="3" format="appended" RangeMin="0"                    RangeMax="1.4142135624"         offset="32"                  />
+      </Points>
+      <Cells>
+        <DataArray type="Int64" Name="connectivity" format="appended" RangeMin=""                     RangeMax=""                     offset="716"                 />
+        <DataArray type="Int64" Name="offsets" format="appended" RangeMin=""                     RangeMax=""                     offset="1068"                />
+        <DataArray type="UInt8" Name="types" format="appended" RangeMin=""                     RangeMax=""                     offset="1124"                />
+      </Cells>
+    </Piece>
+  </UnstructuredGrid>
+  <AppendedData encoding="base64">
+   _EAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA+AEAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADgPwAAAAAAAAAAAAAAAAAAAAAAAAAAAADwPwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAOA/AAAAAAAAAAAAAAAAAADgPwAAAAAAAOA/AAAAAAAAAAAAAAAAAADwPwAAAAAAAOA/AAAAAAAAAAAAAAAAAAAAAAAAAAAAAPA/AAAAAAAAAAAAAAAAAADgPwAAAAAAAPA/AAAAAAAAAAAAAAAAAADwPwAAAAAAAPA/AAAAAAAAAAAAAAAAAAAAAAAAAAAAANA/AAAAAAAAAAAAAAAAAAAAAAAAAAAAAOg/AAAAAAAAAAAAAAAAAADQPwAAAAAAAAAAAAAAAAAAAAAAAAAAAADQPwAAAAAAAOA/AAAAAAAAAAAAAAAAAADQPwAAAAAAAPA/AAAAAAAAAAAAAAAAAADgPwAAAAAAANA/AAAAAAAAAAAAAAAAAADgPwAAAAAAAOg/AAAAAAAAAAAAAAAAAADoPwAAAAAAAAAAAAAAAAAAAAAAAAAAAADoPwAAAAAAAOA/AAAAAAAAAAAAAAAAAADoPwAAAAAAAPA/AAAAAAAAAAAAAAAAAADwPwAAAAAAANA/AAAAAAAAAAAAAAAAAADwPwAAAAAAAOg/AAAAAAAAAAA=AAEAAAAAAAAAAAAAAAAAAAEAAAAAAAAABAAAAAAAAAADAAAAAAAAAAsAAAAAAAAADgAAAAAAAAAMAAAAAAAAAAkAAAAAAAAAAQAAAAAAAAACAAAAAAAAAAUAAAAAAAAABAAAAAAAAAAQAAAAAAAAABMAAAAAAAAAEQAAAAAAAAAOAAAAAAAAAAMAAAAAAAAABAAAAAAAAAAHAAAAAAAAAAYAAAAAAAAADAAAAAAAAAAPAAAAAAAAAA0AAAAAAAAACgAAAAAAAAAEAAAAAAAAAAUAAAAAAAAACAAAAAAAAAAHAAAAAAAAABEAAAAAAAAAFAAAAAAAAAASAAAAAAAAAA8AAAAAAAAAIAAAAAAAAAAIAAAAAAAAABAAAAAAAAAAGAAAAAAAAAAgAAAAAAAAAA==BAAAAAAAAAAXFxcX
+  </AppendedData>
+</VTKFile>

Tests/Data/Mechanics/EvaluatingBbarWithSimpleExamples/simple_b_bar_test.prj

+<?xml version="1.0" encoding="ISO-8859-1"?>
+<OpenGeoSysProject>
+    <mesh>quad_edge_div_2.vtu</mesh>
+    <geometry>quad.gml</geometry>
+    <search_length_algorithm>
+        <type>fixed</type>
+        <value>1e-5</value>
+    </search_length_algorithm>    
+    <processes>
+        <process>
+            <name>SD</name>
+            <type>SMALL_DEFORMATION</type>
+            <integration_order>3</integration_order>
+            <use_b_bar>true</use_b_bar>
+            <constitutive_relation>
+                <type>LinearElasticIsotropic</type>
+                <youngs_modulus>E</youngs_modulus>
+                <poissons_ratio>nu</poissons_ratio>
+            </constitutive_relation>
+            <specific_body_force>0 0</specific_body_force>
+            <process_variables>
+                <process_variable>displacement</process_variable>
+            </process_variables>
+            <secondary_variables>
+                <secondary_variable internal_name="epsilon" output_name="epsilon"/>
+                <secondary_variable internal_name="sigma" output_name="sigma"/>
+            </secondary_variables>
+        </process>
+    </processes>
+    <time_loop>
+        <processes>
+            <process ref="SD">
+                <nonlinear_solver>basic_newton</nonlinear_solver>
+                <convergence_criterion>
+                    <type>PerComponentDeltaX</type>
+                    <norm_type>NORM2</norm_type>
+                    <reltols> 1.0e-9 1.0e-9 </reltols>
+                </convergence_criterion>
+                <time_discretization>
+                    <type>BackwardEuler</type>
+                </time_discretization>
+                <time_stepping>
+                    <type>FixedTimeStepping</type>
+                    <t_initial> 0.0 </t_initial>
+                    <t_end>1</t_end>
+                    <timesteps>
+                        <pair>
+                            <repeat>1</repeat>
+                            <delta_t>1</delta_t>
+                        </pair>
+                    </timesteps>
+                </time_stepping>
+            </process>
+        </processes>
+        <output>
+            <type>VTK</type>
+            <prefix>simple_b_bar_test</prefix>
+            <timesteps>
+                <pair>
+                    <repeat> 1 </repeat>
+                    <each_steps> 1 </each_steps>
+                </pair>
+            </timesteps>
+            <variables>
+                <variable>displacement</variable>
+                <variable>epsilon</variable>
+                <variable>sigma</variable>
+            </variables>
+            <suffix>_ts_{:timestep}_t_{:time}</suffix>
+        </output>
+    </time_loop>
+    <media>
+        <medium>
+            <phases>
+                <phase>
+                    <type>Solid</type>
+                    <properties>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+            </phases>
+        </medium>
+    </media>
+    <parameters>
+        <parameter>
+            <name>E</name>
+            <type>Constant</type>
+            <value>1.0E+10</value>
+        </parameter>
+        <parameter>
+            <name>nu</name>
+            <type>Constant</type>
+            <value>0.2</value>
+        </parameter>
+        <parameter>
+            <name>rho</name>
+            <type>Constant</type>
+            <value>0.0</value>
+        </parameter>
+        <parameter>
+            <name>zero</name>
+            <type>Constant</type>
+            <value>0.0</value>
+        </parameter>
+        <parameter>
+            <name>u0</name>
+            <type>Constant</type>
+            <values>0 0</values>
+        </parameter>
+        <parameter>
+            <name>load</name>
+            <type>Constant</type>
+            <values>-10e+6</values>
+        </parameter>
+    </parameters>
+    <process_variables>
+        <process_variable>
+            <name>displacement</name>
+            <components>2</components>
+            <order>2</order>
+            <initial_condition>u0</initial_condition>
+            <boundary_conditions>
+                <boundary_condition>
+                    <geometrical_set>geometry</geometrical_set>
+                    <geometry>bottom</geometry>
+                    <type>Dirichlet</type>
+                    <component>0</component>
+                    <parameter>zero</parameter>
+                </boundary_condition>
+                <boundary_condition>
+                    <geometrical_set>geometry</geometrical_set>
+                    <geometry>bottom</geometry>
+                    <type>Dirichlet</type>
+                    <component>1</component>
+                    <parameter>zero</parameter>
+                </boundary_condition>
+                <boundary_condition>
+                    <geometrical_set>geometry</geometrical_set>
+                    <geometry>top</geometry>
+                    <type>Neumann</type>
+                    <component>1</component>
+                    <parameter>load</parameter>
+                </boundary_condition>
+            </boundary_conditions>
+        </process_variable>
+    </process_variables>
+    <nonlinear_solvers>
+        <nonlinear_solver>
+            <name>basic_newton</name>
+            <type>Newton</type>
+            <max_iter>10</max_iter>
+            <linear_solver>general_linear_solver</linear_solver>
+        </nonlinear_solver>
+    </nonlinear_solvers>
+    <linear_solvers>
+        <linear_solver>
+            <name>general_linear_solver</name>
+            <eigen>
+                <solver_type>SparseLU</solver_type>
+                <scaling>true</scaling>
+            </eigen>
+        </linear_solver>
+    </linear_solvers>
+</OpenGeoSysProject>