diff --git a/MaterialLib/CMakeLists.txt b/MaterialLib/CMakeLists.txt
index 261e40f102f0a0b43a3b151a739812ca2c445baf..a3a7536d90948486b2e83c2f656446e00cb2c2a9 100644
--- a/MaterialLib/CMakeLists.txt
+++ b/MaterialLib/CMakeLists.txt
@@ -3,6 +3,8 @@ GET_SOURCE_FILES(SOURCES)
GET_SOURCE_FILES(SOURCES_ADSORPTION Adsorption)
set(SOURCES ${SOURCES} ${SOURCES_ADSORPTION})
+APPEND_SOURCE_FILES(SOURCES SolidModels)
+
add_library(MaterialLib ${SOURCES} )
target_link_libraries(MaterialLib
BaseLib
diff --git a/MaterialLib/SolidModels/KelvinVector-impl.h b/MaterialLib/SolidModels/KelvinVector-impl.h
new file mode 100644
index 0000000000000000000000000000000000000000..0474792a9da02cad37b039716d198912b9489ec1
--- /dev/null
+++ b/MaterialLib/SolidModels/KelvinVector-impl.h
@@ -0,0 +1,106 @@
+/**
+ * \copyright
+ * Copyright (c) 2012-2016, OpenGeoSys Community (http://www.opengeosys.org)
+ * Distributed under a Modified BSD License.
+ * See accompanying file LICENSE.txt or
+ * http://www.opengeosys.org/project/license
+ *
+ */
+
+namespace MaterialLib
+{
+namespace SolidModels
+{
+template <int KelvinVectorSize>
+double Invariants<KelvinVectorSize>::equivalentStress(
+ Eigen::Matrix<double, KelvinVectorSize, 1> const& deviatoric_v)
+{
+ assert(std::abs(trace(deviatoric_v)) <
+ std::numeric_limits<double>::epsilon());
+ return std::sqrt(3 * J2(deviatoric_v));
+}
+
+template <int KelvinVectorSize>
+double Invariants<KelvinVectorSize>::J2(
+ Eigen::Matrix<double, KelvinVectorSize, 1> const& deviatoric_v)
+{
+ assert(std::abs(trace(deviatoric_v)) <
+ std::numeric_limits<double>::epsilon());
+ return 0.5 * deviatoric_v.transpose() * deviatoric_v;
+}
+
+/// Third invariant, equal to determinant of a deviatoric tensor.
+/// \note The input vector must have trace equal zero.
+template <int KelvinVectorSize>
+double Invariants<KelvinVectorSize>::J3(
+ Eigen::Matrix<double, KelvinVectorSize, 1> const& deviatoric_v)
+{
+ assert(std::abs(trace(deviatoric_v)) <
+ std::numeric_limits<double>::epsilon());
+ return determinant(deviatoric_v);
+}
+
+/// Trace of the corresponding tensor.
+template <int KelvinVectorSize>
+double Invariants<KelvinVectorSize>::trace(
+ Eigen::Matrix<double, KelvinVectorSize, 1> const& v)
+{
+ return v.template topLeftCorner<3, 1>().sum();
+}
+
+//
+// Initialization of static Invariant variables.
+//
+
+namespace detail
+{
+template <int KelvinVectorSize>
+Eigen::Matrix<double, KelvinVectorSize, KelvinVectorSize>
+initDeviatoricProjection()
+{
+ Eigen::Matrix<double, KelvinVectorSize, KelvinVectorSize> P_dev =
+ Eigen::Matrix<double, KelvinVectorSize, KelvinVectorSize>::Identity();
+
+ P_dev.template topLeftCorner<3, 3>() -=
+ 1. / 3. * Eigen::Matrix<double, 3, 3>::Ones();
+ return P_dev;
+}
+
+template <int KelvinVectorSize>
+Eigen::Matrix<double, KelvinVectorSize, KelvinVectorSize>
+initSphericalProjection()
+{
+ Eigen::Matrix<double, KelvinVectorSize, KelvinVectorSize> P_sph =
+ Eigen::Matrix<double, KelvinVectorSize, KelvinVectorSize>::Zero();
+
+ P_sph.template topLeftCorner<3, 3>().setConstant(1. / 3.);
+ return P_sph;
+}
+
+template <int KelvinVectorSize>
+Eigen::Matrix<double, KelvinVectorSize, 1> initIdentity2()
+{
+ Eigen::Matrix<double, KelvinVectorSize, 1> ivec =
+ Eigen::Matrix<double, KelvinVectorSize, 1>::Zero();
+
+ ivec.template topLeftCorner<3, 1>().setConstant(1.);
+ return ivec;
+}
+} // namespace detail
+
+template <int KelvinVectorSize>
+const Eigen::Matrix<double, KelvinVectorSize, KelvinVectorSize>
+ Invariants<KelvinVectorSize>::deviatoric_projection =
+ detail::initDeviatoricProjection<KelvinVectorSize>();
+
+template <int KelvinVectorSize>
+Eigen::Matrix<double, KelvinVectorSize, KelvinVectorSize> const
+ Invariants<KelvinVectorSize>::spherical_projection =
+ detail::initSphericalProjection<KelvinVectorSize>();
+
+template <int KelvinVectorSize>
+const Eigen::Matrix<double, KelvinVectorSize, 1> Invariants<
+ KelvinVectorSize>::identity2 = detail::initIdentity2<KelvinVectorSize>();
+
+} // namespace SolidModels
+} // namespace MaterialLib
diff --git a/MaterialLib/SolidModels/KelvinVector.cpp b/MaterialLib/SolidModels/KelvinVector.cpp
new file mode 100644
index 0000000000000000000000000000000000000000..ac872fd2aa8b7e0174ba8637e8bda7bb37e7ea4b
--- /dev/null
+++ b/MaterialLib/SolidModels/KelvinVector.cpp
@@ -0,0 +1,61 @@
+/**
+ * \copyright
+ * Copyright (c) 2012-2016, OpenGeoSys Community (http://www.opengeosys.org)
+ * Distributed under a Modified BSD License.
+ * See accompanying file LICENSE.txt or
+ * http://www.opengeosys.org/project/license
+ *
+ */
+
+#include "KelvinVector.h"
+
+namespace MaterialLib
+{
+namespace SolidModels
+{
+template <>
+double Invariants<6>::determinant(Eigen::Matrix<double, 6, 1> const& v)
+{
+ return v(0) * v(1) * v(2) + v(3) * v(4) * v(5) / std::sqrt(2.) -
+ v(3) * v(3) * v(2) / 2. - v(4) * v(4) * v(0) / 2. -
+ v(5) * v(5) * v(1) / 2.;
+}
+
+template <>
+double Invariants<4>::determinant(Eigen::Matrix<double, 4, 1> const& v)
+{
+ return v(2) * (v(0) * v(1) - v(3) * v(3) / 2.);
+}
+
+template <>
+Eigen::Matrix<double, 4, 1, Eigen::ColMajor, 4, 1> inverse(
+ Eigen::Matrix<double, 4, 1, Eigen::ColMajor, 4, 1> const& v)
+{
+ assert(Invariants<4>::determinant(v) != 0);
+
+ Eigen::Matrix<double, 4, 1, Eigen::ColMajor, 4, 1> inv;
+ inv(0) = v(1) * v(2);
+ inv(1) = v(0) * v(2);
+ inv(2) = v(0) * v(1) - v(3) * v(3) / 2.;
+ inv(3) = -v(3) * v(2);
+ return inv / Invariants<4>::determinant(v);
+}
+
+template <>
+Eigen::Matrix<double, 6, 1, Eigen::ColMajor, 6, 1> inverse(
+ Eigen::Matrix<double, 6, 1, Eigen::ColMajor, 6, 1> const& v)
+{
+ assert(Invariants<6>::determinant(v) != 0);
+
+ Eigen::Matrix<double, 6, 1, Eigen::ColMajor, 6, 1> inv;
+ inv(0) = v(1) * v(2) - v(4) * v(4) / 2.;
+ inv(1) = v(0) * v(2) - v(5) * v(5) / 2.;
+ inv(2) = v(0) * v(1) - v(3) * v(3) / 2.;
+ inv(3) = v(4) * v(5) / std::sqrt(2.) - v(3) * v(2);
+ inv(4) = v(3) * v(5) / std::sqrt(2.) - v(4) * v(0);
+ inv(5) = v(4) * v(3) / std::sqrt(2.) - v(1) * v(5);
+ return inv / Invariants<6>::determinant(v);
+}
+
+} // namespace SolidModels
+} // namespace MaterialLib
diff --git a/MaterialLib/SolidModels/KelvinVector.h b/MaterialLib/SolidModels/KelvinVector.h
new file mode 100644
index 0000000000000000000000000000000000000000..fc41442d620e6583002bf0f1671d6a27dcb94e30
--- /dev/null
+++ b/MaterialLib/SolidModels/KelvinVector.h
@@ -0,0 +1,84 @@
+/**
+ * \copyright
+ * Copyright (c) 2012-2016, OpenGeoSys Community (http://www.opengeosys.org)
+ * Distributed under a Modified BSD License.
+ * See accompanying file LICENSE.txt or
+ * http://www.opengeosys.org/project/license
+ *
+ */
+#ifndef MATERIALLIB_SOLIDMODELS_KELVINVECTOR_H
+#define MATERIALLIB_SOLIDMODELS_KELVINVECTOR_H
+
+#include <Eigen/Dense>
+
+namespace MaterialLib
+{
+/// The invariants and the Kelving mapping are explained in detail in the
+/// article "On Advantages of the Kelvin Mapping in Finite Element
+/// Implementations of Deformation Processes" \cite Nagel2016.
+namespace SolidModels
+{
+/// Invariants used in mechanics, based on Kelvin representation of the vectors
+/// and matrices.
+/// The invariants are computed at process creation time.
+template <int KelvinVectorSize>
+struct Invariants final
+{
+ static_assert(KelvinVectorSize == 4 || KelvinVectorSize == 6,
+ "KelvinVector invariants for vectors of size different than "
+ "4 or 6 is not allowed.");
+ /// Kelvin mapping of deviatoric projection tensor. \f$A_{\rm dev} = P_{\rm
+ /// dev}:A\f$ for \f$A\f$ being a second order tensor.
+ static Eigen::Matrix<double, KelvinVectorSize, KelvinVectorSize> const
+ deviatoric_projection;
+ /// Kelvin mapping of spherical projection tensor. \f$A_{\rm sph} = P_{\rm
+ /// sph}:A\f$ for \f$A\f$ being a second order tensor.
+ static Eigen::Matrix<double, KelvinVectorSize, KelvinVectorSize> const
+ spherical_projection;
+ /// Kelvin mapping of 2nd order identity tensor.
+ static Eigen::Matrix<double, KelvinVectorSize, 1> const identity2;
+
+ /// Determinant of a matrix in Kelvin vector representation.
+ static double determinant(
+ Eigen::Matrix<double, KelvinVectorSize, 1> const& v);
+
+ /// The von Mises equivalent stress.
+ /// \note The input vector must have trace equal zero.
+ static double equivalentStress(
+ Eigen::Matrix<double, KelvinVectorSize, 1> const& deviatoric_v);
+
+ /// Second invariant of deviatoric tensor.
+ /// \note The input vector must have trace equal zero.
+ static double J2(
+ Eigen::Matrix<double, KelvinVectorSize, 1> const& deviatoric_v);
+
+ /// Third invariant, equal to determinant of a deviatoric tensor.
+ /// \note The input vector must have trace equal zero.
+ static double J3(
+ Eigen::Matrix<double, KelvinVectorSize, 1> const& deviatoric_v);
+
+ /// Trace of the corresponding tensor.
+ static double trace(Eigen::Matrix<double, KelvinVectorSize, 1> const& v);
+};
+
+//
+// Inverses of a Kelvin vector.
+//
+
+/// Inverse of a matrix in Kelvin vector representation.
+/// There are only implementations for the Kelvin vector size 4 and 6.
+template <int KelvinVectorSize>
+Eigen::Matrix<double, KelvinVectorSize, 1, Eigen::ColMajor, KelvinVectorSize, 1>
+inverse(Eigen::Matrix<double,
+ KelvinVectorSize,
+ 1,
+ Eigen::ColMajor,
+ KelvinVectorSize,
+ 1> const& v);
+
+} // namespace SolidModels
+} // namespace MaterialLib
+
+#include "KelvinVector-impl.h"
+
+#endif // MATERIALLIB_SOLIDMODELS_KELVINVECTOR_H