Tensors

MOOSE provides the following types of tensors.

  • RankTwoTensor/ADRankTwoTensor

  • RankThreeTensor/ADRankThreeTensor

  • RankFourTensor/ADRankFourTensor

  • SymmetricRankTwoTensor/ADSymmetricRankTwoTensor

  • SymmetricRankFourTensor/ADSymmetricRankFourTensor

These tensor classes provide a rich set of methods for commonly used algebraic operations. For a complete list of supported operations, please refer to the corresponding Doxygen documentation.

RankTwoTensor / ADRankThreeTensor

A RankTwoTensor is a second order tensor containing 9 components. No symmetry is assumed. An ADRankTwoTensor provides additional information for automatic differentiation. The complete list of available methods and operators can be found in the RankTwoTensor Doxygen documentation.

RankThreeTensor / ADRankThreeTensor

A RankThreeTensor is a third order tensor containing 27 components. No symmetry is assumed. An ADRankThreeTensor provides additional information for automatic differentiation. The complete list of available methods and operators can be found in the RankThreeTensor Doxygen documentation.

RankFourTensor / ADRankFourTensor

A RankFourTensor is a fourth order tensor containing 81 components. No symmetry is assumed. An ADRankFourTensor provides additional information for automatic differentiation. The complete list of available methods and operators can be found in the RankFourTensor Doxygen documentation.

SymmetricRankTwoTensor / ADSymmetricRankTwoTensor

A SymmetricRankTwoTensor is a symmetric second order tensor containing 6 components. Mandel notation is used internally to store and access the components. An ADSymmetricRankTwoTensor provides additional information for automatic differentiation. The complete list of available methods and operators can be found in the SymmetricRankTwoTensor Doxygen documentation.

SymmetricRankFourTensor / ADSymmetricRankFourTensor

A SymmetricRankFourTensor is a fourth order tensor with minor symmetry containing 36 components. Mandel notation is used internally to store and access the components. An ADSymmetricRankFourTensor provides additional information for automatic differentiation. The complete list of available methods and operators can be found in the SymmetricRankFourTensor Doxygen documentation.