Functions | |
Push forward operations | |
template<int dim, typename Number> | |
Tensor< 1, dim, Number > | push_forward (const Tensor< 1, dim, Number > &V, const Tensor< 2, dim, Number > &F) |
template<int dim, typename Number> | |
Tensor< 2, dim, Number > | push_forward (const Tensor< 2, dim, Number > &T, const Tensor< 2, dim, Number > &F) |
template<int dim, typename Number> | |
SymmetricTensor< 2, dim, Number > | push_forward (const SymmetricTensor< 2, dim, Number > &T, const Tensor< 2, dim, Number > &F) |
template<int dim, typename Number> | |
Tensor< 4, dim, Number > | push_forward (const Tensor< 4, dim, Number > &H, const Tensor< 2, dim, Number > &F) |
template<int dim, typename Number> | |
SymmetricTensor< 4, dim, Number > | push_forward (const SymmetricTensor< 4, dim, Number > &H, const Tensor< 2, dim, Number > &F) |
Pull back operations | |
template<int dim, typename Number> | |
Tensor< 1, dim, Number > | pull_back (const Tensor< 1, dim, Number > &v, const Tensor< 2, dim, Number > &F) |
template<int dim, typename Number> | |
Tensor< 2, dim, Number > | pull_back (const Tensor< 2, dim, Number > &t, const Tensor< 2, dim, Number > &F) |
template<int dim, typename Number> | |
SymmetricTensor< 2, dim, Number > | pull_back (const SymmetricTensor< 2, dim, Number > &t, const Tensor< 2, dim, Number > &F) |
template<int dim, typename Number> | |
Tensor< 4, dim, Number > | pull_back (const Tensor< 4, dim, Number > &h, const Tensor< 2, dim, Number > &F) |
template<int dim, typename Number> | |
SymmetricTensor< 4, dim, Number > | pull_back (const SymmetricTensor< 4, dim, Number > &h, const Tensor< 2, dim, Number > &F) |
Transformation of tensors that are defined in terms of a set of contravariant basis vectors and scale with the inverse of the volume change associated with the mapping.
Tensor< 1, dim, Number > Physics::Transformations::Piola::push_forward | ( | const Tensor< 1, dim, Number > & | V, |
const Tensor< 2, dim, Number > & | F ) |
Return the result of the push forward transformation on a contravariant vector, i.e.
[in] | V | The (referential) vector to be operated on |
[in] | F | The deformation gradient tensor ![]() |
Tensor< 2, dim, Number > Physics::Transformations::Piola::push_forward | ( | const Tensor< 2, dim, Number > & | T, |
const Tensor< 2, dim, Number > & | F ) |
Return the result of the push forward transformation on a rank-2 contravariant tensor, i.e.
[in] | T | The (referential) rank-2 tensor to be operated on |
[in] | F | The deformation gradient tensor ![]() |
SymmetricTensor< 2, dim, Number > Physics::Transformations::Piola::push_forward | ( | const SymmetricTensor< 2, dim, Number > & | T, |
const Tensor< 2, dim, Number > & | F ) |
Return the result of the push forward transformation on a rank-2 contravariant symmetric tensor, i.e.
[in] | T | The (referential) rank-2 symmetric tensor to be operated on |
[in] | F | The deformation gradient tensor ![]() |
Tensor< 4, dim, Number > Physics::Transformations::Piola::push_forward | ( | const Tensor< 4, dim, Number > & | H, |
const Tensor< 2, dim, Number > & | F ) |
Return the result of the push forward transformation on a rank-4 contravariant tensor, i.e. (in index notation):
[in] | H | The (referential) rank-4 tensor to be operated on |
[in] | F | The deformation gradient tensor ![]() |
SymmetricTensor< 4, dim, Number > Physics::Transformations::Piola::push_forward | ( | const SymmetricTensor< 4, dim, Number > & | H, |
const Tensor< 2, dim, Number > & | F ) |
Return the result of the push forward transformation on a rank-4 contravariant symmetric tensor, i.e. (in index notation):
[in] | H | The (referential) rank-4 symmetric tensor to be operated on |
[in] | F | The deformation gradient tensor ![]() |
Tensor< 1, dim, Number > Physics::Transformations::Piola::pull_back | ( | const Tensor< 1, dim, Number > & | v, |
const Tensor< 2, dim, Number > & | F ) |
Return the result of the pull back transformation on a contravariant vector, i.e.
[in] | v | The (spatial) vector to be operated on |
[in] | F | The deformation gradient tensor ![]() |
Tensor< 2, dim, Number > Physics::Transformations::Piola::pull_back | ( | const Tensor< 2, dim, Number > & | t, |
const Tensor< 2, dim, Number > & | F ) |
Return the result of the pull back transformation on a rank-2 contravariant tensor, i.e.
[in] | t | The (spatial) tensor to be operated on |
[in] | F | The deformation gradient tensor ![]() |
SymmetricTensor< 2, dim, Number > Physics::Transformations::Piola::pull_back | ( | const SymmetricTensor< 2, dim, Number > & | t, |
const Tensor< 2, dim, Number > & | F ) |
Return the result of the pull back transformation on a rank-2 contravariant symmetric tensor, i.e.
[in] | t | The (spatial) symmetric tensor to be operated on |
[in] | F | The deformation gradient tensor ![]() |
Tensor< 4, dim, Number > Physics::Transformations::Piola::pull_back | ( | const Tensor< 4, dim, Number > & | h, |
const Tensor< 2, dim, Number > & | F ) |
Return the result of the pull back transformation on a rank-4 contravariant tensor, i.e. (in index notation):
[in] | h | The (spatial) tensor to be operated on |
[in] | F | The deformation gradient tensor ![]() |
SymmetricTensor< 4, dim, Number > Physics::Transformations::Piola::pull_back | ( | const SymmetricTensor< 4, dim, Number > & | h, |
const Tensor< 2, dim, Number > & | F ) |
Return the result of the pull back transformation on a rank-4 contravariant symmetric tensor, i.e. (in index notation):
[in] | h | The (spatial) symmetric tensor to be operated on |
[in] | F | The deformation gradient tensor ![]() |