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Reference documentation for deal.II version 9.5.1
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Namespaces | |
namespace | Contravariant |
namespace | Covariant |
namespace | Piola |
namespace | Rotations |
Functions | |
Special operations | |
template<int dim, typename Number > | |
Tensor< 1, dim, Number > | nansons_formula (const Tensor< 1, dim, Number > &N, const Tensor< 2, dim, Number > &F) |
Basis transformations | |
template<int dim, typename Number > | |
Tensor< 1, dim, Number > | basis_transformation (const Tensor< 1, dim, Number > &V, const Tensor< 2, dim, Number > &B) |
template<int dim, typename Number > | |
Tensor< 2, dim, Number > | basis_transformation (const Tensor< 2, dim, Number > &T, const Tensor< 2, dim, Number > &B) |
template<int dim, typename Number > | |
SymmetricTensor< 2, dim, Number > | basis_transformation (const SymmetricTensor< 2, dim, Number > &T, const Tensor< 2, dim, Number > &B) |
template<int dim, typename Number > | |
Tensor< 4, dim, Number > | basis_transformation (const Tensor< 4, dim, Number > &H, const Tensor< 2, dim, Number > &B) |
template<int dim, typename Number > | |
SymmetricTensor< 4, dim, Number > | basis_transformation (const SymmetricTensor< 4, dim, Number > &H, const Tensor< 2, dim, Number > &B) |
A collection of operations to assist in the transformation of tensor quantities from the reference to spatial configuration, and vice versa. These types of transformation are typically used to re-express quantities measured or computed in one configuration in terms of a second configuration.
We will use the same notation for the coordinates
As a further point on notation, we will follow Holzapfel (2007) and denote the push forward transformation as
Tensor< 1, dim, Number > Physics::Transformations::nansons_formula | ( | const Tensor< 1, dim, Number > & | N, |
const Tensor< 2, dim, Number > & | F ) |
Return the result of applying Nanson's formula for the transformation of the material surface area element
The returned result is the spatial normal scaled by the ratio of areas between the reference and spatial surface elements, i.e.
[in] | N | The referential normal unit vector ![]() |
[in] | F | The deformation gradient tensor ![]() |
Tensor< 1, dim, Number > Physics::Transformations::basis_transformation | ( | const Tensor< 1, dim, Number > & | V, |
const Tensor< 2, dim, Number > & | B ) |
Return a vector with a changed basis, i.e.
[in] | V | The vector to be transformed ![]() |
[in] | B | The transformation matrix ![]() |
Tensor< 2, dim, Number > Physics::Transformations::basis_transformation | ( | const Tensor< 2, dim, Number > & | T, |
const Tensor< 2, dim, Number > & | B ) |
Return a rank-2 tensor with a changed basis, i.e.
[in] | T | The tensor to be transformed ![]() |
[in] | B | The transformation matrix ![]() |
SymmetricTensor< 2, dim, Number > Physics::Transformations::basis_transformation | ( | const SymmetricTensor< 2, dim, Number > & | T, |
const Tensor< 2, dim, Number > & | B ) |
Return a symmetric rank-2 tensor with a changed basis, i.e.
[in] | T | The tensor to be transformed ![]() |
[in] | B | The transformation matrix ![]() |
Tensor< 4, dim, Number > Physics::Transformations::basis_transformation | ( | const Tensor< 4, dim, Number > & | H, |
const Tensor< 2, dim, Number > & | B ) |
Return a rank-4 tensor with a changed basis, i.e. (in index notation):
[in] | H | The tensor to be transformed ![]() |
[in] | B | The transformation matrix ![]() |
SymmetricTensor< 4, dim, Number > Physics::Transformations::basis_transformation | ( | const SymmetricTensor< 4, dim, Number > & | H, |
const Tensor< 2, dim, Number > & | B ) |
Return a symmetric rank-4 tensor with a changed basis, i.e. (in index notation):
[in] | H | The tensor to be transformed ![]() |
[in] | B | The transformation matrix ![]() |