The symmetric fourth order tensor, with symmetry in the first two dimensionss as well as in the last two dimensions. More...

Detailed Description

The symmetric fourth order tensor, with symmetry in the first two dimensionss as well as in the last two dimensions.

Mandel notation is used, and so the storage space is (6, 6).

#include <SSR4.h>

Inheritance diagram for SSR4:

[legend]

Public Member Functions
	SSR4 (const R4 &T)
	Initialize with the symmetrized fourth order tensor.

SSR4	rotate (const Rot &r) const
	Rotate.

DTensor< SSR4, Rot, neml2::Tensor >	drotate (const Rot &r) const
	Derivative of the rotated tensor w.r.t. the Rodrigues vector.

DTensor< SSR4, SSR4, neml2::Tensor >	drotate_self (const Rot &r) const
	Derivative of the rotated tensor w.r.t. itself.

Scalar	operator() (Size i, Size j, Size k, Size l) const
	Accessor.

SSR4	transpose_minor () const
	Transpose minor axes, no-op.

SSR4	transpose_major () const
	Transpose major axes.

Public Member Functions inherited from PrimitiveTensor< SSR4, 6, 6 >
	PrimitiveTensor ()=default
	Special member functions.

	PrimitiveTensor (const ATensor &tensor, Size intmd_dim)
	Construct from an ATensor and infer dynamic shape.

	PrimitiveTensor (const ATensor &tensor, Size dynamic_dim, Size intmd_dim)
	Construct from an ATensor and extract dynamic shape given dynamic dimension.

	PrimitiveTensor (const ATensor &tensor, const TraceableTensorShape &dynamic_shape, Size intmd_dim)
	Construct from an ATensor given dynamic shape.

	PrimitiveTensor (const TensorBase< Derived2 > &tensor)
	Copy constructor.

	operator neml2::Tensor () const
	Implicit conversion to a Tensor (discards information on the fixed base shape)

Scalar	operator() (Args... i) const
	Single-element accessor.

Public Member Functions inherited from TensorBase< SSR4 >
	TensorBase ()=default
	Default constructor.

	TensorBase (const ATensor &tensor, Size dynamic_dim, Size intmd_dim)
	Construct from an ATensor with given dynamic dimension.

	TensorBase (const ATensor &tensor, TraceableTensorShape dynamic_shape, Size intmd_dim)
	Construct from an ATensor with given dynamic shape.

	TensorBase (const TensorBase< Derived2 > &tensor)
	Copy constructor.

	TensorBase (double)=delete

	TensorBase (float)=delete

	TensorBase (int)=delete

SSR4	variable_data () const
	Variable data without function graph.

SSR4	contiguous () const

SSR4	clone () const
	Clone (take ownership)

SSR4	detach () const
	Discard function graph.

SSR4	to (const TensorOptions &options) const
	Change tensor options.

SSR4	operator- () const
	Negation.

Size	batch_dim () const

Size	base_dim () const

Size	dynamic_dim () const

Size	static_dim () const

Size	intmd_dim () const

TraceableTensorShape	batch_sizes () const

TensorShapeRef	base_sizes () const

const TraceableTensorShape &	dynamic_sizes () const

TensorShapeRef	static_sizes () const

TensorShapeRef	intmd_sizes () const

TraceableSize	batch_size (Size i) const

Size	base_size (Size i) const

const TraceableSize &	dynamic_size (Size i) const

Size	static_size (Size i) const

Size	intmd_size (Size i) const

SSR4	dynamic_index (indexing::TensorIndicesRef indices) const

SSR4	intmd_index (indexing::TensorIndicesRef indices) const

neml2::Tensor	base_index (indexing::TensorIndicesRef indices) const

SSR4	dynamic_slice (Size d, const indexing::Slice &index) const

SSR4	intmd_slice (Size d, const indexing::Slice &index) const

neml2::Tensor	base_slice (Size d, const indexing::Slice &index) const

void	dynamic_index_put_ (indexing::TensorIndicesRef indices, const ATensor &other)

void	dynamic_index_put_ (indexing::TensorIndicesRef indices, const CScalar &v)

void	intmd_index_put_ (indexing::TensorIndicesRef indices, const ATensor &other)

void	intmd_index_put_ (indexing::TensorIndicesRef indices, const CScalar &v)

void	base_index_put_ (indexing::TensorIndicesRef indices, const ATensor &other)

void	base_index_put_ (indexing::TensorIndicesRef indices, const CScalar &v)

SSR4	dynamic_expand (const TraceableTensorShape &shape) const

SSR4	intmd_expand (TensorShapeRef shape) const

neml2::Tensor	base_expand (TensorShapeRef shape) const

SSR4	batch_expand (const TraceableTensorShape &dynamic_shape, TensorShapeRef intmd_shape) const

neml2::Tensor	static_expand (TensorShapeRef intmd_shape, TensorShapeRef base_shape) const

SSR4	dynamic_expand (const TraceableSize &size, Size d) const

SSR4	intmd_expand (Size size, Size d) const

neml2::Tensor	base_expand (Size size, Size d) const

SSR4	dynamic_expand_as (const neml2::Tensor &other) const

SSR4	intmd_expand_as (const neml2::Tensor &other) const

neml2::Tensor	base_expand_as (const neml2::Tensor &other) const

SSR4	batch_expand_as (const neml2::Tensor &other) const

neml2::Tensor	static_expand_as (const neml2::Tensor &other) const

SSR4	dynamic_reshape (const TraceableTensorShape &shape) const

SSR4	intmd_reshape (TensorShapeRef shape) const

neml2::Tensor	base_reshape (TensorShapeRef shape) const

SSR4	batch_reshape (const TraceableTensorShape &dynamic_shape, TensorShapeRef intmd_shape) const

neml2::Tensor	static_reshape (TensorShapeRef intmd_shape, TensorShapeRef base_shape) const

SSR4	dynamic_squeeze (Size d) const

SSR4	intmd_squeeze (Size d) const

neml2::Tensor	base_squeeze (Size d) const

SSR4	dynamic_unsqueeze (Size d, Size n=1) const

SSR4	intmd_unsqueeze (Size d, Size n=1) const

neml2::Tensor	base_unsqueeze (Size d, Size n=1) const

SSR4	dynamic_transpose (Size d1, Size d2) const

SSR4	intmd_transpose (Size d1, Size d2) const

neml2::Tensor	base_transpose (Size d1, Size d2) const

SSR4	dynamic_movedim (Size old_dim, Size new_dim) const

SSR4	intmd_movedim (Size old_dim, Size new_dim) const

neml2::Tensor	base_movedim (Size old_dim, Size new_dim) const

SSR4	dynamic_flatten () const

SSR4	intmd_flatten () const

neml2::Tensor	base_flatten () const

SSR4	batch_flatten () const
	Flatten batch dimensions.

neml2::Tensor	static_flatten () const
	Flatten static dimensions.

Static Public Member Functions
static SSR4	identity (const TensorOptions &options=default_tensor_options())
	Create the identity tensor \(\delta_{ij}\delta_{kl}\).

static SSR4	identity_sym (const TensorOptions &options=default_tensor_options())
	Create the symmetric identity tensor \(\delta_{ik}\delta_{jl}/2 + \delta_{il}\delta_{jk}/2\).

static SSR4	identity_vol (const TensorOptions &options=default_tensor_options())
	Create the volumetric identity tensor \(\delta_{ij}\delta_{kl}/3\).

static SSR4	identity_dev (const TensorOptions &options=default_tensor_options())
	Create the deviatoric identity tensor \(\delta_{ik}\delta_{jl}/2 + \delta_{il}\delta_{jk}/2 - \delta_{ij}\delta_{kl}/3\).

static SSR4	identity_C1 (const TensorOptions &options=default_tensor_options())
	Building block for C1 constant.

static SSR4	identity_C2 (const TensorOptions &options=default_tensor_options())
	Building block for C2 constant.

static SSR4	identity_C3 (const TensorOptions &options=default_tensor_options())
	Building block for C3 constant.

static SSR4	isotropic_E_nu (const Scalar &E, const Scalar &nu)
	Create the fourth order elasticity tensor given the Young's modulus and the Poisson's ratio.

static SSR4	isotropic_E_nu (const double &E, const double &nu, const TensorOptions &options=default_tensor_options())
	Create the fourth order elasticity tensor given the Young's modulus and the Poisson's ratio.

static SSR4	fill_C1_C2_C3 (const Scalar &C1, const Scalar &C2, const Scalar &C3)
	Create the fourth order elasticity tensor given the three non-zero coefficients.

static SSR4	fill_C1_C2_C3 (const double &C1, const double &C2, const double &C3, const TensorOptions &options=default_tensor_options())
	Create the fourth order elasticity tensor given the three non-zero coefficients.

Static Public Member Functions inherited from PrimitiveTensor< SSR4, 6, 6 >
static SSR4	create (const TensorDataContainer &data, Size intmd_dim=0, const TensorOptions &options=default_tensor_options())
	Arbitrary tensor from a nested container with inferred batch dimension.

static SSR4	einsum (c10::string_view equation, TensorList tensors)
	Einstein summation along base dimensions.

static SSR4	empty (const TensorOptions &options=default_tensor_options())

static SSR4	empty (const TraceableTensorShape &dynamic_shape, TensorShapeRef intmd_shape={}, const TensorOptions &options=default_tensor_options())

static SSR4	zeros (const TensorOptions &options=default_tensor_options())

static SSR4	zeros (const TraceableTensorShape &dynamic_shape, TensorShapeRef intmd_shape={}, const TensorOptions &options=default_tensor_options())

static SSR4	ones (const TensorOptions &options=default_tensor_options())

static SSR4	ones (const TraceableTensorShape &dynamic_shape, TensorShapeRef intmd_shape={}, const TensorOptions &options=default_tensor_options())

static SSR4	full (const CScalar &init, const TensorOptions &options=default_tensor_options())

static SSR4	full (const TraceableTensorShape &dynamic_shape, TensorShapeRef intmd_shape, const CScalar &init, const TensorOptions &options=default_tensor_options())

static SSR4	rand (const TensorOptions &options=default_tensor_options())

static SSR4	rand (const TraceableTensorShape &dynamic_shape, TensorShapeRef intmd_shape, const TensorOptions &options=default_tensor_options())

static SSR4	fill (Args &&... args)

Static Public Member Functions inherited from TensorBase< SSR4 >
static SSR4	empty_like (const SSR4 &other)

static SSR4	zeros_like (const SSR4 &other)
	Zero tensor like another, i.e. same batch and base shapes, same tensor options, etc.

static SSR4	ones_like (const SSR4 &other)
	Unit tensor like another, i.e. same batch and base shapes, same tensor options, etc.

static SSR4	full_like (const SSR4 &other, const CScalar &init)

static SSR4	rand_like (const SSR4 &other)

Additional Inherited Members
Public Types inherited from PrimitiveTensor< SSR4, 6, 6 >
using	base_sizes_sequence
	Base shape sequence.

Static Public Attributes inherited from PrimitiveTensor< SSR4, 6, 6 >
static const TensorShape	const_base_sizes
	The base shape.

static constexpr Size	const_base_dim
	The base dim.

static constexpr Size	const_base_numel
	The base numel.

Protected Member Functions inherited from PrimitiveTensor< SSR4, 6, 6 >
void	validate_shapes_and_dims () const
	Validate shapes and dimensions.

Protected Member Functions inherited from TensorBase< SSR4 >
void	validate_shapes_and_dims () const
	Validate shapes and dimensions.

Constructor & Destructor Documentation

◆ SSR4()

SSR4 ( const R4 & T )

Initialize with the symmetrized fourth order tensor.

Member Function Documentation

◆ drotate()

DTensor< SSR4, Rot, neml2::Tensor > drotate ( const Rot & r ) const

Derivative of the rotated tensor w.r.t. the Rodrigues vector.

◆ drotate_self()

DTensor< SSR4, SSR4, neml2::Tensor > drotate_self ( const Rot & r ) const

Derivative of the rotated tensor w.r.t. itself.

◆ fill_C1_C2_C3() [1/2]

SSR4 fill_C1_C2_C3	(	const double &	C1,
		const double &	C2,
		const double &	C3,
		const TensorOptions &	options = default_tensor_options() )

static

Create the fourth order elasticity tensor given the three non-zero coefficients.

◆ fill_C1_C2_C3() [2/2]

SSR4 fill_C1_C2_C3	(	const Scalar &	C1,
		const Scalar &	C2,
		const Scalar &	C3 )

static

Create the fourth order elasticity tensor given the three non-zero coefficients.

◆ identity()

SSR4 identity ( const TensorOptions & options = default_tensor_options() )

staticnodiscard

Create the identity tensor \(\delta_{ij}\delta_{kl}\).

◆ identity_C1()

SSR4 identity_C1 ( const TensorOptions & options = default_tensor_options() )

static

Building block for C1 constant.

◆ identity_C2()

SSR4 identity_C2 ( const TensorOptions & options = default_tensor_options() )

static

Building block for C2 constant.

◆ identity_C3()

SSR4 identity_C3 ( const TensorOptions & options = default_tensor_options() )

static

Building block for C3 constant.

◆ identity_dev()

SSR4 identity_dev ( const TensorOptions & options = default_tensor_options() )

static

Create the deviatoric identity tensor \(\delta_{ik}\delta_{jl}/2 + \delta_{il}\delta_{jk}/2 - \delta_{ij}\delta_{kl}/3\).

◆ identity_sym()

SSR4 identity_sym ( const TensorOptions & options = default_tensor_options() )

static

Create the symmetric identity tensor \(\delta_{ik}\delta_{jl}/2 + \delta_{il}\delta_{jk}/2\).

◆ identity_vol()

SSR4 identity_vol ( const TensorOptions & options = default_tensor_options() )

static

Create the volumetric identity tensor \(\delta_{ij}\delta_{kl}/3\).

◆ isotropic_E_nu() [1/2]

SSR4 isotropic_E_nu	(	const double &	E,
		const double &	nu,
		const TensorOptions &	options = default_tensor_options() )

static

Create the fourth order elasticity tensor given the Young's modulus and the Poisson's ratio.

◆ isotropic_E_nu() [2/2]

SSR4 isotropic_E_nu	(	const Scalar &	E,
		const Scalar &	nu )

static

Create the fourth order elasticity tensor given the Young's modulus and the Poisson's ratio.

◆ operator()()

Scalar operator()	(	Size	i,
		Size	j,
		Size	k,
		Size	l ) const

Accessor.

◆ rotate()

SSR4 rotate ( const Rot & r ) const

Rotate.

◆ transpose_major()

SSR4 transpose_major ( ) const

Transpose major axes.

◆ transpose_minor()

SSR4 transpose_minor ( ) const

Transpose minor axes, no-op.

Detailed Description

Public Member Functions

Static Public Member Functions

Additional Inherited Members

Constructor & Destructor Documentation

◆ SSR4()

Member Function Documentation

◆ drotate()

◆ drotate_self()

◆ fill_C1_C2_C3() [1/2]

◆ fill_C1_C2_C3() [2/2]

◆ identity()

◆ identity_C1()

◆ identity_C2()

◆ identity_C3()

◆ identity_dev()

◆ identity_sym()

◆ identity_vol()

◆ isotropic_E_nu() [1/2]

◆ isotropic_E_nu() [2/2]

◆ operator()()

◆ rotate()

◆ transpose_major()

◆ transpose_minor()