SSR4 Class Reference

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:

Public Member Functions
	SSR4 (const R4 &T)
	Initialize with the symmetrized fourth order tensor.
SSR4	rotate (const Rot &r) const
	Rotate.
SSFR5	drotate (const Rot &r) const
	Derivative of the rotated tensor w.r.t. the Rodrigues vector.
SSSSR8	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	inverse () const
	Inversion.
SSSSR8	dinverse () const
	Derivative of inverse with respect to self.
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 batch_dim)
	Construct from another ATensor given batch dimension.
	PrimitiveTensor (const ATensor &tensor, const TraceableTensorShape &batch_shape)
	Construct from another ATensor given batch shape.
	PrimitiveTensor (const Tensor &tensor)
	Copy constructor.
	PrimitiveTensor (const ATensor &tensor)
	Construct from another ATensor and infer batch dimension.
	operator Tensor () const
	Implicit conversion to a Tensor and loses information on the fixed base shape.
Public Member Functions inherited from TensorBase< SSR4 >
	TensorBase ()=default
	Special member functions.
	TensorBase (const ATensor &tensor, Size batch_dim)
	Construct from another ATensor with given batch dimension.
	TensorBase (const ATensor &tensor, const TraceableTensorShape &batch_shape)
	Construct from another ATensor with given batch shape.
	TensorBase (const neml2::Tensor &tensor)
	Copy constructor.
	TensorBase (Real)=delete
SSR4	variable_data () const
SSR4	clone () const
SSR4	detach () const
	Discard function graph.
SSR4	to (const TensorOptions &options) const
	Change tensor options.
SSR4	operator- () const
	Negation.
bool	batched () const
	Whether the tensor is batched.
Size	batch_dim () const
	Return the number of batch dimensions.
Size	base_dim () const
	Return the number of base dimensions.
const TraceableTensorShape &	batch_sizes () const
	Return the batch size.
TraceableSize	batch_size (Size index) const
	Return the size of a batch axis.
TensorShapeRef	base_sizes () const
	Return the base size.
Size	base_size (Size index) const
	Return the size of a base axis.
Size	base_storage () const
	Return the flattened storage needed just for the base indices.
SSR4	batch_index (indexing::TensorIndicesRef indices) const
	Get a tensor by slicing on the batch dimensions.
neml2::Tensor	base_index (indexing::TensorIndicesRef indices) const
	Get a tensor by slicing on the base dimensions.
SSR4	batch_slice (Size dim, const indexing::Slice &index) const
	Get a tensor by slicing along a batch dimension.
neml2::Tensor	base_slice (Size dim, const indexing::Slice &index) const
	Get a tensor by slicing along a base dimension.
void	batch_index_put_ (indexing::TensorIndicesRef indices, const ATensor &other)
void	batch_index_put_ (indexing::TensorIndicesRef indices, Real v)
void	base_index_put_ (indexing::TensorIndicesRef indices, const ATensor &other)
void	base_index_put_ (indexing::TensorIndicesRef indices, Real v)
SSR4	batch_expand (const TraceableTensorShape &batch_shape) const
SSR4	batch_expand (const TraceableSize &batch_size, Size dim) const
	Return a new view of the tensor with values broadcast along a given batch dimension.
neml2::Tensor	base_expand (TensorShapeRef base_shape) const
	Return a new view of the tensor with values broadcast along the base dimensions.
neml2::Tensor	base_expand (Size base_size, Size dim) const
	Return a new view of the tensor with values broadcast along a given base dimension.
SSR4	batch_expand_as (const neml2::Tensor &other) const
	Expand the batch to have the same shape as another tensor.
neml2::Tensor	base_expand_as (const neml2::Tensor &other) const
	Expand the base to have the same shape as another tensor.
SSR4	batch_expand_copy (const TraceableTensorShape &batch_shape) const
	Return a new tensor with values broadcast along the batch dimensions.
neml2::Tensor	base_expand_copy (TensorShapeRef base_shape) const
	Return a new tensor with values broadcast along the base dimensions.
SSR4	batch_reshape (const TraceableTensorShape &batch_shape) const
	Reshape batch dimensions.
neml2::Tensor	base_reshape (TensorShapeRef base_shape) const
	Reshape base dimensions.
SSR4	batch_unsqueeze (Size d) const
	Unsqueeze a batch dimension.
neml2::Tensor	base_unsqueeze (Size d) const
	Unsqueeze a base dimension.
SSR4	batch_transpose (Size d1, Size d2) const
	Transpose two batch dimensions.
neml2::Tensor	base_transpose (Size d1, Size d2) const
	Transpose two base dimensions.
neml2::Tensor	base_flatten () const
	Flatten base 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 Real &E, const Real &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 Real &C1, const Real &C2, const Real &C3, const TensorOptions &options=default_tensor_options())
	Create the fourth order elasticity tensor given the three non-zero coefficients.
static SSSSR8	identity_map (const TensorOptions &options=default_tensor_options())
	The derivative of a SSR4 with respect to itself.
Static Public Member Functions inherited from PrimitiveTensor< SSR4, 6, 6 >
static SSR4	create (const TensorDataContainer &data, const TensorOptions &options=default_tensor_options())
	Arbitrary tensor from a nested container with inferred batch dimension.
static SSR4	empty (const TensorOptions &options=default_tensor_options())
	Unbatched empty tensor.
static SSR4	empty (const TraceableTensorShape &batch_shape, const TensorOptions &options=default_tensor_options())
	Empty tensor given batch shape.
static SSR4	zeros (const TensorOptions &options=default_tensor_options())
	Unbatched zero tensor.
static SSR4	zeros (const TraceableTensorShape &batch_shape, const TensorOptions &options=default_tensor_options())
	Zero tensor given batch shape.
static SSR4	ones (const TensorOptions &options=default_tensor_options())
	Unbatched unit tensor.
static SSR4	ones (const TraceableTensorShape &batch_shape, const TensorOptions &options=default_tensor_options())
	Unit tensor given batch shape.
static SSR4	full (Real init, const TensorOptions &options=default_tensor_options())
	Unbatched tensor filled with a given value given base shape.
static SSR4	full (const TraceableTensorShape &batch_shape, Real init, const TensorOptions &options=default_tensor_options())
	Full tensor given batch shape.
static Tensor	identity_map (const TensorOptions &)
	Derived tensor classes should define identity_map where appropriate.
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, Real init)
static SSR4	linspace (const SSR4 &start, const SSR4 &end, Size nstep, Size dim=0)
	Create a new tensor by adding a new batch dimension with linear spacing between start and end.
static SSR4	logspace (const SSR4 &start, const SSR4 &end, Size nstep, Size dim=0, Real base=10)
	log-space equivalent of the linspace named constructor

Additional Inherited Members
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 const Size	const_base_storage
	The base storage.

Constructor & Destructor Documentation

SSR4()

SSR4

(

const R4 &

T

)

Initialize with the symmetrized fourth order tensor.

Member Function Documentation

dinverse()

SSSSR8 dinverse

(

)

const

Derivative of inverse with respect to self.

drotate()

SSFR5 drotate

(

const Rot &

r

)

const

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

drotate_self()

SSSSR8 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 Real & C1, const Real & C2, const Real & 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_map()

SSSSR8 identity_map ( const TensorOptions & options = default_tensor_options() )

staticnodiscard

The derivative of a SSR4 with respect to itself.

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 ${\delta }_{ij}{\delta }_{kl}/3$.

inverse()

SSR4 inverse

(

)

const

Inversion.

isotropic_E_nu() [1/2]

SSR4 isotropic_E_nu ( const Real & E, const Real & 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.