SymmetricRankTwoTensorTempl< T > Class Template Reference

SymmetricRankTwoTensorTempl is designed to handle the Stress or Strain Tensor for an anisotropic material. More...

#include <SymmetricRankTwoTensor.h>

Public Types
enum	InitMethod { initNone, initIdentity }
enum	FillMethod { autodetect = 0, isotropic1 = 1, diagonal3 = 3, symmetric6 = 6 }
	To fill up the 6 entries in the 2nd-order tensor, fillFromInputVector is called with one of the following fill_methods. More...
typedef T	value_type
	For generic programming. More...

Public Member Functions
	SymmetricRankTwoTensorTempl ()
	Default constructor; fills to zero. More...
	SymmetricRankTwoTensorTempl (const InitMethod)
	Select specific initialization pattern. More...
	SymmetricRankTwoTensorTempl (const std::vector< T > &input)
	Constructor that proxies the fillFromInputVector method. More...
	SymmetricRankTwoTensorTempl (const T &S11, const T &S22, const T &S33, const T &S23, const T &S13, const T &S12)
	Initialization list replacement constructors, 6 arguments. More...
	operator RankTwoTensorTempl< T > ()
	SymmetricRankTwoTensorTempl (const TensorValue< T > &a)
	Copy constructor from TensorValue<T> More...
	SymmetricRankTwoTensorTempl (const TypeTensor< T > &a)
	Copy constructor from TypeTensor<T> More...
template<typename T2 >
	SymmetricRankTwoTensorTempl (const SymmetricRankTwoTensorTempl< T2 > &a)
	Construct from other template. More...
void	fillFromInputVector (const std::vector< T > &input, FillMethod fill_method=autodetect)
	fillFromInputVector takes 1, 3, or 6 inputs to fill in the symmmetric Rank-2 tensor. More...
void	fillFromScalarVariable (const VariableValue &scalar_variable)
	fillFromScalarVariable takes FIRST/THIRD/SIXTH order scalar variable to fill in the Rank-2 tensor. More...
T &	operator() (unsigned int i)
	Gets the raw value for the index specified. Takes index = 0,1,2,3,4,5. More...
T	operator() (unsigned int i) const
	Gets the raw value for the index specified. More...
T	operator() (unsigned int i, unsigned int j) const
	Gets the value for the index specified. More...
libMesh::VectorValue< T >	row (const unsigned int n) const
	get the specified row of the tensor More...
libMesh::VectorValue< T >	column (const unsigned int n) const
	get the specified column of the tensor More...
SymmetricRankTwoTensorTempl< T >	square () const
	Returns the matrix squared. More...
T	tr () const
	Returns the trace. More...
void	zero ()
	Set all components to zero. More...
void	rotate (const TypeTensor< T > &R)
	rotates the tensor data given a rank two tensor rotation tensor _vals[i][j] = R_ij * R_jl * _vals[k][l] More...
SymmetricRankTwoTensorTempl< T >	transpose () const
	Returns a matrix that is the transpose of the matrix this was called on. More...
template<typename T2 >
SymmetricRankTwoTensorTempl< T > &	operator= (const SymmetricRankTwoTensorTempl< T2 > &a)
	sets _vals to a, and returns _vals More...
template<typename Scalar >
boostcopy::enable_if_c< libMesh::ScalarTraits< Scalar >::value, SymmetricRankTwoTensorTempl & >::type	operator= (const Scalar &libmesh_dbg_var(p))
	Assignment-from-scalar operator. More...
SymmetricRankTwoTensorTempl< T > &	operator+= (const SymmetricRankTwoTensorTempl< T > &a)
	adds a to _vals More...
template<typename T2 >
SymmetricRankTwoTensorTempl< typename libMesh::CompareTypes< T, T2 >::supertype >	operator+ (const SymmetricRankTwoTensorTempl< T2 > &a) const
	returns _vals + a More...
SymmetricRankTwoTensorTempl< T > &	operator-= (const SymmetricRankTwoTensorTempl< T > &a)
	sets _vals -= a and returns vals More...
template<typename T2 >
SymmetricRankTwoTensorTempl< typename libMesh::CompareTypes< T, T2 >::supertype >	operator- (const SymmetricRankTwoTensorTempl< T2 > &a) const
	returns _vals - a More...
SymmetricRankTwoTensorTempl< T >	operator- () const
	returns -_vals More...
SymmetricRankTwoTensorTempl< T > &	operator*= (const T &a)
	performs _vals *= a More...
template<typename T2 >
auto	operator* (const T2 &a) const -> typename std::enable_if< libMesh::ScalarTraits< T2 >::value, SymmetricRankTwoTensorTempl< decltype(T() *T2())>>::type
	returns _vals*a More...
SymmetricRankTwoTensorTempl< T > &	operator/= (const T &a)
	performs _vals /= a More...
template<typename T2 >
auto	operator/ (const T2 &a) const -> typename std::enable_if< libMesh::ScalarTraits< T2 >::value, SymmetricRankTwoTensorTempl< decltype(T()/T2())>>::type
	returns _vals/a More...
template<typename T2 >
TypeVector< typename libMesh::CompareTypes< T, T2 >::supertype >	operator* (const TypeVector< T2 > &a) const
	Defines multiplication with a vector to get a vector. More...
template<typename T2 >
bool	operator== (const SymmetricRankTwoTensorTempl< T2 > &a) const
	Defines logical equality with another SymmetricRankTwoTensorTempl<T2> More...
bool	isSymmetric () const
	Test for symmetry. Surprisingly this is always true. More...
template<typename T2 >
bool	operator!= (const SymmetricRankTwoTensorTempl< T2 > &a) const
	Defines logical inequality with another SymmetricRankTwoTensorTempl<T2> More...
SymmetricRankTwoTensorTempl< T > &	operator= (const ColumnMajorMatrixTempl< T > &a)
	Sets _vals to the values in a ColumnMajorMatrix (must be 3x3) More...
T	doubleContraction (const SymmetricRankTwoTensorTempl< T > &a) const
	returns _vals_ij * a_ij (sum on i, j) More...
SymmetricRankFourTensorTempl< T >	outerProduct (const SymmetricRankTwoTensorTempl< T > &a) const
	returns C_ijkl = a_ij * b_kl More...
SymmetricRankFourTensorTempl< T >	positiveProjectionEigenDecomposition (std::vector< T > &, RankTwoTensorTempl< T > &) const
	return positive projection tensor of eigen-decomposition More...
SymmetricRankTwoTensorTempl< T >	deviatoric () const
	returns A_ij - de_ij*tr(A)/3, where A are the _vals More...
T	trace () const
	returns the trace of the tensor, ie _vals[i][i] (sum i = 0, 1, 2) More...
SymmetricRankTwoTensorTempl< T >	inverse () const
	retuns the inverse of the tensor More...
SymmetricRankTwoTensorTempl< T >	dtrace () const
	Denote the _vals[i][j] by A_ij, then this returns d(trace)/dA_ij. More...
T	generalSecondInvariant () const
	Calculates the second invariant (I2) of a tensor. More...
T	secondInvariant () const
	Denote the _vals[i][j] by A_ij, then S_ij = A_ij - de_ij*tr(A)/3 Then this returns (S_ij + S_ji)*(S_ij + S_ji)/8 Note the explicit symmeterisation. More...
SymmetricRankTwoTensorTempl< T >	dsecondInvariant () const
	Denote the _vals[i][j] by A_ij, then this returns d(secondInvariant)/dA_ij. More...
SymmetricRankFourTensorTempl< T >	d2secondInvariant () const
	Denote the _vals[i][j] by A_ij, then this returns d^2(secondInvariant)/dA_ij/dA_kl. More...
T	sin3Lode (const T &r0, const T &r0_value) const
	Sin(3*Lode_angle) If secondInvariant() <= r0 then return r0_value This is to gaurd against precision-loss errors. More...
SymmetricRankTwoTensorTempl< T >	dsin3Lode (const T &r0) const
	d(sin3Lode)/dA_ij If secondInvariant() <= r0 then return zero This is to gaurd against precision-loss errors. More...
T	thirdInvariant () const
	Denote the _vals[i][j] by A_ij, then S_ij = A_ij - de_ij*tr(A)/3 Then this returns det(S + S.transpose())/2 Note the explicit symmeterisation. More...
SymmetricRankTwoTensorTempl< T >	dthirdInvariant () const
	Denote the _vals[i][j] by A_ij, then this returns d(thirdInvariant()/dA_ij. More...
SymmetricRankFourTensorTempl< T >	d2thirdInvariant () const
	Denote the _vals[i][j] by A_ij, then this returns d^2(thirdInvariant)/dA_ij/dA_kl. More...
T	det () const
SymmetricRankTwoTensorTempl< T >	ddet () const
	Denote the _vals[i][j] by A_ij, then this returns d(det)/dA_ij. More...
void	print (std::ostream &stm=Moose::out) const
	Print the rank two tensor. More...
void	printReal (std::ostream &stm=Moose::out) const
	Print the Real part of the ADReal rank two tensor. More...
void	printADReal (unsigned int nDual, std::ostream &stm=Moose::out) const
	Print the Real part of the ADReal rank two tensor along with its first nDual dual numbers. More...
void	addIa (const T &a)
	Add identity times a to _vals. More...
T	L2norm () const
	Sqrt(_vals[i][j]*_vals[i][j]) More...
void	surfaceFillFromInputVector (const std::vector< T > &input)
	sets _vals[0][0], _vals[0][1], _vals[1][0], _vals[1][1] to input, and the remainder to zero More...
void	symmetricEigenvalues (std::vector< T > &eigvals) const
	computes eigenvalues, assuming tens is symmetric, and places them in ascending order in eigvals More...
void	symmetricEigenvaluesEigenvectors (std::vector< T > &eigvals, RankTwoTensorTempl< T > &eigvecs) const
	computes eigenvalues and eigenvectors, assuming tens is symmetric, and places them in ascending order in eigvals. More...
SymmetricRankTwoTensorTempl< T >	initialContraction (const SymmetricRankFourTensorTempl< T > &b) const
	returns this_ij * b_ijkl More...
void	setToIdentity ()
	set the tensor to the identity matrix More...

Static Public Member Functions
static constexpr Real	mandelFactor (unsigned int i)
	returns the 1 or sqrt(2) prefactor in the Mandel notation for the index i ranging from 0-5. More...
static SymmetricRankTwoTensorTempl	identity ()
static SymmetricRankTwoTensorTempl	initializeSymmetric (const TypeVector< T > &v0, const TypeVector< T > &v1, const TypeVector< T > &v2)
	named constructor for initializing symmetrically More...
static MooseEnum	fillMethodEnum ()
	Static method for use in validParams for getting the "fill_method". More...
static SymmetricRankTwoTensorTempl< T >	timesTranspose (const RankTwoTensorTempl< T > &)
	return the matrix multiplied with its transpose A*A^T (guaranteed symmetric) More...
static SymmetricRankTwoTensorTempl< T >	timesTranspose (const SymmetricRankTwoTensorTempl< T > &)
static SymmetricRankTwoTensorTempl< T >	transposeTimes (const RankTwoTensorTempl< T > &)
	return the matrix multiplied with its transpose A^T*A (guaranteed symmetric) More...
static SymmetricRankTwoTensorTempl< T >	transposeTimes (const SymmetricRankTwoTensorTempl< T > &)
static SymmetricRankTwoTensorTempl< T >	plusTranspose (const RankTwoTensorTempl< T > &)
	return the matrix plus its transpose A-A^T (guaranteed symmetric) More...
static SymmetricRankTwoTensorTempl< T >	plusTranspose (const SymmetricRankTwoTensorTempl< T > &)
static void	initRandom (unsigned int)
	This function initializes random seed based on a user-defined number. More...
static SymmetricRankTwoTensorTempl< T >	genRandomSymmTensor (T, T)
	This function generates a random symmetric rank two tensor. More...
static SymmetricRankTwoTensorTempl< T >	selfOuterProduct (const TypeVector< T > &)
	SymmetricRankTwoTensorTempl<T> from outer product of a vector with itself. More...

Static Public Attributes
static constexpr unsigned int	full_index [6][2] = {{0, 0}, {1, 1}, {2, 2}, {1, 2}, {0, 2}, {0, 1}}
static constexpr unsigned int	reverse_index [3][3] = {{0, 5, 4}, {5, 1, 3}, {4, 3, 2}}
static constexpr unsigned int	Ndim = Moose::dim
	tensor dimension and Mandel vector length More...
static constexpr unsigned int	N = Ndim + (Ndim * (Ndim - 1)) / 2

Protected Member Functions
void	syev (const char *calculation_type, std::vector< T > &eigvals, std::vector< T > &a) const
	Uses the petscblaslapack.h LAPACKsyev_ routine to find, for symmetric _vals: (1) the eigenvalues (if calculation_type == "N") (2) the eigenvalues and eigenvectors (if calculation_type == "V") More...

Private Member Functions
	SymmetricRankTwoTensorTempl (const T &S11, const T &S21, const T &S31, const T &S12, const T &S22, const T &S32, const T &S13, const T &S23, const T &S33)
	Initialization list replacement constructors, 9 arguments (for internal use only) More...

Static Private Member Functions
static SymmetricRankTwoTensorTempl	fromRawComponents (const T &S11, const T &S22, const T &S33, const T &S23, const T &S13, const T &S12)

Private Attributes
std::array< T, N >	_vals

Static Private Attributes
static constexpr std::array< Real, N >	identityCoords = {{1, 1, 1, 0, 0, 0}}

Friends
template<class T2 >
class	SymmetricRankFourTensorTempl
std::ostream &	operator<< (std::ostream &os, const SymmetricRankTwoTensorTempl< T > &t)
template<class T2 >
void	dataStore (std::ostream &, SymmetricRankTwoTensorTempl< T2 > &, void *)
template<class T2 >
void	dataLoad (std::istream &, SymmetricRankTwoTensorTempl< T2 > &, void *)

Detailed Description

template<typename T>
class SymmetricRankTwoTensorTempl< T >

SymmetricRankTwoTensorTempl is designed to handle the Stress or Strain Tensor for an anisotropic material.

It is designed to reduce the redundancies of the Complete tensor classes for regular mechanics problems and to enable use of the Mandel notation.

Definition at line 75 of file SymmetricRankTwoTensor.h.

Member Typedef Documentation

value_type

template<typename T>

typedef T SymmetricRankTwoTensorTempl< T >::value_type

For generic programming.

Definition at line 79 of file SymmetricRankTwoTensor.h.

Member Enumeration Documentation

FillMethod

template<typename T>

enum SymmetricRankTwoTensorTempl::FillMethod

To fill up the 6 entries in the 2nd-order tensor, fillFromInputVector is called with one of the following fill_methods.

See the fill*FromInputVector functions for more details

Enumerator
autodetect
isotropic1
diagonal3
symmetric6

Definition at line 113 of file SymmetricRankTwoTensor.h.

  {
    autodetect = 0,
    isotropic1 = 1,
    diagonal3 = 3,
    symmetric6 = 6
  };

InitMethod

template<typename T>

enum SymmetricRankTwoTensorTempl::InitMethod

Enumerator
initNone
initIdentity

Definition at line 96 of file SymmetricRankTwoTensor.h.

  {
    initNone,
    initIdentity
  };

Constructor & Destructor Documentation

SymmetricRankTwoTensorTempl() [1/8]

template<typename T >

SymmetricRankTwoTensorTempl< T >::SymmetricRankTwoTensorTempl

(

)

Default constructor; fills to zero.

Definition at line 56 of file SymmetricRankTwoTensorImplementation.h.

Referenced by SymmetricRankTwoTensorTempl< Real >::identity().

{
  std::fill(_vals.begin(), _vals.end(), 0.0);
}

SymmetricRankTwoTensorTempl() [2/8]

template<typename T >

SymmetricRankTwoTensorTempl< T >::SymmetricRankTwoTensorTempl

(

const InitMethod

init

)

Select specific initialization pattern.

Definition at line 62 of file SymmetricRankTwoTensorImplementation.h.

{
  switch (init)
  {
    case initNone:
      break;

    case initIdentity:
      setToIdentity();
      break;

    default:
      mooseError("Unknown SymmetricRankTwoTensorTempl initialization pattern.");
  }
}

SymmetricRankTwoTensorTempl() [3/8]

template<typename T>

SymmetricRankTwoTensorTempl< T >::SymmetricRankTwoTensorTempl ( const std::vector< T > &  input )

inline

Constructor that proxies the fillFromInputVector method.

Definition at line 122 of file SymmetricRankTwoTensor.h.

{ this->fillFromInputVector(input); };

SymmetricRankTwoTensorTempl() [4/8]

template<typename T>

SymmetricRankTwoTensorTempl< T >::SymmetricRankTwoTensorTempl	(	const T &	S11,
		const T &	S22,
		const T &	S33,
		const T &	S23,
		const T &	S13,
		const T &	S12
	)

Initialization list replacement constructors, 6 arguments.

Definition at line 79 of file SymmetricRankTwoTensorImplementation.h.

{
  _vals[0] = S11;
  _vals[1] = S22;
  _vals[2] = S33;
  _vals[3] = mandelFactor(3) * S23;
  _vals[4] = mandelFactor(4) * S13;
  _vals[5] = mandelFactor(5) * S12;
}

SymmetricRankTwoTensorTempl() [5/8]

template<typename T>

SymmetricRankTwoTensorTempl< T >::SymmetricRankTwoTensorTempl ( const T &  S11, const T &  S21, const T &  S31, const T &  S12, const T &  S22, const T &  S32, const T &  S13, const T &  S23, const T &  S33  )

private

Initialization list replacement constructors, 9 arguments (for internal use only)

Definition at line 105 of file SymmetricRankTwoTensorImplementation.h.

{
  _vals[0] = S11;
  _vals[1] = S22;
  _vals[2] = S33;
  _vals[3] = (S23 + S32) / mandelFactor(3);
  _vals[4] = (S13 + S31) / mandelFactor(4);
  _vals[5] = (S12 + S21) / mandelFactor(5);
}

SymmetricRankTwoTensorTempl() [6/8]

template<typename T>

SymmetricRankTwoTensorTempl< T >::SymmetricRankTwoTensorTempl ( const TensorValue< T > &  a )

explicit

Copy constructor from TensorValue<T>

Definition at line 139 of file SymmetricRankTwoTensorImplementation.h.

{
  _vals[0] = a(0, 0);
  _vals[1] = a(1, 1);
  _vals[2] = a(2, 2);
  _vals[3] = (a(1, 2) + a(2, 1)) / mandelFactor(3);
  _vals[4] = (a(0, 2) + a(2, 0)) / mandelFactor(4);
  _vals[5] = (a(0, 1) + a(1, 0)) / mandelFactor(5);
}

SymmetricRankTwoTensorTempl() [7/8]

template<typename T>

SymmetricRankTwoTensorTempl< T >::SymmetricRankTwoTensorTempl ( const TypeTensor< T > &  a )

explicit

Copy constructor from TypeTensor<T>

Definition at line 150 of file SymmetricRankTwoTensorImplementation.h.

{
  _vals[0] = a(0, 0);
  _vals[1] = a(1, 1);
  _vals[2] = a(2, 2);
  _vals[3] = (a(1, 2) + a(2, 1)) / mandelFactor(3);
  _vals[4] = (a(0, 2) + a(2, 0)) / mandelFactor(4);
  _vals[5] = (a(0, 1) + a(1, 0)) / mandelFactor(5);
}

SymmetricRankTwoTensorTempl() [8/8]

template<typename T>

template<typename T2 >

SymmetricRankTwoTensorTempl< T >::SymmetricRankTwoTensorTempl ( const SymmetricRankTwoTensorTempl< T2 > &  a )

inline

Construct from other template.

Definition at line 156 of file SymmetricRankTwoTensor.h.

  {
    for (const auto i : make_range(N))
      _vals[i] = a(i);
  }

Member Function Documentation

addIa()

template<typename T>

void SymmetricRankTwoTensorTempl< T >::addIa

(

const T &

a

)

Add identity times a to _vals.

Definition at line 657 of file SymmetricRankTwoTensorImplementation.h.

Referenced by SymmetricRankTwoTensorTempl< Real >::deviatoric().

{
  for (unsigned int i = 0; i < 3; ++i)
    _vals[i] += a;
}

column()

template<typename T>

libMesh::VectorValue<T> SymmetricRankTwoTensorTempl< T >::column ( const unsigned int  n ) const

inline

get the specified column of the tensor

Definition at line 206 of file SymmetricRankTwoTensor.h.

{ return row(n); }

d2secondInvariant()

template<typename T >

SymmetricRankFourTensorTempl< T > SymmetricRankTwoTensorTempl< T >::d2secondInvariant

(

)

const

Denote the _vals[i][j] by A_ij, then this returns d^2(secondInvariant)/dA_ij/dA_kl.

Definition at line 501 of file SymmetricRankTwoTensorImplementation.h.

{
  SymmetricRankFourTensorTempl<T> result;

  for (auto i : make_range(N))
    for (auto j : make_range(N))
      result(i, j) = 0.5 * (i == j) + 0.5 * (i == j) - (1.0 / 3.0) * (i < 3) * (j < 3);

  return result;
}

d2thirdInvariant()

template<typename T >

SymmetricRankFourTensorTempl< T > SymmetricRankTwoTensorTempl< T >::d2thirdInvariant

(

)

const

Denote the _vals[i][j] by A_ij, then this returns d^2(thirdInvariant)/dA_ij/dA_kl.

Definition at line 571 of file SymmetricRankTwoTensorImplementation.h.

{
  const auto s = SymmetricRankTwoTensorTempl<T>::plusTranspose(deviatoric()) * 0.5;

  SymmetricRankFourTensorTempl<T> d2;
  for (auto i : make_range(N))
    for (auto j : make_range(N))
      d2(i, j) = Real(i < 3) * s(j) / 3.0 / (j < 3 ? 1 : MathUtils::sqrt2) +
                 Real(j < 3) * s(i) / 3.0 / (i < 3 ? 1 : MathUtils::sqrt2);

  d2(0, 1) += s(2);
  d2(0, 2) += s(1);
  d2(0, 3) -= s(3) / MathUtils::sqrt2;

  d2(1, 0) += s(2);
  d2(1, 2) += s(0);
  d2(1, 4) -= s(4) / MathUtils::sqrt2;

  d2(2, 0) += s(1);
  d2(2, 1) += s(0);
  d2(2, 5) -= s(5) / MathUtils::sqrt2;

  d2(3, 0) -= s(3) / MathUtils::sqrt2;
  d2(3, 3) -= s(0) / 2.0;
  d2(3, 4) += s(5) / 2.0 / MathUtils::sqrt2;
  d2(3, 5) += s(4) / 2.0 / MathUtils::sqrt2;

  d2(4, 1) -= s(4) / MathUtils::sqrt2;
  d2(4, 3) += s(5) / 2.0 / MathUtils::sqrt2;
  d2(4, 4) -= s(1) / 2.0;
  d2(4, 5) += s(3) / 2.0 / MathUtils::sqrt2;

  d2(5, 2) -= s(5) / MathUtils::sqrt2;
  d2(5, 3) += s(4) / 2.0 / MathUtils::sqrt2;
  d2(5, 4) += s(3) / 2.0 / MathUtils::sqrt2;
  d2(5, 5) -= s(2) / 2.0;

  for (auto i : make_range(N))
    for (auto j : make_range(N))
      d2(i, j) *= SymmetricRankFourTensorTempl<T>::mandelFactor(i, j);

  return d2;
}

ddet()

template<typename T >

SymmetricRankTwoTensorTempl< T > SymmetricRankTwoTensorTempl< T >::ddet

(

)

const

Denote the _vals[i][j] by A_ij, then this returns d(det)/dA_ij.

Definition at line 628 of file SymmetricRankTwoTensorImplementation.h.

{
  return SymmetricRankTwoTensorTempl<T>(
      _vals[2] * _vals[1] - _vals[3] * _vals[3] / 2.0,
      _vals[0] * _vals[2] - _vals[4] * _vals[4] / 2.0,
      _vals[0] * _vals[1] - _vals[5] * _vals[5] / 2.0,
      _vals[4] * _vals[5] / 2.0 - _vals[0] * _vals[3] / MathUtils::sqrt2,
      _vals[5] * _vals[3] / 2.0 - _vals[4] * _vals[1] / MathUtils::sqrt2,
      _vals[4] * _vals[3] / 2.0 - _vals[5] * _vals[2] / MathUtils::sqrt2);
}

det()

template<typename T >

T SymmetricRankTwoTensorTempl< T >::det

(

)

const

Definition at line 617 of file SymmetricRankTwoTensorImplementation.h.

{
  return _vals[0] * (_vals[2] * _vals[1] - _vals[3] * _vals[3] / 2.0) -
         _vals[5] / MathUtils::sqrt2 *
             (_vals[2] * _vals[5] / MathUtils::sqrt2 - _vals[3] * _vals[4] / 2.0) +
         _vals[4] / MathUtils::sqrt2 *
             (_vals[3] * _vals[5] / 2.0 - _vals[1] * _vals[4] / MathUtils::sqrt2);
}

deviatoric()

template<typename T >

SymmetricRankTwoTensorTempl< T > SymmetricRankTwoTensorTempl< T >::deviatoric

(

)

const

returns A_ij - de_ij*tr(A)/3, where A are the _vals

Definition at line 463 of file SymmetricRankTwoTensorImplementation.h.

{
  SymmetricRankTwoTensorTempl<T> deviatoric(*this);
  deviatoric.addIa(-1.0 / 3.0 * this->tr());
  return deviatoric;
}

doubleContraction()

template<typename T>

T SymmetricRankTwoTensorTempl< T >::doubleContraction

(

const SymmetricRankTwoTensorTempl< T > &

a

)

const

returns _vals_ij * a_ij (sum on i, j)

Definition at line 438 of file SymmetricRankTwoTensorImplementation.h.

{
  T sum = 0;
  for (unsigned int i = 0; i < N; ++i)
    sum += _vals[i] * b._vals[i];
  return sum;
}

dsecondInvariant()

template<typename T >

SymmetricRankTwoTensorTempl< T > SymmetricRankTwoTensorTempl< T >::dsecondInvariant

(

)

const

Denote the _vals[i][j] by A_ij, then this returns d(secondInvariant)/dA_ij.

Definition at line 494 of file SymmetricRankTwoTensorImplementation.h.

{
  return SymmetricRankTwoTensorTempl<T>::plusTranspose(deviatoric()) * 0.5;
}

dsin3Lode()

template<typename T>

SymmetricRankTwoTensorTempl< T > SymmetricRankTwoTensorTempl< T >::dsin3Lode

(

const T &

r0

)

const

d(sin3Lode)/dA_ij If secondInvariant() <= r0 then return zero This is to gaurd against precision-loss errors.

Note that sin(3*Lode_angle) is not defined for secondInvariant() = 0

Definition at line 668 of file SymmetricRankTwoTensor.h.

{
  if (MooseUtils::IsLikeReal<T>::value)
  {
    T bar = secondInvariant();
    if (bar <= r0)
      return SymmetricRankTwoTensorTempl<T>();
    else
      return -1.5 * std::sqrt(3.0) *
             (dthirdInvariant() / std::pow(bar, 1.5) -
              1.5 * dsecondInvariant() * thirdInvariant() / std::pow(bar, 2.5));
  }
  else
    mooseError("dsin3Lode is only available for ordered tensor component types");
}

dthirdInvariant()

template<typename T >

SymmetricRankTwoTensorTempl< T > SymmetricRankTwoTensorTempl< T >::dthirdInvariant

(

)

const

Denote the _vals[i][j] by A_ij, then this returns d(thirdInvariant()/dA_ij.

Definition at line 557 of file SymmetricRankTwoTensorImplementation.h.

{
  const auto s = SymmetricRankTwoTensorTempl<T>::plusTranspose(deviatoric()) * 0.5;
  const T s3 = secondInvariant() / 3.0;
  return SymmetricRankTwoTensorTempl<T>(s(1) * s(2) - s(3) * s(3) / 2.0 + s3,
                                        s(0) * s(2) - s(4) * s(4) / 2.0 + s3,
                                        s(0) * s(1) - s(5) * s(5) / 2.0 + s3,
                                        s(5) * s(4) / 2.0 - s(0) * s(3) / MathUtils::sqrt2,
                                        s(5) * s(3) / 2.0 - s(1) * s(4) / MathUtils::sqrt2,
                                        s(4) * s(3) / 2.0 - s(5) * s(2) / MathUtils::sqrt2);
}

dtrace()

template<typename T >

SymmetricRankTwoTensorTempl< T > SymmetricRankTwoTensorTempl< T >::dtrace

(

)

const

Denote the _vals[i][j] by A_ij, then this returns d(trace)/dA_ij.

Definition at line 538 of file SymmetricRankTwoTensorImplementation.h.

{
  return SymmetricRankTwoTensorTempl<T>(1, 1, 1, 0, 0, 0);
}

fillFromInputVector()

template<typename T>

void SymmetricRankTwoTensorTempl< T >::fillFromInputVector	(	const std::vector< T > &	input,
		FillMethod	fill_method = autodetect
	)

fillFromInputVector takes 1, 3, or 6 inputs to fill in the symmmetric Rank-2 tensor.

Definition at line 173 of file SymmetricRankTwoTensorImplementation.h.

Referenced by GenericConstantSymmetricRankTwoTensorTempl< is_ad >::GenericConstantSymmetricRankTwoTensorTempl(), and SymmetricRankTwoTensorTempl< Real >::SymmetricRankTwoTensorTempl().

{
  if (fill_method != autodetect && fill_method != input.size())
    mooseError("Expected an input vector size of ",
               fill_method,
               " to fill the SymmetricRankTwoTensorTempl");

  switch (input.size())
  {
    case 1:
      _vals[0] = input[0];
      _vals[1] = input[0];
      _vals[2] = input[0];
      _vals[3] = 0.0;
      _vals[4] = 0.0;
      _vals[5] = 0.0;
      break;

    case 3:
      _vals[0] = input[0];
      _vals[1] = input[1];
      _vals[2] = input[2];
      _vals[3] = 0.0;
      _vals[4] = 0.0;
      _vals[5] = 0.0;
      break;

    case 6:
      _vals[0] = input[0];
      _vals[1] = input[1];
      _vals[2] = input[2];
      _vals[3] = mandelFactor(3) * input[3];
      _vals[4] = mandelFactor(4) * input[4];
      _vals[5] = mandelFactor(5) * input[5];
      break;

    default:
      mooseError("Please check the number of entries in the input vector for building "
                 "a SymmetricRankTwoTensorTempl. It must be 1, 3, 6");
  }
}

fillFromScalarVariable()

template<typename T >

void SymmetricRankTwoTensorTempl< T >::fillFromScalarVariable

(

const VariableValue &

scalar_variable

)

fillFromScalarVariable takes FIRST/THIRD/SIXTH order scalar variable to fill in the Rank-2 tensor.

Definition at line 218 of file SymmetricRankTwoTensorImplementation.h.

{
  switch (scalar_variable.size())
  {
    case 1:
      _vals[0] = scalar_variable[0];
      _vals[1] = 0.0;
      _vals[2] = 0.0;
      _vals[3] = 0.0;
      _vals[4] = 0.0;
      _vals[5] = 0.0;
      break;

    case 3:
      _vals[0] = scalar_variable[0];
      _vals[1] = scalar_variable[1];
      _vals[2] = 0.0;
      _vals[3] = 0.0;
      _vals[4] = 0.0;
      _vals[5] = mandelFactor(5) * scalar_variable[2];
      break;

    case 6:
      _vals[0] = scalar_variable[0];
      _vals[1] = scalar_variable[1];
      _vals[2] = scalar_variable[2];
      _vals[3] = mandelFactor(3) * scalar_variable[3];
      _vals[4] = mandelFactor(4) * scalar_variable[4];
      _vals[5] = mandelFactor(5) * scalar_variable[5];
      break;

    default:
      mooseError("Only FIRST, THIRD, or SIXTH order scalar variable can be used to build "
                 "a SymmetricRankTwoTensorTempl.");
  }
}

fillMethodEnum()

template<typename T >

MooseEnum SymmetricRankTwoTensorTempl< T >::fillMethodEnum ( )

static

Static method for use in validParams for getting the "fill_method".

Definition at line 50 of file SymmetricRankTwoTensorImplementation.h.

{
  return MooseEnum("autodetect=0 isotropic1=1 diagonal3=3 symmetric6=6", "autodetect");
}

fromRawComponents()

template<typename T>

SymmetricRankTwoTensorTempl< T > SymmetricRankTwoTensorTempl< T >::fromRawComponents ( const T &  S11, const T &  S22, const T &  S33, const T &  S23, const T &  S13, const T &  S12  )

staticprivate

Definition at line 125 of file SymmetricRankTwoTensorImplementation.h.

Referenced by SymmetricRankTwoTensorTempl< Real >::timesTranspose().

{
  SymmetricRankTwoTensorTempl<T> ret(SymmetricRankTwoTensorTempl<T>::initNone);
  ret._vals[0] = S11;
  ret._vals[1] = S22;
  ret._vals[2] = S33;
  ret._vals[3] = S23;
  ret._vals[4] = S13;
  ret._vals[5] = S12;
  return ret;
}

generalSecondInvariant()

template<typename T >

T SymmetricRankTwoTensorTempl< T >::generalSecondInvariant

(

)

const

Calculates the second invariant (I2) of a tensor.

Definition at line 472 of file SymmetricRankTwoTensorImplementation.h.

{
  return _vals[0] * _vals[1] + _vals[0] * _vals[2] + _vals[1] * _vals[2] -
         (_vals[3] * _vals[3] + _vals[4] * _vals[4] + _vals[5] * _vals[5]) / 2.0;
}

genRandomSymmTensor()

template<typename T>

SymmetricRankTwoTensorTempl< T > SymmetricRankTwoTensorTempl< T >::genRandomSymmTensor ( T  scale, T  offset  )

static

This function generates a random symmetric rank two tensor.

The first real scales the random number. The second real offsets the uniform random number

Definition at line 718 of file SymmetricRankTwoTensorImplementation.h.

{
  auto r = [&]() { return (MooseRandom::rand() + offset) * scale; };
  return SymmetricRankTwoTensorTempl<T>(r(), r(), r(), r(), r(), r());
}

identity()

template<typename T>

static SymmetricRankTwoTensorTempl SymmetricRankTwoTensorTempl< T >::identity ( )

inlinestatic

Definition at line 163 of file SymmetricRankTwoTensor.h.

  {
    return SymmetricRankTwoTensorTempl(initIdentity);
  }

initialContraction()

template<typename T>

SymmetricRankTwoTensorTempl< T > SymmetricRankTwoTensorTempl< T >::initialContraction

(

const SymmetricRankFourTensorTempl< T > &

b

)

const

returns this_ij * b_ijkl

Definition at line 734 of file SymmetricRankTwoTensorImplementation.h.

{
  SymmetricRankTwoTensorTempl<T> result;
  for (auto i : make_range(N))
    for (auto j : make_range(N))
      result(j) += (*this)(i)*b(i, j);
  return result;
}

initializeSymmetric()

template<typename T>

SymmetricRankTwoTensorTempl< T > SymmetricRankTwoTensorTempl< T >::initializeSymmetric ( const TypeVector< T > &  v0, const TypeVector< T > &  v1, const TypeVector< T > &  v2  )

static

named constructor for initializing symmetrically

Definition at line 163 of file SymmetricRankTwoTensorImplementation.h.

{
  return SymmetricRankTwoTensorTempl<T>(
      v0(0), v1(0), v2(0), v0(1), v1(1), v2(1), v0(2), v1(2), v2(2));
}

initRandom()

template<typename T >

void SymmetricRankTwoTensorTempl< T >::initRandom ( unsigned int  rand_seed )

static

This function initializes random seed based on a user-defined number.

Definition at line 711 of file SymmetricRankTwoTensorImplementation.h.

{
  MooseRandom::seed(rand_seed);
}

inverse()

template<typename T >

SymmetricRankTwoTensorTempl< T > SymmetricRankTwoTensorTempl< T >::inverse

(

)

const

retuns the inverse of the tensor

Definition at line 521 of file SymmetricRankTwoTensorImplementation.h.

{
  const auto d = det();
  if (d == 0.0)
    mooseException("Matrix not invertible");
  const SymmetricRankTwoTensorTempl<T> inv(
      _vals[2] * _vals[1] - _vals[3] * _vals[3] / 2.0,
      _vals[2] * _vals[0] - _vals[4] * _vals[4] / 2.0,
      _vals[0] * _vals[1] - _vals[5] * _vals[5] / 2.0,
      _vals[5] * _vals[4] / 2.0 - _vals[0] * _vals[3] / MathUtils::sqrt2,
      _vals[5] * _vals[3] / 2.0 - _vals[4] * _vals[1] / MathUtils::sqrt2,
      _vals[4] * _vals[3] / 2.0 - _vals[2] * _vals[5] / MathUtils::sqrt2);
  return inv * 1.0 / d;
}

isSymmetric()

template<typename T>

bool SymmetricRankTwoTensorTempl< T >::isSymmetric ( ) const

inline

Test for symmetry. Surprisingly this is always true.

Definition at line 309 of file SymmetricRankTwoTensor.h.

{ return true; }

L2norm()

template<typename T >

T SymmetricRankTwoTensorTempl< T >::L2norm

(

)

const

Sqrt(_vals[i][j]*_vals[i][j])

Definition at line 665 of file SymmetricRankTwoTensorImplementation.h.

{
  T norm = _vals[0] * _vals[0];
  for (unsigned int i = 1; i < N; ++i)
    norm += _vals[i] * _vals[i];
  return norm == 0.0 ? 0.0 : std::sqrt(norm);
}

mandelFactor()

template<typename T>

static constexpr Real SymmetricRankTwoTensorTempl< T >::mandelFactor ( unsigned int  i )

inlinestatic

returns the 1 or sqrt(2) prefactor in the Mandel notation for the index i ranging from 0-5.

Definition at line 93 of file SymmetricRankTwoTensor.h.

Referenced by SymmetricRankFourTensorTempl< T >::mandelFactor(), and SymmetricRankTwoTensorTempl< Real >::operator()().

{ return i < Ndim ? 1.0 : MathUtils::sqrt2; }

operator RankTwoTensorTempl< T >()

template<typename T >

SymmetricRankTwoTensorTempl< T >::operator RankTwoTensorTempl< T > ( )

explicit

Definition at line 91 of file SymmetricRankTwoTensorImplementation.h.

{
  return RankTwoTensorTempl<T>(_vals[0],
                               _vals[5] / mandelFactor(5),
                               _vals[4] / mandelFactor(4),
                               _vals[5] / mandelFactor(5),
                               _vals[1],
                               _vals[3] / mandelFactor(3),
                               _vals[4] / mandelFactor(4),
                               _vals[3] / mandelFactor(3),
                               _vals[2]);
}

operator!=()

template<typename T >

template<typename T2 >

bool SymmetricRankTwoTensorTempl< T >::operator!=

(

const SymmetricRankTwoTensorTempl< T2 > &

a

)

const

Defines logical inequality with another SymmetricRankTwoTensorTempl<T2>

Definition at line 573 of file SymmetricRankTwoTensor.h.

{
  for (std::size_t i = 0; i < N; ++i)
    if (_vals[i] != a._vals[i])
      return true;
  return false;
}

operator()() [1/3]

template<typename T>

T& SymmetricRankTwoTensorTempl< T >::operator() ( unsigned int  i )

inline

Gets the raw value for the index specified. Takes index = 0,1,2,3,4,5.

Definition at line 185 of file SymmetricRankTwoTensor.h.

{ return _vals[i]; }

operator()() [2/3]

template<typename T>

T SymmetricRankTwoTensorTempl< T >::operator() ( unsigned int  i ) const

inline

Gets the raw value for the index specified.

Takes index = 0,1,2 used for const

Definition at line 191 of file SymmetricRankTwoTensor.h.

{ return _vals[i]; }

operator()() [3/3]

template<typename T>

T SymmetricRankTwoTensorTempl< T >::operator() ( unsigned int  i, unsigned int  j  ) const

inline

Gets the value for the index specified.

Takes index = 0,1,2

Definition at line 196 of file SymmetricRankTwoTensor.h.

  {
    const auto a = reverse_index[i][j];
    return _vals[a] / mandelFactor(a);
  }

operator*() [1/2]

template<typename T>

template<typename T2 >

auto SymmetricRankTwoTensorTempl< T >::operator*

(

const T2 &

a

)

const -> typename std::enable_if<libMesh::ScalarTraits<T2>::value, SymmetricRankTwoTensorTempl<decltype(T() * T2())>>::type

returns _vals*a

Definition at line 524 of file SymmetricRankTwoTensor.h.

{
  SymmetricRankTwoTensorTempl<decltype(T() * T2())> result;
  for (const auto i : make_range(N))
    result._vals[i] = _vals[i] * a;
  return result;
}

operator*() [2/2]

template<typename T>

template<typename T2 >

TypeVector< typename libMesh::CompareTypes< T, T2 >::supertype > SymmetricRankTwoTensorTempl< T >::operator*

(

const TypeVector< T2 > &

a

)

const

Defines multiplication with a vector to get a vector.

Definition at line 551 of file SymmetricRankTwoTensor.h.

{
  TypeVector<typename libMesh::CompareTypes<T, T2>::supertype> ret;
  ret(0) = a(0) * _vals[0] + a(1) * _vals[5] + a(2) * _vals[4];
  ret(1) = a(0) * _vals[5] + a(1) * _vals[1] + a(2) * _vals[3];
  ret(2) = a(0) * _vals[4] + a(1) * _vals[3] + a(2) * _vals[2];
}

operator*=()

template<typename T>

SymmetricRankTwoTensorTempl< T > & SymmetricRankTwoTensorTempl< T >::operator*=

(

const T &

a

)

performs _vals *= a

Definition at line 420 of file SymmetricRankTwoTensorImplementation.h.

{
  for (std::size_t i = 0; i < N; ++i)
    _vals[i] *= a;
  return *this;
}

operator+()

template<typename T >

template<typename T2 >

SymmetricRankTwoTensorTempl< typename libMesh::CompareTypes< T, T2 >::supertype > SymmetricRankTwoTensorTempl< T >::operator+

(

const SymmetricRankTwoTensorTempl< T2 > &

a

)

const

returns _vals + a

Definition at line 390 of file SymmetricRankTwoTensorImplementation.h.

{
  SymmetricRankTwoTensorTempl<typename libMesh::CompareTypes<T, T2>::supertype> result;
  for (std::size_t i = 0; i < N; ++i)
    result(i) = _vals[i] + a(i);
  return result;
}

operator+=()

template<typename T>

SymmetricRankTwoTensorTempl< T > & SymmetricRankTwoTensorTempl< T >::operator+=

(

const SymmetricRankTwoTensorTempl< T > &

a

)

adds a to _vals

Definition at line 371 of file SymmetricRankTwoTensorImplementation.h.

{
  for (std::size_t i = 0; i < N; ++i)
    _vals[i] += a._vals[i];
  return *this;
}

operator-() [1/2]

template<typename T >

template<typename T2 >

SymmetricRankTwoTensorTempl< typename libMesh::CompareTypes< T, T2 >::supertype > SymmetricRankTwoTensorTempl< T >::operator-

(

const SymmetricRankTwoTensorTempl< T2 > &

a

)

const

returns _vals - a

Definition at line 401 of file SymmetricRankTwoTensorImplementation.h.

{
  SymmetricRankTwoTensorTempl<typename libMesh::CompareTypes<T, T2>::supertype> result(
      SymmetricRankTwoTensorTempl<typename libMesh::CompareTypes<T, T2>::supertype>::initNone);
  for (std::size_t i = 0; i < N; ++i)
    result(i) = _vals[i] - a(i);
  return result;
}

operator-() [2/2]

template<typename T >

SymmetricRankTwoTensorTempl< T > SymmetricRankTwoTensorTempl< T >::operator-

(

)

const

returns -_vals

Definition at line 413 of file SymmetricRankTwoTensorImplementation.h.

{
  return (*this) * -1.0;
}

operator-=()

template<typename T>

SymmetricRankTwoTensorTempl< T > & SymmetricRankTwoTensorTempl< T >::operator-=

(

const SymmetricRankTwoTensorTempl< T > &

a

)

sets _vals -= a and returns vals

Definition at line 380 of file SymmetricRankTwoTensorImplementation.h.

{
  for (std::size_t i = 0; i < N; ++i)
    _vals[i] -= a._vals[i];
  return *this;
}

operator/()

template<typename T>

template<typename T2 >

auto SymmetricRankTwoTensorTempl< T >::operator/

(

const T2 &

a

)

const -> typename std::enable_if<libMesh::ScalarTraits<T2>::value, SymmetricRankTwoTensorTempl<decltype(T() / T2())>>::type

returns _vals/a

Definition at line 537 of file SymmetricRankTwoTensor.h.

{
  SymmetricRankTwoTensorTempl<decltype(T() / T2())> result;
  for (const auto i : make_range(N))
    result._vals[i] = _vals[i] / a;
  return result;
}

operator/=()

template<typename T>

SymmetricRankTwoTensorTempl< T > & SymmetricRankTwoTensorTempl< T >::operator/=

(

const T &

a

)

performs _vals /= a

Definition at line 429 of file SymmetricRankTwoTensorImplementation.h.

{
  for (std::size_t i = 0; i < N; ++i)
    _vals[i] /= a;
  return *this;
}

operator=() [1/3]

template<typename T >

template<typename T2 >

SymmetricRankTwoTensorTempl< T > & SymmetricRankTwoTensorTempl< T >::operator=

(

const SymmetricRankTwoTensorTempl< T2 > &

a

)

sets _vals to a, and returns _vals

Definition at line 687 of file SymmetricRankTwoTensor.h.

{
  for (const auto i : make_range(N))
    (*this)(i) = a(i);
  return *this;
}

operator=() [2/3]

template<typename T>

template<typename Scalar >

boostcopy::enable_if_c<libMesh::ScalarTraits<Scalar>::value, SymmetricRankTwoTensorTempl &>::type SymmetricRankTwoTensorTempl< T >::operator= ( const Scalar &  libmesh_dbg_varp )

inline

Assignment-from-scalar operator.

Used only to zero out vectors.

Definition at line 255 of file SymmetricRankTwoTensor.h.

  {
    libmesh_assert_equal_to(p, Scalar(0));
    this->zero();
    return *this;
  }

operator=() [3/3]

template<typename T>

SymmetricRankTwoTensorTempl<T>& SymmetricRankTwoTensorTempl< T >::operator=

(

const ColumnMajorMatrixTempl< T > &

a

)

Sets _vals to the values in a ColumnMajorMatrix (must be 3x3)

operator==()

template<typename T >

template<typename T2 >

bool SymmetricRankTwoTensorTempl< T >::operator==

(

const SymmetricRankTwoTensorTempl< T2 > &

a

)

const

Defines logical equality with another SymmetricRankTwoTensorTempl<T2>

Definition at line 562 of file SymmetricRankTwoTensor.h.

{
  for (std::size_t i = 0; i < N; ++i)
    if (_vals[i] != a._vals[i])
      return false;
  return true;
}

outerProduct()

template<typename T>

SymmetricRankFourTensorTempl< T > SymmetricRankTwoTensorTempl< T >::outerProduct

(

const SymmetricRankTwoTensorTempl< T > &

a

)

const

returns C_ijkl = a_ij * b_kl

Definition at line 448 of file SymmetricRankTwoTensorImplementation.h.

{
  SymmetricRankFourTensorTempl<T> result;
  unsigned int index = 0;
  for (unsigned int i = 0; i < N; ++i)
  {
    const T & a = _vals[i];
    for (unsigned int j = 0; j < N; ++j)
      result._vals[index++] = a * b._vals[j];
  }
  return result;
}

plusTranspose() [1/2]

template<typename T>

SymmetricRankTwoTensorTempl< T > SymmetricRankTwoTensorTempl< T >::plusTranspose ( const RankTwoTensorTempl< T > &  a )

static

return the matrix plus its transpose A-A^T (guaranteed symmetric)

Definition at line 340 of file SymmetricRankTwoTensorImplementation.h.

Referenced by SymmetricRankTwoTensorTempl< Real >::d2thirdInvariant(), SymmetricRankTwoTensorTempl< Real >::dsecondInvariant(), SymmetricRankTwoTensorTempl< Real >::dthirdInvariant(), and SymmetricRankTwoTensorTempl< Real >::thirdInvariant().

{
  return SymmetricRankTwoTensorTempl<T>(
             a(0, 0), a(0, 1), a(0, 2), a(1, 0), a(1, 1), a(1, 2), a(2, 0), a(2, 1), a(2, 2)) *
         2.0;
}

plusTranspose() [2/2]

template<typename T>

SymmetricRankTwoTensorTempl< T > SymmetricRankTwoTensorTempl< T >::plusTranspose ( const SymmetricRankTwoTensorTempl< T > &  a )

static

Definition at line 349 of file SymmetricRankTwoTensorImplementation.h.

{
  return a * 2.0;
}

positiveProjectionEigenDecomposition()

template<typename T>

SymmetricRankFourTensorTempl< T > SymmetricRankTwoTensorTempl< T >::positiveProjectionEigenDecomposition	(	std::vector< T > &	eigval,
		RankTwoTensorTempl< T > &	eigvec
	)		const

return positive projection tensor of eigen-decomposition

Definition at line 583 of file SymmetricRankTwoTensor.h.

{
  // The calculate of projection tensor follows
  // C. Miehe and M. Lambrecht, Commun. Numer. Meth. Engng 2001; 17:337~353

  // Compute eigenvectors and eigenvalues of this tensor
  if (MooseUtils::IsLikeReal<T>::value)
  {
    this->symmetricEigenvaluesEigenvectors(eigval, eigvec);

    // Separate out positive and negative eigen values
    std::array<T, N> epos;
    std::array<T, N> d;
    for (unsigned int i = 0; i < N; ++i)
    {
      epos[i] = (std::abs(eigval[i]) + eigval[i]) / 2.0;
      d[i] = 0 < eigval[i] ? 1.0 : 0.0;
    }

    // projection tensor
    SymmetricRankFourTensorTempl<T> proj_pos;

    for (unsigned int a = 0; a < Ndim; ++a)
    {
      const auto Ma = SymmetricRankTwoTensorTempl<T>::selfOuterProduct(eigvec.column(a));
      proj_pos += d[a] * Ma.outerProduct(Ma);
    }

    for (const auto a : make_range(Ndim))
      for (const auto b : make_range(a))
      {
        const auto Ma = SymmetricRankTwoTensorTempl<T>::selfOuterProduct(eigvec.column(a));
        const auto Mb = SymmetricRankTwoTensorTempl<T>::selfOuterProduct(eigvec.column(b));

        SymmetricRankFourTensorTempl<T> Gabba(SymmetricRankFourTensorTempl<T>::initNone);
        for (const auto aa : make_range(N))
          for (const auto bb : make_range(N))
          {
            const auto i = SymmetricRankFourTensorTempl<T>::full_index[aa][bb][0];
            const auto j = SymmetricRankFourTensorTempl<T>::full_index[aa][bb][1];
            const auto k = SymmetricRankFourTensorTempl<T>::full_index[aa][bb][2];
            const auto l = SymmetricRankFourTensorTempl<T>::full_index[aa][bb][3];

            Gabba(aa, bb) = (Ma(i, k) * Mb(j, l) + Ma(i, l) * Mb(j, k) + Ma(j, l) * Mb(i, k) +
                             Ma(j, k) * Mb(i, l)) *
                            SymmetricRankFourTensorTempl<T>::mandelFactor(aa, bb);
          }

        T theta_ab;
        if (!MooseUtils::relativeFuzzyEqual(eigval[a], eigval[b]))
          theta_ab = 0.5 * (epos[a] - epos[b]) / (eigval[a] - eigval[b]);
        else
          theta_ab = 0.25 * (d[a] + d[b]);

        proj_pos += theta_ab * Gabba;
      }
    return proj_pos;
  }
  else
    mooseError("positiveProjectionEigenDecomposition is only available for ordered tensor "
               "component types");
}

print()

template<typename T >

void SymmetricRankTwoTensorTempl< T >::print

(

std::ostream &

stm = Moose::out

)

const

Print the rank two tensor.

Definition at line 641 of file SymmetricRankTwoTensorImplementation.h.

{
  for (std::size_t i = 0; i < N; ++i)
    stm << std::setw(15) << _vals[i] << std::endl;
}

printADReal()

template<typename T>

void SymmetricRankTwoTensorTempl< T >::printADReal	(	unsigned int	nDual,
		std::ostream &	stm = Moose::out
	)		const

Print the Real part of the ADReal rank two tensor along with its first nDual dual numbers.

printReal()

template<typename T >

void SymmetricRankTwoTensorTempl< T >::printReal

(

std::ostream &

stm = Moose::out

)

const

Print the Real part of the ADReal rank two tensor.

Definition at line 649 of file SymmetricRankTwoTensorImplementation.h.

{
  for (std::size_t i = 0; i < N; ++i)
    stm << std::setw(15) << MetaPhysicL::raw_value(_vals[i]) << std::endl;
}

rotate()

template<typename T>

void SymmetricRankTwoTensorTempl< T >::rotate

(

const TypeTensor< T > &

R

)

rotates the tensor data given a rank two tensor rotation tensor _vals[i][j] = R_ij * R_jl * _vals[k][l]

Parameters

R	rotation matrix as a TypeTensor

Definition at line 257 of file SymmetricRankTwoTensorImplementation.h.

{
  auto M = SymmetricRankFourTensorTempl<T>::rotationMatrix(R);
  *this = M * (*this);
}

row()

template<typename T >

libMesh::VectorValue< T > SymmetricRankTwoTensorTempl< T >::row

(

const unsigned int

n

)

const

get the specified row of the tensor

multiply vector v with row n of this tensor

Definition at line 273 of file SymmetricRankTwoTensorImplementation.h.

Referenced by SymmetricRankTwoTensorTempl< Real >::column().

{
  switch (n)
  {
    case 0:
      return libMesh::VectorValue<T>(
          _vals[0], _vals[5] / mandelFactor(5), _vals[4] / mandelFactor(4));
    case 1:
      return libMesh::VectorValue<T>(
          _vals[5] / mandelFactor(5), _vals[1], _vals[3] / mandelFactor(3));
    case 2:
      return libMesh::VectorValue<T>(
          _vals[4] / mandelFactor(4), _vals[3] / mandelFactor(3), _vals[2]);
    default:
      mooseError("Invalid row");
  }
}

secondInvariant()

template<typename T >

T SymmetricRankTwoTensorTempl< T >::secondInvariant

(

)

const

Denote the _vals[i][j] by A_ij, then S_ij = A_ij - de_ij*tr(A)/3 Then this returns (S_ij + S_ji)*(S_ij + S_ji)/8 Note the explicit symmeterisation.

Definition at line 480 of file SymmetricRankTwoTensorImplementation.h.

{
  T result;
  result = Utility::pow<2>(_vals[0] - _vals[1]) / 6.0;
  result += Utility::pow<2>(_vals[0] - _vals[2]) / 6.0;
  result += Utility::pow<2>(_vals[1] - _vals[2]) / 6.0;
  result += Utility::pow<2>(_vals[5]) / 2.0;
  result += Utility::pow<2>(_vals[4]) / 2.0;
  result += Utility::pow<2>(_vals[3]) / 2.0;
  return result;
}

selfOuterProduct()

template<typename T>

SymmetricRankTwoTensorTempl< T > SymmetricRankTwoTensorTempl< T >::selfOuterProduct ( const TypeVector< T > &  v )

static

SymmetricRankTwoTensorTempl<T> from outer product of a vector with itself.

Definition at line 726 of file SymmetricRankTwoTensorImplementation.h.

Referenced by SymmetricRankTwoTensorTempl< Real >::positiveProjectionEigenDecomposition().

{
  return SymmetricRankTwoTensorTempl<T>(
      v(0) * v(0), v(1) * v(1), v(2) * v(2), v(1) * v(2), v(0) * v(2), v(0) * v(1));
}

setToIdentity()

template<typename T >

void SymmetricRankTwoTensorTempl< T >::setToIdentity

(

)

set the tensor to the identity matrix

Definition at line 745 of file SymmetricRankTwoTensorImplementation.h.

{
  std::copy(identityCoords.begin(), identityCoords.end(), _vals.begin());
}

sin3Lode()

template<typename T>

T SymmetricRankTwoTensorTempl< T >::sin3Lode	(	const T &	r0,
		const T &	r0_value
	)		const

Sin(3*Lode_angle) If secondInvariant() <= r0 then return r0_value This is to gaurd against precision-loss errors.

Note that sin(3*Lode_angle) is not defined for secondInvariant() = 0

Definition at line 649 of file SymmetricRankTwoTensor.h.

{
  if (MooseUtils::IsLikeReal<T>::value)
  {
    T bar = secondInvariant();
    if (bar <= r0)
      // in this case the Lode angle is not defined
      return r0_value;
    else
      // the min and max here gaurd against precision-loss when bar is tiny but nonzero.
      return std::max(std::min(thirdInvariant() * -1.5 * std::sqrt(3.0) / std::pow(bar, 1.5), 1.0),
                      -1.0);
  }
  else
    mooseError("sin3Lode is only available for ordered tensor component types");
}

square()

template<typename T >

SymmetricRankTwoTensorTempl< T > SymmetricRankTwoTensorTempl< T >::square

(

)

const

Returns the matrix squared.

Definition at line 356 of file SymmetricRankTwoTensorImplementation.h.

{
  return SymmetricRankTwoTensorTempl<T>::timesTranspose(*this);
}

surfaceFillFromInputVector()

template<typename T>

void SymmetricRankTwoTensorTempl< T >::surfaceFillFromInputVector

(

const std::vector< T > &

input

)

sets _vals[0][0], _vals[0][1], _vals[1][0], _vals[1][1] to input, and the remainder to zero

syev()

template<typename T>

void SymmetricRankTwoTensorTempl< T >::syev ( const char *  calculation_type, std::vector< T > &  eigvals, std::vector< T > &  a  ) const

protected

Uses the petscblaslapack.h LAPACKsyev_ routine to find, for symmetric _vals: (1) the eigenvalues (if calculation_type == "N") (2) the eigenvalues and eigenvectors (if calculation_type == "V")

Parameters

calculation_type	If "N" then calculation eigenvalues only
eigvals	Eigenvalues are placed in this array, in ascending order
a	Eigenvectors are placed in this array if calculation_type == "V". See code in dsymmetricEigenvalues for extracting eigenvectors from the a output.

Definition at line 675 of file SymmetricRankTwoTensorImplementation.h.

{
  mooseError("The syev method is only supported for Real valued tensors");
}

symmetricEigenvalues()

template<typename T>

void SymmetricRankTwoTensorTempl< T >::symmetricEigenvalues

(

std::vector< T > &

eigvals

)

const

computes eigenvalues, assuming tens is symmetric, and places them in ascending order in eigvals

Definition at line 687 of file SymmetricRankTwoTensorImplementation.h.

{
  RankTwoTensorTempl<T> a;
  symmetricEigenvaluesEigenvectors(eigvals, a);
}

symmetricEigenvaluesEigenvectors()

template<typename T>

void SymmetricRankTwoTensorTempl< T >::symmetricEigenvaluesEigenvectors	(	std::vector< T > &	eigvals,
		RankTwoTensorTempl< T > &	eigvecs
	)		const

computes eigenvalues and eigenvectors, assuming tens is symmetric, and places them in ascending order in eigvals.

eigvecs is a matrix with the first column being the first eigenvector, the second column being the second, etc.

Definition at line 698 of file SymmetricRankTwoTensorImplementation.h.

{
  mooseError(
      "symmetricEigenvaluesEigenvectors is only available for ordered tensor component types");
}

thirdInvariant()

template<typename T >

T SymmetricRankTwoTensorTempl< T >::thirdInvariant

(

)

const

Denote the _vals[i][j] by A_ij, then S_ij = A_ij - de_ij*tr(A)/3 Then this returns det(S + S.transpose())/2 Note the explicit symmeterisation.

Definition at line 545 of file SymmetricRankTwoTensorImplementation.h.

{
  const auto s = SymmetricRankTwoTensorTempl<T>::plusTranspose(deviatoric()) * 0.5;
  return s(0) * (s(1) * s(2) - s(3) / MathUtils::sqrt2 * s(3) / MathUtils::sqrt2) -
         s(5) / MathUtils::sqrt2 *
             (s(5) / MathUtils::sqrt2 * s(2) - s(3) / MathUtils::sqrt2 * s(4) / MathUtils::sqrt2) +
         s(4) / MathUtils::sqrt2 *
             (s(5) / MathUtils::sqrt2 * s(3) / MathUtils::sqrt2 - s(1) * s(4) / MathUtils::sqrt2);
}

timesTranspose() [1/2]

template<typename T>

SymmetricRankTwoTensorTempl< T > SymmetricRankTwoTensorTempl< T >::timesTranspose ( const RankTwoTensorTempl< T > &  a )

static

return the matrix multiplied with its transpose A*A^T (guaranteed symmetric)

Definition at line 293 of file SymmetricRankTwoTensorImplementation.h.

Referenced by SymmetricRankTwoTensorTempl< Real >::square().

{
  return SymmetricRankTwoTensorTempl<T>(a(0, 0) * a(0, 0) + a(0, 1) * a(0, 1) + a(0, 2) * a(0, 2),
                                        a(1, 0) * a(1, 0) + a(1, 1) * a(1, 1) + a(1, 2) * a(1, 2),
                                        a(2, 0) * a(2, 0) + a(2, 1) * a(2, 1) + a(2, 2) * a(2, 2),
                                        a(1, 0) * a(2, 0) + a(1, 1) * a(2, 1) + a(1, 2) * a(2, 2),
                                        a(0, 0) * a(2, 0) + a(0, 1) * a(2, 1) + a(0, 2) * a(2, 2),
                                        a(0, 0) * a(1, 0) + a(0, 1) * a(1, 1) + a(0, 2) * a(1, 2));
}

timesTranspose() [2/2]

template<typename T>

SymmetricRankTwoTensorTempl< T > SymmetricRankTwoTensorTempl< T >::timesTranspose ( const SymmetricRankTwoTensorTempl< T > &  a )

static

Definition at line 305 of file SymmetricRankTwoTensorImplementation.h.

{
  return SymmetricRankTwoTensorTempl<T>::fromRawComponents(
      a._vals[0] * a._vals[0] + a._vals[4] * a._vals[4] / 2.0 + a._vals[5] * a._vals[5] / 2.0,
      a._vals[1] * a._vals[1] + a._vals[3] * a._vals[3] / 2.0 + a._vals[5] * a._vals[5] / 2.0,
      a._vals[2] * a._vals[2] + a._vals[3] * a._vals[3] / 2.0 + a._vals[4] * a._vals[4] / 2.0,
      a._vals[1] * a._vals[3] + a._vals[2] * a._vals[3] +
          a._vals[4] * a._vals[5] / MathUtils::sqrt2,
      a._vals[0] * a._vals[4] + a._vals[2] * a._vals[4] +
          a._vals[3] * a._vals[5] / MathUtils::sqrt2,
      a._vals[0] * a._vals[5] + a._vals[1] * a._vals[5] +
          a._vals[3] * a._vals[4] / MathUtils::sqrt2);
}

tr()

template<typename T>

T SymmetricRankTwoTensorTempl< T >::tr ( ) const

inline

Returns the trace.

Definition at line 227 of file SymmetricRankTwoTensor.h.

{ return _vals[0] + _vals[1] + _vals[2]; }

trace()

template<typename T >

T SymmetricRankTwoTensorTempl< T >::trace

(

)

const

returns the trace of the tensor, ie _vals[i][i] (sum i = 0, 1, 2)

Definition at line 514 of file SymmetricRankTwoTensorImplementation.h.

{
  return tr();
}

transpose()

template<typename T >

SymmetricRankTwoTensorTempl< T > SymmetricRankTwoTensorTempl< T >::transpose

(

)

const

Returns a matrix that is the transpose of the matrix this was called on.

This is a non-operation.

Definition at line 265 of file SymmetricRankTwoTensorImplementation.h.

{
  return *this;
}

transposeTimes() [1/2]

template<typename T>

SymmetricRankTwoTensorTempl< T > SymmetricRankTwoTensorTempl< T >::transposeTimes ( const RankTwoTensorTempl< T > &  a )

static

return the matrix multiplied with its transpose A^T*A (guaranteed symmetric)

Definition at line 321 of file SymmetricRankTwoTensorImplementation.h.

{
  return SymmetricRankTwoTensorTempl<T>(a(0, 0) * a(0, 0) + a(1, 0) * a(1, 0) + a(2, 0) * a(2, 0),
                                        a(0, 1) * a(0, 1) + a(1, 1) * a(1, 1) + a(2, 1) * a(2, 1),
                                        a(0, 2) * a(0, 2) + a(1, 2) * a(1, 2) + a(2, 2) * a(2, 2),
                                        a(0, 1) * a(0, 2) + a(1, 1) * a(1, 2) + a(2, 1) * a(2, 2),
                                        a(0, 0) * a(0, 2) + a(1, 0) * a(1, 2) + a(2, 0) * a(2, 2),
                                        a(0, 0) * a(0, 1) + a(1, 0) * a(1, 1) + a(2, 0) * a(2, 1));
}

transposeTimes() [2/2]

template<typename T>

SymmetricRankTwoTensorTempl< T > SymmetricRankTwoTensorTempl< T >::transposeTimes ( const SymmetricRankTwoTensorTempl< T > &  a )

static

Definition at line 333 of file SymmetricRankTwoTensorImplementation.h.

{
  return timesTranspose(a);
}

zero()

template<typename T >

void SymmetricRankTwoTensorTempl< T >::zero

(

)

Set all components to zero.

Definition at line 363 of file SymmetricRankTwoTensorImplementation.h.

Referenced by SymmetricRankTwoTensorTempl< Real >::operator=().

{
  for (std::size_t i = 0; i < N; ++i)
    _vals[i] = 0.0;
}

Friends And Related Function Documentation

dataLoad

template<typename T>

template<class T2 >

void dataLoad ( std::istream &  , SymmetricRankTwoTensorTempl< T2 > &  , void *    )

friend

dataStore

template<typename T>

template<class T2 >

void dataStore ( std::ostream &  , SymmetricRankTwoTensorTempl< T2 > &  , void *    )

friend

operator<<

template<typename T>

std::ostream& operator<< ( std::ostream &  os, const SymmetricRankTwoTensorTempl< T > &  t  )

friend

Definition at line 422 of file SymmetricRankTwoTensor.h.

  {
    t.print(os);
    return os;
  }

SymmetricRankFourTensorTempl

template<typename T>

template<class T2 >

friend class SymmetricRankFourTensorTempl

friend

Definition at line 500 of file SymmetricRankTwoTensor.h.

Member Data Documentation

_vals

template<typename T>

std::array<T, N> SymmetricRankTwoTensorTempl< T >::_vals

private

Definition at line 492 of file SymmetricRankTwoTensor.h.

Referenced by dataLoad(), dataStore(), SymmetricRankTwoTensorTempl< Real >::doubleContraction(), SymmetricRankTwoTensorTempl< Real >::fromRawComponents(), SymmetricRankTwoTensorTempl< Real >::operator!=(), SymmetricRankTwoTensorTempl< Real >::operator()(), SymmetricRankFourTensorTempl< T >::operator*(), SymmetricRankTwoTensorTempl< Real >::operator*(), SymmetricRankTwoTensorTempl< Real >::operator+=(), SymmetricRankTwoTensorTempl< Real >::operator-=(), SymmetricRankTwoTensorTempl< Real >::operator/(), SymmetricRankTwoTensorTempl< Real >::operator==(), SymmetricRankTwoTensorTempl< Real >::outerProduct(), SymmetricRankTwoTensorTempl< Real >::SymmetricRankTwoTensorTempl(), SymmetricRankTwoTensorTempl< Real >::timesTranspose(), and SymmetricRankTwoTensorTempl< Real >::tr().

full_index

template<typename T>

constexpr unsigned int SymmetricRankTwoTensorTempl< T >::full_index[6][2] = {{0, 0}, {1, 1}, {2, 2}, {1, 2}, {0, 2}, {0, 1}}

static

Definition at line 87 of file SymmetricRankTwoTensor.h.

identityCoords

template<typename T>

constexpr std::array< Real, SymmetricRankTwoTensorTempl< T >::N > SymmetricRankTwoTensorTempl< T >::identityCoords = {{1, 1, 1, 0, 0, 0}}

staticprivate

Definition at line 489 of file SymmetricRankTwoTensor.h.

N

template<typename T>

constexpr unsigned int SymmetricRankTwoTensorTempl< T >::N = Ndim + (Ndim * (Ndim - 1)) / 2

static

Definition at line 83 of file SymmetricRankTwoTensor.h.

Referenced by SymmetricRankTwoTensorTempl< Real >::SymmetricRankTwoTensorTempl().

Ndim

template<typename T>

constexpr unsigned int SymmetricRankTwoTensorTempl< T >::Ndim = Moose::dim

static

tensor dimension and Mandel vector length

Definition at line 82 of file SymmetricRankTwoTensor.h.

Referenced by SymmetricRankTwoTensorTempl< Real >::mandelFactor().

reverse_index

template<typename T>

constexpr unsigned int SymmetricRankTwoTensorTempl< T >::reverse_index[3][3] = {{0, 5, 4}, {5, 1, 3}, {4, 3, 2}}

static

Definition at line 90 of file SymmetricRankTwoTensor.h.

Referenced by SymmetricRankTwoTensorTempl< Real >::operator()().

---

The documentation for this class was generated from the following files:

• include/utils/SymmetricRankTwoTensor.h
• include/utils/SymmetricRankTwoTensorImplementation.h