RankThreeTensorTempl< T > Class Template Reference

RankThreeTensor is designed to handle any N-dimensional third order tensor, r. More...

#include <RankThreeTensor.h>

Public Types
enum	InitMethod { initNone }
	Initialization method. More...
enum	FillMethod { automatic, general, plane_normal }
	To fill up the 27 entries in the 3rd-order tensor, fillFromInputVector is called with one of the following fill_methods. More...

Public Member Functions
	RankThreeTensorTempl ()
	Default constructor; fills to zero. More...
template<typename T2 >
	RankThreeTensorTempl (const RankThreeTensorTempl< T2 > &copy)
	Construct from other class template instantiation. More...
	RankThreeTensorTempl (const InitMethod)
	Select specific initialization pattern. More...
	RankThreeTensorTempl (const std::vector< T > &, FillMethod method=automatic)
	Fill from vector. More...
T &	operator() (unsigned int i, unsigned int j, unsigned int k)
	Gets the value for the index specified. Takes index = 0,1,2. More...
T	operator() (unsigned int i, unsigned int j, unsigned int k) const
	Gets the value for the index specified. Takes index = 0,1,2. Used for const. More...
RankThreeTensorTempl< T > &	operator= (const T &value)
	Assignment-from-scalar operator. More...
void	zero ()
	Zeros out the tensor. More...
void	print (std::ostream &stm=Moose::out) const
	Print the rank three tensor. More...
RankThreeTensorTempl< T > &	operator= (const RankThreeTensorTempl< T > &a)
	copies values from "a" into this tensor More...
VectorValue< T >	operator* (const RankTwoTensorTempl< T > &a) const
	b_i = r_ijk * a_jk More...
RankThreeTensorTempl< T >	operator* (const T a) const
	r_ijk*a More...
RankThreeTensorTempl< T > &	operator*= (const T a)
	r_ijk *= a More...
RankThreeTensorTempl< T >	operator/ (const T a) const
	r_ijk/a More...
RankThreeTensorTempl< T > &	operator/= (const T a)
	r_ijk /= a for all i, j, k More...
RankThreeTensorTempl< T > &	operator+= (const RankThreeTensorTempl< T > &a)
	r_ijk += a_ijk for all i, j, k More...
RankThreeTensorTempl< T >	operator+ (const RankThreeTensorTempl< T > &a) const
	r_ijkl + a_ijk More...
RankThreeTensorTempl< T > &	operator-= (const RankThreeTensorTempl< T > &a)
	r_ijk -= a_ijk More...
RankThreeTensorTempl< T >	operator- (const RankThreeTensorTempl< T > &a) const
	r_ijk - a_ijk More...
RankThreeTensorTempl< T >	operator- () const
	-r_ijk More...
T	L2norm () const
	(r_ijk*r_ijk) More...
template<class T2 >
void	rotate (const T2 &R)
	Rotate the tensor using r_ijk = R_im R_in R_ko r_mno. More...
void	rotate (const TensorValue< T > &R)
	Rotate the tensor using r_ijk = R_im R_in R_ko r_mno. More...
void	fillFromInputVector (const std::vector< T > &input, FillMethod fill_method=automatic)
	fillFromInputVector takes some number of inputs to fill the Rank-3 tensor. More...
void	fillFromPlaneNormal (const VectorValue< T > &input)
	Fills RankThreeTensor from plane normal vectors ref. More...
RankFourTensorTempl< T >	mixedProductRankFour (const RankTwoTensorTempl< T > &a) const
	Creates fourth order tensor D_{ijkl}=A_{mij}*b_{mn}*A_{nkl} where A is rank 3 and b is rank 2. More...
VectorValue< T >	doubleContraction (const RankTwoTensorTempl< T > &b) const
	Creates a vector from the double contraction of a rank three and rank two tensor. More...

Static Public Member Functions
static MooseEnum	fillMethodEnum ()
	Static method for use in validParams for getting the "fill_method". More...

Protected Member Functions
void	fillGeneralFromInputVector (const std::vector< T > &input)

Protected Attributes
T	_vals [N3]
	The values of the rank-three tensor stored by index=((i * LIBMESH_DIM + j) * LIBMESH_DIM + k) More...

Static Protected Attributes
static constexpr unsigned int	N = LIBMESH_DIM
	Dimensionality of rank-three tensor. More...
static constexpr unsigned int	N2 = N * N
static constexpr unsigned int	N3 = N * N * N

Friends
template<class T2 >
class	RankTwoTensorTempl
template<class T2 >
class	RankThreeTensorTempl
template<class T2 >
class	RankFourTensorTempl
template<class T2 >
void	dataStore (std::ostream &, RankThreeTensorTempl< T2 > &, void *)
template<class T2 >
void	dataLoad (std::istream &, RankThreeTensorTempl< T2 > &, void *)

Detailed Description

template<typename T>
class RankThreeTensorTempl< T >

RankThreeTensor is designed to handle any N-dimensional third order tensor, r.

Definition at line 31 of file RankThreeTensor.h.

Member Enumeration Documentation

FillMethod

template<typename T>

enum RankThreeTensorTempl::FillMethod

To fill up the 27 entries in the 3rd-order tensor, fillFromInputVector is called with one of the following fill_methods.

See the fill*FromInputVector functions for more details

Enumerator
automatic
general
plane_normal

Definition at line 70 of file RankThreeTensor.h.

  {
    automatic,
    general,
    plane_normal
  };

InitMethod

template<typename T>

enum RankThreeTensorTempl::InitMethod

Initialization method.

Enumerator
initNone

Definition at line 60 of file RankThreeTensor.h.

  {
    initNone
  };

Constructor & Destructor Documentation

RankThreeTensorTempl() [1/4]

template<typename T >

RankThreeTensorTempl< T >::RankThreeTensorTempl

(

)

Default constructor; fills to zero.

Definition at line 54 of file RankThreeTensor.C.

{
  mooseAssert(N == 3, "RankThreeTensor is currently only tested for 3 dimensions.");

  for (unsigned int i = 0; i < N3; ++i)
    _vals[i] = 0;
}

RankThreeTensorTempl() [2/4]

template<typename T >

template<typename T2 >

RankThreeTensorTempl< T >::RankThreeTensorTempl

(

const RankThreeTensorTempl< T2 > &

copy

)

Construct from other class template instantiation.

Definition at line 227 of file RankThreeTensor.h.

{
  for (unsigned int i = 0; i < N3; ++i)
    _vals[i] = copy._vals[i];
}

RankThreeTensorTempl() [3/4]

template<typename T >

RankThreeTensorTempl< T >::RankThreeTensorTempl

(

const InitMethod

init

)

Select specific initialization pattern.

Definition at line 63 of file RankThreeTensor.C.

{
  switch (init)
  {
    case initNone:
      break;

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

RankThreeTensorTempl() [4/4]

template<typename T>

RankThreeTensorTempl< T >::RankThreeTensorTempl	(	const std::vector< T > &	input,
		FillMethod	method = automatic
	)

Fill from vector.

Definition at line 76 of file RankThreeTensor.C.

{
  fillFromInputVector(input, fill_method);
}

Member Function Documentation

doubleContraction()

template<typename T>

VectorValue< T > RankThreeTensorTempl< T >::doubleContraction

(

const RankTwoTensorTempl< T > &

b

)

const

Creates a vector from the double contraction of a rank three and rank two tensor.

c_i = A_{ijk} * b_{jk}

Definition at line 363 of file RankThreeTensor.C.

{
  VectorValue<T> result;

  for (unsigned int i = 0; i < N; ++i)
    for (unsigned int j = 0; j < N2; ++j)
      result(i) += _vals[i * N2 + j] * b._coords[j];

  return result;
}

fillFromInputVector()

template<typename T>

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

fillFromInputVector takes some number of inputs to fill the Rank-3 tensor.

Parameters

input	the numbers that will be placed in the tensor
fill_method	this can be: general (use fillGeneralFromInputVector) more fill_methods to be implemented soon!

Definition at line 239 of file RankThreeTensor.C.

{
  zero();

  if (fill_method == automatic)
  {
    if (input.size() == 27)
      fill_method = general;
    else if (input.size() == 3)
      fill_method = plane_normal;
    else
      mooseError("Unsupported automatic fill method, use 27 values for 'general' and 3 for "
                 "'plane_normal', the supplied size was ",
                 input.size(),
                 ".");
  }

  if (fill_method == general)
    fillGeneralFromInputVector(input);

  else if (fill_method == plane_normal)
  {
    if (input.size() != 3)
      mooseError("To use fillFromPlaneNormal, your input must have size 3, the supplied size was ",
                 input.size(),
                 ".");
    fillFromPlaneNormal(VectorValue<T>(input[0], input[1], input[2]));
  }

  else
    // This is un-reachable unless a FillMethod is added and the if statement is not updated
    mooseError("fillFromInputVector called with unknown fill_method of ", fill_method);
}

fillFromPlaneNormal()

template<typename T>

void RankThreeTensorTempl< T >::fillFromPlaneNormal

(

const VectorValue< T > &

input

)

Fills RankThreeTensor from plane normal vectors ref.

Kuhl et. al. Int. J. Solids Struct. 38(2001) 2933-2952

Parameters

input

plane normal vector

Definition at line 275 of file RankThreeTensor.C.

{
  unsigned int index = 0;
  for (unsigned int i = 0; i < N; ++i)
  {
    const T a = input(i);
    for (unsigned int j = 0; j < N; ++j)
    {
      const T b = input(j);
      for (unsigned int k = 0; k < N; ++k)
      {
        const T c = input(k);
        T sum = 0;
        sum = -2 * a * b * c;
        if (i == j)
          sum += c;
        if (i == k)
          sum += b;
        _vals[index++] = sum / 2.0;
      }
    }
  }
}

fillGeneralFromInputVector()

template<typename T>

void RankThreeTensorTempl< T >::fillGeneralFromInputVector ( const std::vector< T > &  input )

protected

Definition at line 349 of file RankThreeTensor.C.

{
  if (input.size() != 27)
    mooseError(
        "To use fillGeneralFromInputVector, your input must have size 27, the supplied size was ",
        input.size(),
        ".");

  for (unsigned int i = 0; i < N3; ++i)
    _vals[i] = input[i];
}

fillMethodEnum()

template<typename T >

MooseEnum RankThreeTensorTempl< T >::fillMethodEnum ( )

static

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

Definition at line 48 of file RankThreeTensor.C.

{
  return MooseEnum("general plane_normal");
}

L2norm()

template<typename T >

T RankThreeTensorTempl< T >::L2norm

(

)

const

(r_ijk*r_ijk)

Definition at line 227 of file RankThreeTensor.C.

{
  T l2 = 0;

  for (unsigned int i = 0; i < N3; ++i)
    l2 += Utility::pow<2>(_vals[i]);

  return std::sqrt(l2);
}

mixedProductRankFour()

template<typename T>

RankFourTensorTempl< T > RankThreeTensorTempl< T >::mixedProductRankFour

(

const RankTwoTensorTempl< T > &

a

)

const

Creates fourth order tensor D_{ijkl}=A_{mij}*b_{mn}*A_{nkl} where A is rank 3 and b is rank 2.

Parameters

a	RankThreeTensor A in the equation above

Definition at line 301 of file RankThreeTensor.C.

{
  RankFourTensorTempl<T> result;

  unsigned int index = 0;
  for (unsigned int i = 0; i < N; ++i)
    for (unsigned int j = 0; j < N; ++j)
      for (unsigned int k = 0; k < N; ++k)
        for (unsigned int l = 0; l < N; ++l)
        {
          for (unsigned int m = 0; m < N; ++m)
            for (unsigned int n = 0; n < N; ++n)
              result._vals[index] += (*this)(m, i, j) * a(m, n) * (*this)(n, k, l);
          index++;
        }

  return result;
}

operator()() [1/2]

template<typename T>

T& RankThreeTensorTempl< T >::operator() ( unsigned int  i, unsigned int  j, unsigned int  k  )

inline

Gets the value for the index specified. Takes index = 0,1,2.

Definition at line 93 of file RankThreeTensor.h.

  {
    return _vals[((i * N + j) * N + k)];
  }

operator()() [2/2]

template<typename T>

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

inline

Gets the value for the index specified. Takes index = 0,1,2. Used for const.

Definition at line 99 of file RankThreeTensor.h.

  {
    return _vals[((i * N + j) * N + k)];
  }

operator*() [1/2]

template<typename T>

VectorValue< T > RankThreeTensorTempl< T >::operator*

(

const RankTwoTensorTempl< T > &

a

)

const

b_i = r_ijk * a_jk

Definition at line 109 of file RankThreeTensor.C.

{
  VectorValue<T> result;

  for (unsigned int i = 0; i < N; ++i)
  {
    T sum = 0;
    unsigned int i1 = i * N2;
    for (unsigned int j1 = 0; j1 < N2; j1 += N)
      for (unsigned int k = 0; k < N; ++k)
        sum += _vals[i1 + j1 + k] * a._coords[j1 + k];
    result(i) = sum;
  }

  return result;
}

operator*() [2/2]

template<typename T>

RankThreeTensorTempl< T > RankThreeTensorTempl< T >::operator*

(

const T

a

)

const

r_ijk*a

Definition at line 127 of file RankThreeTensor.C.

{
  RankThreeTensorTempl<T> result;

  for (unsigned int i = 0; i < N3; ++i)
    result._vals[i] = _vals[i] * b;

  return result;
}

operator*=()

template<typename T>

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

(

const T

a

)

r_ijk *= a

Definition at line 139 of file RankThreeTensor.C.

{
  for (unsigned int i = 0; i < N3; ++i)
    _vals[i] *= a;

  return *this;
}

operator+()

template<typename T>

RankThreeTensorTempl< T > RankThreeTensorTempl< T >::operator+

(

const RankThreeTensorTempl< T > &

a

)

const

r_ijkl + a_ijk

Definition at line 181 of file RankThreeTensor.C.

{
  RankThreeTensorTempl<T> result;

  for (unsigned int i = 0; i < N3; ++i)
    result._vals[i] = _vals[i] + b._vals[i];

  return result;
}

operator+=()

template<typename T>

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

(

const RankThreeTensorTempl< T > &

a

)

r_ijk += a_ijk for all i, j, k

Definition at line 171 of file RankThreeTensor.C.

{
  for (unsigned int i = 0; i < N3; ++i)
    _vals[i] += a._vals[i];

  return *this;
}

operator-() [1/2]

template<typename T>

RankThreeTensorTempl< T > RankThreeTensorTempl< T >::operator-

(

const RankThreeTensorTempl< T > &

a

)

const

r_ijk - a_ijk

Definition at line 203 of file RankThreeTensor.C.

{
  RankThreeTensorTempl<T> result;

  for (unsigned int i = 0; i < N3; ++i)
    result._vals[i] = _vals[i] - b._vals[i];

  return result;
}

operator-() [2/2]

template<typename T>

RankThreeTensorTempl< T > RankThreeTensorTempl< T >::operator-

(

)

const

-r_ijk

Definition at line 215 of file RankThreeTensor.C.

{
  RankThreeTensorTempl<T> result;

  for (unsigned int i = 0; i < N3; ++i)
    result._vals[i] = -_vals[i];

  return result;
}

operator-=()

template<typename T>

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

(

const RankThreeTensorTempl< T > &

a

)

r_ijk -= a_ijk

Definition at line 193 of file RankThreeTensor.C.

{
  for (unsigned int i = 0; i < N3; ++i)
    _vals[i] -= a._vals[i];

  return *this;
}

operator/()

template<typename T>

RankThreeTensorTempl< T > RankThreeTensorTempl< T >::operator/

(

const T

a

)

const

r_ijk/a

Definition at line 149 of file RankThreeTensor.C.

{
  RankThreeTensorTempl<T> result;

  for (unsigned int i = 0; i < N3; ++i)
    result._vals[i] = _vals[i] / b;

  return result;
}

operator/=()

template<typename T>

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

(

const T

a

)

r_ijk /= a for all i, j, k

Definition at line 161 of file RankThreeTensor.C.

{
  for (unsigned int i = 0; i < N3; ++i)
    _vals[i] /= a;

  return *this;
}

operator=() [1/2]

template<typename T>

RankThreeTensorTempl< T > & RankThreeTensorTempl< T >::operator=

(

const T &

value

)

Assignment-from-scalar operator.

Definition at line 91 of file RankThreeTensor.C.

{
  for (unsigned int i = 0; i < N3; ++i)
    _vals[i] = value;
  return *this;
}

operator=() [2/2]

template<typename T>

RankThreeTensorTempl< T > & RankThreeTensorTempl< T >::operator=

(

const RankThreeTensorTempl< T > &

a

)

copies values from "a" into this tensor

Definition at line 100 of file RankThreeTensor.C.

{
  for (unsigned int i = 0; i < N3; ++i)
    _vals[i] = a._vals[i];

  return *this;
}

print()

template<typename T >

void RankThreeTensorTempl< T >::print

(

std::ostream &

stm = Moose::out

)

const

Print the rank three tensor.

Definition at line 376 of file RankThreeTensor.C.

{
  for (unsigned int i = 0; i < N; ++i)
  {
    stm << "a(" << i << ", j, k) = \n";
    for (unsigned int j = 0; j < N; ++j)
    {
      for (unsigned int k = 0; k < N; ++k)
        stm << std::setw(15) << (*this)(i, j, k) << ' ';
      stm << "\n";
    }
    stm << "\n";
  }
}

rotate() [1/2]

template<typename T >

template<class T2 >

void RankThreeTensorTempl< T >::rotate

(

const T2 &

R

)

Rotate the tensor using r_ijk = R_im R_in R_ko r_mno.

Definition at line 236 of file RankThreeTensor.h.

{
  unsigned int index = 0;
  for (unsigned int i = 0; i < N; ++i)
    for (unsigned int j = 0; j < N; ++j)
      for (unsigned int k = 0; k < N; ++k)
      {
        unsigned int index2 = 0;
        T sum = 0.0;
        for (unsigned int m = 0; m < N; ++m)
        {
          T a = R(i, m);
          for (unsigned int n = 0; n < N; ++n)
          {
            T ab = a * R(j, n);
            for (unsigned int o = 0; o < N; ++o)
              sum += ab * R(k, o) * _vals[index2++];
          }
        }
        _vals[index++] = sum;
      }
}

rotate() [2/2]

template<typename T>

void RankThreeTensorTempl< T >::rotate

(

const TensorValue< T > &

R

)

Rotate the tensor using r_ijk = R_im R_in R_ko r_mno.

Definition at line 322 of file RankThreeTensor.C.

{
  RankThreeTensorTempl<T> old = *this;

  unsigned int index = 0;
  for (unsigned int i = 0; i < N; ++i)
    for (unsigned int j = 0; j < N; ++j)
      for (unsigned int k = 0; k < N; ++k)
      {
        T sum = 0.0;
        unsigned int index2 = 0;
        for (unsigned int m = 0; m < N; ++m)
        {
          T a = R(i, m);
          for (unsigned int n = 0; n < N; ++n)
          {
            T ab = a * R(j, n);
            for (unsigned int o = 0; o < N; ++o)
              sum += ab * R(k, o) * old._vals[index2++];
          }
        }
        _vals[index++] = sum;
      }
}

zero()

template<typename T >

void RankThreeTensorTempl< T >::zero

(

)

Zeros out the tensor.

Definition at line 83 of file RankThreeTensor.C.

{
  for (unsigned int i = 0; i < N3; ++i)
    _vals[i] = 0;
}

Friends And Related Function Documentation

dataLoad

template<typename T>

template<class T2 >

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

friend

dataStore

template<typename T>

template<class T2 >

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

friend

RankFourTensorTempl

template<typename T>

template<class T2 >

friend class RankFourTensorTempl

friend

Definition at line 219 of file RankThreeTensor.h.

RankThreeTensorTempl

template<typename T>

template<class T2 >

friend class RankThreeTensorTempl

friend

Definition at line 216 of file RankThreeTensor.h.

RankTwoTensorTempl

template<typename T>

template<class T2 >

friend class RankTwoTensorTempl

friend

Definition at line 213 of file RankThreeTensor.h.

Member Data Documentation

_vals

template<typename T>

T RankThreeTensorTempl< T >::_vals[N3]

protected

The values of the rank-three tensor stored by index=((i * LIBMESH_DIM + j) * LIBMESH_DIM + k)

Definition at line 202 of file RankThreeTensor.h.

Referenced by dataLoad(), dataStore(), RankThreeTensorTempl< Real >::operator()(), RankThreeTensorTempl< Real >::operator*(), RankFourTensorTempl< Real >::operator*(), RankThreeTensorTempl< Real >::operator+(), RankThreeTensorTempl< Real >::operator+=(), RankThreeTensorTempl< Real >::operator-(), RankThreeTensorTempl< Real >::operator-=(), RankThreeTensorTempl< Real >::operator/(), RankFourTensorTempl< Real >::operator/(), RankThreeTensorTempl< Real >::operator=(), RankFourTensorTempl< Real >::RankFourTensorTempl(), RankThreeTensorTempl< Real >::RankThreeTensorTempl(), and RankThreeTensorTempl< Real >::rotate().

N

template<typename T>

constexpr unsigned int RankThreeTensorTempl< T >::N = LIBMESH_DIM

staticprotected

Dimensionality of rank-three tensor.

Definition at line 197 of file RankThreeTensor.h.

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

N2

template<typename T>

constexpr unsigned int RankThreeTensorTempl< T >::N2 = N * N

staticprotected

Definition at line 198 of file RankThreeTensor.h.

N3

template<typename T>

constexpr unsigned int RankThreeTensorTempl< T >::N3 = N * N * N

staticprotected

Definition at line 199 of file RankThreeTensor.h.

---

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

• include/utils/RankThreeTensor.h
• src/utils/RankThreeTensor.C