MoFEM::Tensor2SymmetricDeviatorBasis Struct Reference

#include "src/finite_elements/UserDataOperators.hpp"

Static Public Member Functions
static const FTensor::Dg< double, 3, 5 > &	getBasis ()
	Basis columns (11-22)/sqrt(2), (11+22-2*33)/sqrt(6), 12, 13, 23.
template<typename T , int Size>
static FTensor::Tensor2_symmetric< double, 3 >	getTensor (const FTensor::Tensor1< T, Size > &t_coordinates, const double theta=0.)
	Reconstruct D + theta*I/3; input may be an owning tensor or a view.
template<typename Tensor >
static FTensor::Tensor1< double, 5 >	getCoordinates (const Tensor &t_tensor)
	Project a full or symmetric tensor onto the five orthonormal columns.

Detailed Description

Orthonormal coordinates for three-dimensional symmetric deviators. Three coordinates retain the planar E1, E2, E3 subspace; five span all symmetric trace-free tensors. Both reconstructions return a 3x3 tensor.

Definition at line 1366 of file UserDataOperators.hpp.

Member Function Documentation

getBasis()

static const FTensor::Dg< double, 3, 5 > & MoFEM::Tensor2SymmetricDeviatorBasis::getBasis ( )

inlinestatic

Basis columns (11-22)/sqrt(2), (11+22-2*33)/sqrt(6), 12, 13, 23.

Definition at line 1368 of file UserDataOperators.hpp.

                                                   {
    static const auto t_basis = [] {
      FTENSOR_INDEXES(3, i, j);
      FTensor::Index<'A', 5> A;
      FTensor::Dg<double, 3, 5> t_basis;
      t_basis(i, j, A) = 0.;
      constexpr double inverse_sqrt_two = 0.70710678118654752440;
      constexpr double inverse_sqrt_six = 0.40824829046386301637;
      t_basis(0, 0, 0) = inverse_sqrt_two;
      t_basis(1, 1, 0) = -inverse_sqrt_two;
      t_basis(0, 0, 1) = inverse_sqrt_six;
      t_basis(1, 1, 1) = inverse_sqrt_six;
      t_basis(2, 2, 1) = -2. * inverse_sqrt_six;
      t_basis(0, 1, 2) = inverse_sqrt_two;
      t_basis(0, 2, 3) = inverse_sqrt_two;
      t_basis(1, 2, 4) = inverse_sqrt_two;
      return t_basis;
    }();
    return t_basis;
  }

getCoordinates()

template<typename Tensor >

static FTensor::Tensor1< double, 5 > MoFEM::Tensor2SymmetricDeviatorBasis::getCoordinates ( const Tensor &  t_tensor )

inlinestatic

Project a full or symmetric tensor onto the five orthonormal columns.

Definition at line 1407 of file UserDataOperators.hpp.

                                                                          {
    FTENSOR_INDEXES(3, i, j);
    FTensor::Index<'A', 5> A;
    const auto &t_basis = getBasis();
    FTensor::Tensor1<double, 5> t_coordinates;
    t_coordinates(A) = t_basis(i, j, A) * t_tensor(i, j);
    return t_coordinates;
  }

getTensor()

template<typename T , int Size>

static FTensor::Tensor2_symmetric< double, 3 > MoFEM::Tensor2SymmetricDeviatorBasis::getTensor ( const FTensor::Tensor1< T, Size > &  t_coordinates, const double  theta = 0.  )

inlinestatic

Reconstruct D + theta*I/3; input may be an owning tensor or a view.

Definition at line 1392 of file UserDataOperators.hpp.

                                     {
    static_assert(Size == 3 || Size == 5, "Expected three or five coordinates");
    FTENSOR_INDEXES(3, i, j);
    FTensor::Index<'A', Size> A;
    constexpr auto t_identity = FTensor::Kronecker_Delta_symmetric<int>();
    const auto &t_basis = getBasis();
    FTensor::Tensor2_symmetric<double, 3> t_tensor;
    t_tensor(i, j) =
        t_basis(i, j, A) * t_coordinates(A) + (theta / 3.) * t_identity(i, j);
    return t_tensor;
  }

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The documentation for this struct was generated from the following file:

• src/finite_elements/UserDataOperators.hpp