Defines an Isotropic Elasticity Tensor. More...

#include <AnisotropicElasticityTensor.h>

Inheritance diagram for AnisotropicElasticityTensor:

Public Member Functions
	AnisotropicElasticityTensor ()

virtual	~AnisotropicElasticityTensor ()

void	setFirstEulerAngle (const Real a1)
	Set the first euler angle. More...

void	setSecondEulerAngle (const Real a2)
	Set the second euler angle. More...

void	setThirdEulerAngle (const Real a3)
	Set the third euler angle. More...

void	setMaterialConstantc11 (const Real c11)
	Set the material constant c11. More...

void	setMaterialConstantc12 (const Real c12)
	Set the material constant c22. More...

void	setMaterialConstantc44 (const Real c44)
	Set the material constant c44. More...

void	calculate (unsigned int qp)
	Public function that will be called whenever the values for this matrix need to be filled in. More...

virtual ColumnMajorMatrix	calculateDerivative (unsigned int qp, unsigned int i)

Protected Member Functions
virtual void	calculateEntries (unsigned int qp)
	Fill in the matrix. More...

Protected Attributes
std::vector< Real >	_euler_angle

Real	_c11

Real	_c12

Real	_c44

bool	_constant
	Whether or not the matrix is constant for all of time and space. More...

bool	_values_computed
	Whether or not the values have been computed once. More...

Detailed Description

Defines an Isotropic Elasticity Tensor.

The input is any two of the following:

Youngs Modulus Poissons Ration First and Second Lame Coefficients (lambda and mu) Bulk Modulus

Internally this class uses the Lame Coefficients. Everything is is transformed to these coefficients.

Note that by default this tensor is constant... meaning that it never changes after the first time it is computed.

If you want to modify this behavior you can pass in false to the constructor.

Definition at line 37 of file AnisotropicElasticityTensor.h.

Constructor & Destructor Documentation

◆ AnisotropicElasticityTensor()

AnisotropicElasticityTensor::AnisotropicElasticityTensor ( )

Definition at line 12 of file AnisotropicElasticityTensor.C.

   : ElasticityTensor(false), _euler_angle(3), _c11(0), _c12(0), _c44(0)
 {
 }

◆ ~AnisotropicElasticityTensor()

virtual AnisotropicElasticityTensor::~AnisotropicElasticityTensor ( )

inlinevirtual

Definition at line 42 of file AnisotropicElasticityTensor.h.

42 {}

Member Function Documentation

◆ calculate()

void ElasticityTensor::calculate ( unsigned int qp )

inherited

Public function that will be called whenever the values for this matrix need to be filled in.

Definition at line 18 of file ElasticityTensor.C.

 {
   if (!_constant || !_values_computed)
   {
     calculateEntries(qp);
     _values_computed = true;
   }
 }

◆ calculateDerivative()

ColumnMajorMatrix ElasticityTensor::calculateDerivative	(	unsigned int	qp,
		unsigned int	i
	)

virtualinherited

Definition at line 28 of file ElasticityTensor.C.

 {
   ColumnMajorMatrix m(9, 9);
   return m;
 }

◆ calculateEntries()

void AnisotropicElasticityTensor::calculateEntries ( unsigned int qp )

protectedvirtual

Fill in the matrix.

Implements ElasticityTensor.

Definition at line 54 of file AnisotropicElasticityTensor.C.

 {
  
   // form_r_matrix();
   // Form rotation matrix from Euler angles
   const Real phi1 = _euler_angle[0] * (M_PI / 180.0);
   const Real phi = _euler_angle[1] * (M_PI / 180.0);
   const Real phi2 = _euler_angle[2] * (M_PI / 180.0);
  
   Real cp1 = cos(phi1);
   Real cp2 = cos(phi2);
   Real cp = cos(phi);
  
   Real sp1 = sin(phi1);
   Real sp2 = sin(phi2);
   Real sp = sin(phi);
  
   DenseMatrix<Real> R; // Rotational Matrix
   R(0, 0) = cp1 * cp2 - sp1 * sp2 * cp;
   R(0, 1) = sp1 * cp2 + cp1 * sp2 * cp;
   R(0, 2) = sp2 * sp;
   R(1, 0) = -cp1 * sp2 - sp1 * cp2 * cp;
   R(1, 1) = -sp1 * sp2 + cp1 * cp2 * cp;
   R(1, 2) = cp2 * sp;
   R(2, 0) = sp1 * sp;
   R(2, 1) = -cp1 * sp;
   R(2, 2) = cp;
  
   // Initialize material Dt matrix
   DenseMatrix<Real> Dt; // 6 x 6 Material Matrix
   Dt(0, 0) = Dt(1, 1) = Dt(2, 2) = _c11;
   Dt(0, 1) = Dt(0, 2) = Dt(1, 0) = Dt(2, 0) = Dt(1, 2) = Dt(2, 1) = _c12;
   Dt(3, 3) = Dt(4, 4) = Dt(5, 5) = 2 * _c44;
  
   // Form Q = R dyadic R and Q transpose
   DenseMatrix<Real> Q, Qt; // Q = R (dyadic) R and Q transpose
   for (unsigned int i = 0; i < 3; i++)
     for (unsigned int j = 0; j < 3; j++)
       for (unsigned int k = 0; k < 3; k++)
         for (unsigned int l = 0; l < 3; l++)
           Q(((i * 3) + k), ((j * 3) + l)) = R(i, j) * R(k, l);
  
   for (unsigned int p = 0; p < 9; p++)
     for (unsigned int q = 0; q < 9; q++)
       Qt(q, p) = Q(p, q);
  
   // Form two kinds of transformation matrix
   // TransD6toD9 transfroms Dt[6][6] to Dmat[9][9]
   // TransD9toD6 transforms Dmat[9][9] to Dt[6][6]
   DenseMatrix<Real> trans_d6_to_d9, transpose_trans_d6_to_d9;
   DenseMatrix<Real> trans_d9_to_d6, transpose_trans_d9_to_d6;
   Real sqrt2 = std::sqrt(2.0);
   Real a = 1 / sqrt2;
  
   trans_d6_to_d9(0, 0) = trans_d6_to_d9(4, 1) = trans_d6_to_d9(8, 2) = 1.0;
   trans_d6_to_d9(1, 3) = trans_d6_to_d9(3, 3) = a;
   trans_d6_to_d9(2, 4) = trans_d6_to_d9(6, 4) = a;
   trans_d6_to_d9(5, 5) = trans_d6_to_d9(7, 5) = a;
  
   for (unsigned int i = 0; i < 9; i++)
     for (unsigned int j = 0; j < 6; j++)
       transpose_trans_d6_to_d9(j, i) = trans_d6_to_d9(i, j);
  
   trans_d9_to_d6(0, 0) = trans_d9_to_d6(1, 4) = trans_d9_to_d6(2, 8) = 1.0;
   trans_d9_to_d6(3, 3) = trans_d9_to_d6(4, 6) = trans_d9_to_d6(5, 7) = sqrt2;
  
   for (unsigned int i = 0; i < 6; i++)
     for (unsigned int j = 0; j < 9; j++)
       transpose_trans_d9_to_d6(j, i) = trans_d9_to_d6(i, j);
  
   // The function makes use of TransD6toD9 matrix to transfrom Dt[6][6] to Dmat[9][9]
   // Dmat = T * Dt * TT
  
   DenseMatrix<Real> outputMatrix(9, 6);
  
   outputMatrix = trans_d6_to_d9;
   outputMatrix.right_multiply(Dt);
  
   DenseMatrix<Real> Dmat; // 9 x 9 Material Matrix
   Dmat = outputMatrix;
   Dmat.right_multiply(transpose_trans_d6_to_d9);
  
   // The function makes use of Q matrix to rotate Dmat[9][9] to QDmat[9][9]
   // QDmat = QT * Dmat * Q
  
   DenseMatrix<Real> outputMatrix99(9, 9);
  
   outputMatrix99 = Qt;
   outputMatrix99.right_multiply(Dmat);
  
   DenseMatrix<Real> QDmat; // Rotated Material Matrix
   QDmat = outputMatrix99;
   QDmat.right_multiply(Q);
  
   // Convert 9X9 matrix QDmat to 81 vector
  
   unsigned int count = 0;
  
   for (unsigned int j = 0; j < 9; j++)
     for (unsigned int i = 0; i < 9; i++)
     {
       _values[count] = QDmat(i, j);
       count = count + 1;
     }
 }