Chaste  Release::2018.1
AbstractMaterialLaw.cpp
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35 
36 #include "AbstractMaterialLaw.hpp"
37 
38 template<unsigned DIM>
40  : mpChangeOfBasisMatrix(nullptr)
41 {
42 }
43 
44 template<unsigned DIM>
45 void AbstractMaterialLaw<DIM>::ComputeCauchyStress(c_matrix<double,DIM,DIM>& rF,
46  double pressure,
47  c_matrix<double,DIM,DIM>& rSigma)
48 {
49  double detF = Determinant(rF);
50 
51  c_matrix<double,DIM,DIM> C = prod(trans(rF), rF);
52  c_matrix<double,DIM,DIM> invC = Inverse(C);
53 
54  c_matrix<double,DIM,DIM> T;
55 
56  static FourthOrderTensor<DIM,DIM,DIM,DIM> dTdE; // not filled in, made static for efficiency
57 
58  ComputeStressAndStressDerivative(C, invC, pressure, T, dTdE, false);
59 
60  /*
61  * Looping is probably more eficient then doing rSigma = (1/detF)*rF*T*transpose(rF),
62  * which doesn't seem to compile anyway, as rF is a Tensor<2,DIM> and T is a
63  * SymmetricTensor<2,DIM>.
64  */
65  for (unsigned i=0; i<DIM; i++)
66  {
67  for (unsigned j=0; j<DIM; j++)
68  {
69  rSigma(i,j) = 0.0;
70  for (unsigned M=0; M<DIM; M++)
71  {
72  for (unsigned N=0; N<DIM; N++)
73  {
74  rSigma(i,j) += rF(i,M)*T(M,N)*rF(j,N);
75  }
76  }
77  rSigma(i,j) /= detF;
78  }
79  }
80 }
81 
82 template<unsigned DIM>
84  double pressure,
85  c_matrix<double,DIM,DIM>& rS)
86 {
87  c_matrix<double,DIM,DIM> C = prod(trans(rF), rF);
88  c_matrix<double,DIM,DIM> invC = Inverse(C);
89 
90  c_matrix<double,DIM,DIM> T;
91 
92  static FourthOrderTensor<DIM,DIM,DIM,DIM> dTdE; // not filled in, made static for efficiency
93 
94  ComputeStressAndStressDerivative(C, invC, pressure, T, dTdE, false);
95 
96  rS = prod(T, trans(rF));
97 }
98 
99 template<unsigned DIM>
101  double pressure,
102  c_matrix<double,DIM,DIM>& rT)
103 {
104  c_matrix<double,DIM,DIM> invC = Inverse(rC);
105 
106  static FourthOrderTensor<DIM,DIM,DIM,DIM> dTdE; // not filled in, made static for efficiency
107 
108  ComputeStressAndStressDerivative(rC, invC, pressure, rT, dTdE, false);
109 }
110 
111 // LCOV_EXCL_START
112 template<unsigned DIM>
114 {
115  EXCEPTION("[the material law you are using]::ScaleMaterialParameters() has not been implemented\n");
116 }
117 // LCOV_EXCL_STOP
118 
119 template<unsigned DIM>
120 void AbstractMaterialLaw<DIM>::SetChangeOfBasisMatrix(c_matrix<double,DIM,DIM>& rChangeOfBasisMatrix)
121 {
122  mpChangeOfBasisMatrix = &rChangeOfBasisMatrix;
123 }
124 
125 template<unsigned DIM>
127 {
128  mpChangeOfBasisMatrix = nullptr;
129 }
130 
131 template<unsigned DIM>
132 void AbstractMaterialLaw<DIM>::ComputeTransformedDeformationTensor(c_matrix<double,DIM,DIM>& rC, c_matrix<double,DIM,DIM>& rInvC,
133  c_matrix<double,DIM,DIM>& rCTransformed, c_matrix<double,DIM,DIM>& rInvCTransformed)
134 {
135  // Writing the local coordinate system as fibre/sheet/normal, as in cardiac problems..
136 
137  // Let P be the change-of-basis matrix P = (\mathbf{m}_f, \mathbf{m}_s, \mathbf{m}_n).
138  // The transformed C for the fibre/sheet basis is C* = P^T C P.
139  if (mpChangeOfBasisMatrix)
140  {
141  // C* = P^T C P, and ditto inv(C)
142  rCTransformed = prod(trans(*mpChangeOfBasisMatrix),(c_matrix<double,DIM,DIM>)prod(rC,*mpChangeOfBasisMatrix)); // C* = P^T C P
143  rInvCTransformed = prod(trans(*mpChangeOfBasisMatrix),(c_matrix<double,DIM,DIM>)prod(rInvC,*mpChangeOfBasisMatrix)); // invC* = P^T invC P
144  }
145  else
146  {
147  rCTransformed = rC;
148  rInvCTransformed = rInvC;
149  }
150 }
151 
152 template<unsigned DIM>
155  bool transformDTdE)
156 {
157  // T = P T* P^T and dTdE_{MNPQ} = P_{Mm}P_{Nn}P_{Pp}P_{Qq} dT*dE*_{mnpq}
158  if (mpChangeOfBasisMatrix)
159  {
160  static c_matrix<double,DIM,DIM> T_transformed_times_Ptrans;
161  T_transformed_times_Ptrans = prod(rT, trans(*mpChangeOfBasisMatrix));
162 
163  rT = prod(*mpChangeOfBasisMatrix, T_transformed_times_Ptrans); // T = P T* P^T
164 
165  // dTdE_{MNPQ} = P_{Mm}P_{Nn}P_{Pp}P_{Qq} dT*dE*_{mnpq}
166  if (transformDTdE)
167  {
169  temp.template SetAsContractionOnFirstDimension<DIM>(*mpChangeOfBasisMatrix, rDTdE);
170  rDTdE.template SetAsContractionOnSecondDimension<DIM>(*mpChangeOfBasisMatrix, temp);
171  temp.template SetAsContractionOnThirdDimension<DIM>(*mpChangeOfBasisMatrix, rDTdE);
172  rDTdE.template SetAsContractionOnFourthDimension<DIM>(*mpChangeOfBasisMatrix, temp);
173  }
174  }
175 }
176 
177 // Explicit instantiation
178 template class AbstractMaterialLaw<2>;
179 template class AbstractMaterialLaw<3>;
void TransformStressAndStressDerivative(c_matrix< double, DIM, DIM > &rT, FourthOrderTensor< DIM, DIM, DIM, DIM > &rDTdE, bool transformDTdE)
boost::numeric::ublas::c_matrix< T, 1, 1 > Inverse(const boost::numeric::ublas::c_matrix< T, 1, 1 > &rM)
#define EXCEPTION(message)
Definition: Exception.hpp:143
T Determinant(const boost::numeric::ublas::c_matrix< T, 1, 1 > &rM)
void ComputeCauchyStress(c_matrix< double, DIM, DIM > &rF, double pressure, c_matrix< double, DIM, DIM > &rSigma)
void Compute1stPiolaKirchoffStress(c_matrix< double, DIM, DIM > &rF, double pressure, c_matrix< double, DIM, DIM > &rS)
void ComputeTransformedDeformationTensor(c_matrix< double, DIM, DIM > &rC, c_matrix< double, DIM, DIM > &rInvC, c_matrix< double, DIM, DIM > &rCTransformed, c_matrix< double, DIM, DIM > &rInvCTransformed)
void Compute2ndPiolaKirchoffStress(c_matrix< double, DIM, DIM > &rC, double pressure, c_matrix< double, DIM, DIM > &rT)
void SetChangeOfBasisMatrix(c_matrix< double, DIM, DIM > &rChangeOfBasisMatrix)
virtual void ScaleMaterialParameters(double scaleFactor)