Chaste Commit::baa90ac2819b962188b7562f2326be23c47859a7
AbstractIsotropicIncompressibleMaterialLaw.cpp
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34*/
35
36#include "AbstractIsotropicIncompressibleMaterialLaw.hpp"
37
38template<unsigned DIM>
42
43template<unsigned DIM>
45 c_matrix<double,DIM,DIM>& rC,
46 c_matrix<double,DIM,DIM>& rInvC,
47 double pressure,
48 c_matrix<double,DIM,DIM>& rT,
50 bool computeDTdE)
51{
52 assert((DIM==2) || (DIM==3)); // LCOV_EXCL_LINE
53
54 static c_matrix<double,DIM,DIM> identity = identity_matrix<double>(DIM);
55
56 double I1 = Trace(rC);
57 double I2 = SecondInvariant(rC);
58
59 double w1 = Get_dW_dI1(I1, I2);
60 double w2; // only computed if DIM==3
61
62 // Compute stress: **** See FiniteElementImplementations document. ****
63 //
64 // T = dW_dE
65 // = 2 * w1 * dI1_dC_MN + 2 * w2 * dI1_dC_MN - p * invC
66 // = 2 * w1 * delta_MN + 2 * w2 * (I1 delta_MN - C_MN) - p * invC
67 //
68 // (where w1 = dW/dI1, etc).
69
70 rT = 2*w1*identity - pressure*rInvC;
71 if (DIM==3)
72 {
73 w2 = Get_dW_dI2(I1, I2);
74 rT += 2*w2*(I1*identity - rC);
75 }
76
77 // Compute stress derivative if required: **** See FiniteElementImplementations document. ****
78 //
79 // The stress derivative dT_{MN}/dE_{PQ} is
80 //
81 // dT_dE = 4 * w11 * dI1_dC_MN * dI1_dC_PQ
82 // + 4 * w1 * d2I1_dC2
83 // + 4 * w22 * dI2_dC_MN * dI2_dC_PQ
84 // + 4 * w2 * d2I2_dC2
85 // + 4 * w12 * (dI1_dC_MN*dI2_dC_PQ + dI1_dC_PQ*dI2_dC_MN)
86 // - 2 * pressure * d_invC_dC;
87 //
88 // where
89 // dI1_dC_MN = (M==N); // ie delta_{MN}
90 // dI1_dC_PQ = (P==Q);
91 // d2I1_dC2 = 0;
92 //
93 // dI2_dC_MN = I1*(M==N)-C[M][N];
94 // dI2_dC_PQ = I1*(P==Q)-C[P][Q];
95 // d2I2_dC2 = (M==N)*(P==Q)-(M==P)*(N==Q);
96 //
97 // d_invC_dC = -invC[M][P]*invC[Q][N];
98 //
99 if (computeDTdE)
100 {
101 double w11 = Get_d2W_dI1(I1,I2);
102
103 double w12;
104 double w22;
105
106 if (DIM==3)
107 {
108 w22 = Get_d2W_dI2(I1, I2);
109 w12 = Get_d2W_dI1I2(I1, I2);
110 }
111
112 for (unsigned M=0; M<DIM; M++)
113 {
114 for (unsigned N=0; N<DIM; N++)
115 {
116 for (unsigned P=0; P<DIM; P++)
117 {
118 for (unsigned Q=0; Q<DIM; Q++)
119 {
120 rDTdE(M,N,P,Q) = 4 * w11 * (M==N) * (P==Q)
121 + 2 * pressure * rInvC(M,P) * rInvC(Q,N);
122
123 if (DIM==3)
124 {
125 rDTdE(M,N,P,Q) += 4 * w22 * (I1*(M==N) - rC(M,N)) * (I1*(P==Q) - rC(P,Q))
126 + 4 * w2 * ((M==N)*(P==Q) - (M==P)*(N==Q))
127 + 4 * w12 * ((M==N)*(I1*(P==Q) - rC(P,Q)) + (P==Q)*(I1*(M==N) - rC(M,N)));
128 }
129 }
130 }
131 }
133 }
134}
135
136template <unsigned DIM>
138{
139 if constexpr (DIM == 2)
140 {
141 return 2 * Get_dW_dI1(2, 0);
143 else if constexpr (DIM == 3)
144 {
145 return 2 * Get_dW_dI1(3, 3) + 4 * Get_dW_dI2(3, 3);
146 }
147 else
148 {
150 }
152
153// Explicit instantiation
#define NEVER_REACHED
T SecondInvariant(const c_matrix< T, 3, 3 > &rM)
T Trace(const c_matrix< T, 1, 1 > &rM)
void ComputeStressAndStressDerivative(c_matrix< double, DIM, DIM > &rC, c_matrix< double, DIM, DIM > &rInvC, double pressure, c_matrix< double, DIM, DIM > &rT, FourthOrderTensor< DIM, DIM, DIM, DIM > &rDTdE, bool computeDTdE)