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mooney_cc.C
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#include "mooney_cc.h"
#include "defines.h"
#include <math.h>
#include "poro_elastic_cc.h"
#if MOONEY
void MooneyCurrentConfig::init_for_qp(VectorValue<Gradient> & grad_u, Number & p_current, unsigned int qp) {
this->current_qp = qp;
#if INCOMPRESSIBLE
//this->p_current = p_current;
this->p_solid = p_current;
#endif
F.zero();
S.zero();
{
RealTensor invF;
invF.zero();
for (unsigned int i = 0; i < 3; ++i)
for (unsigned int j = 0; j < 3; ++j) {
#if MOVING_MESH
invF(i, j) += grad_u(i)(j);
#endif
#if FIXED_MESH
F(i, j) += grad_u(i)(j);
#endif
//std::cout << "invF " << invF<< std::endl;
}
#if MOVING_MESH
F.add(inv(invF));
#endif
}
if (F.det() < -TOLERANCE) {
std::cout << "detF < 0" << std::endl;
libmesh_error();
}
this->Ft = F.transpose();
this->C = Ft*F;
this->c_update(C);
if (this->calculate_linearized_stiffness) {
this->calculate_tangent();
}
this->calculate_stress();
}
void MooneyCurrentConfig::init_for_qp(VectorValue<Gradient> & grad_u, Number & p_current, unsigned int qp, Real m) {
this->current_qp = qp;
this->m = m;
#if INCOMPRESSIBLE
//this->p_current = p_current;
this->p_solid = p_current;
#endif
F.zero();
S.zero();
{
RealTensor invF;
invF.zero();
for (unsigned int i = 0; i < 3; ++i)
for (unsigned int j = 0; j < 3; ++j) {
#if MOVING_MESH
invF(i, j) += grad_u(i)(j);
#endif
#if FIXED_MESH
F(i, j) += grad_u(i)(j);
#endif
//std::cout << "invF " << invF<< std::endl;
}
#if MOVING_MESH
F.add(inv(invF));
#endif
}
if (F.det() < -TOLERANCE) {
std::cout << "detF < 0" << std::endl;
libmesh_error();
}
this->Ft = F.transpose();
this->C = Ft*F;
this->c_update(C);
if (this->calculate_linearized_stiffness) {
this->calculate_tangent();
}
this->calculate_stress();
}
void MooneyCurrentConfig::calculate_tangent() {
Real mu = E / (2 * (1 + nu));
Real lambda = E * nu / ((1 + nu) * (1 - 2 * nu));
Real detF = F.det();
C_mat.resize(6, 6);
/*
#if COMPRESSIBLE
for (unsigned int i = 0; i < 3; ++i) {
for (unsigned int j = 0; j < 3; ++j) {
if (i == j) {
C_mat(i, j) = 2 * mu + lambda;
C_mat(i + 3, j + 3) = mu - 0.5 * lambda * (detF * detF - 1);
} else {
C_mat(i, j) = lambda * detF * detF;
}
}
}
#endif
*/
#if INCOMPRESSIBLE
Real fac=0.5*p_current*detF;
Real delta_a=fac*(1.0/2.0);
DenseMatrix<Real> invCinvC_mat;
invCinvC_mat.resize(6, 6);
tensorOtensor_to_voigt(Identity,Identity,invCinvC_mat);
invCinvC_mat.scale(delta_a);
C_mat+=invCinvC_mat;
Real delta_b=fac*(-1.0);
DenseMatrix<Real> Z_mat;
Z_mat.resize(6, 6);
z_ref_to_voigt(Identity,Identity,Z_mat);
Z_mat.scale(delta_b);
C_mat+=Z_mat;
#endif
Real delta_a=-2*K1*(1.0/3.0);
DenseMatrix<Real> ICinv_mat;
ICinv_mat.resize(6, 6);
tensorOtensor_to_voigt(b,Identity,ICinv_mat);
ICinv_mat.scale(delta_a*pow(I_3,(-1.0/3.0)));
C_mat+=ICinv_mat;
Real delta_b=2*K2;
DenseMatrix<Real> II_mat;
II_mat.resize(6, 6);
tensorOtensor_to_voigt(b,b,II_mat);
II_mat.scale(delta_b*pow(I_3,(-2.0/3.0)));
C_mat+=II_mat;
ICinv_mat.resize(6, 6);
tensorOtensor_to_voigt(b,Identity,ICinv_mat);
ICinv_mat.scale(-delta_b*(2.0/3.0)*I_1*pow(I_3,(-2.0/3.0)));
C_mat+=ICinv_mat;
Real delta_c=-2*K2;
DenseMatrix<Real> CinvC_mat;
CinvC_mat.resize(6, 6);
tensorOtensor_to_voigt(b*C,Identity,CinvC_mat);
CinvC_mat.scale(delta_c*(-2.0/3.0)*pow(I_3,(-2.0/3.0)));
C_mat+=CinvC_mat;
DenseMatrix<Real> I_mat;
I_mat.resize(6, 6);
z_ref_to_voigt(b,b,I_mat);
I_mat.scale(delta_c*pow(I_3,(-2.0/3.0)));
C_mat+=I_mat;
Real delta_d=-(2.0/3.0)*K1;
DenseMatrix<Real> invCI_mat;
invCI_mat.resize(6, 6);
tensorOtensor_to_voigt(Identity,b,invCI_mat);
invCI_mat.scale(delta_d*pow(I_3,(-1.0/3.0)));
C_mat+=invCI_mat;
DenseMatrix<Real> invCinvC_mat;
invCinvC_mat.resize(6, 6);
tensorOtensor_to_voigt(Identity,Identity,invCinvC_mat);
invCinvC_mat.scale(delta_d*(-1.0/3.0)*I_1*pow(I_3,(-1.0/3.0)));
C_mat+=invCinvC_mat;
DenseMatrix<Real> Z_mat;
Z_mat.resize(6, 6);
z_ref_to_voigt(Identity,Identity,Z_mat);
Z_mat.scale(delta_d*(-1.0)*I_1*pow(I_3,(-1.0/3.0)));
C_mat+=Z_mat;
Real delta_e=-(4.0/3.0)*K2;
invCI_mat.resize(6, 6);
tensorOtensor_to_voigt(Identity,b,invCI_mat);
invCI_mat.scale(delta_e*pow(I_3,(-2.0/3.0)));
C_mat+=invCI_mat;
invCinvC_mat.resize(6, 6);
tensorOtensor_to_voigt(Identity,Identity,invCinvC_mat);
invCinvC_mat.scale(delta_e*(-2.0/3.0)*I_1*pow(I_3,(-2.0/3.0)));
C_mat+=invCinvC_mat;
Z_mat.resize(6, 6);
z_ref_to_voigt(Identity,Identity,Z_mat);
Z_mat.scale(delta_e*(-1.0)*I_1*pow(I_3,(-2.0/3.0)));
C_mat+=Z_mat;
}
void MooneyCurrentConfig::calculate_stress() {
double mu = E / (2.0 * (1.0 + nu));
double lambda = E * nu / ((1 + nu) * (1 - 2 * nu));
Real detF = F.det();
RealTensor Ft = F.transpose();
RealTensor C = Ft * F;
RealTensor b = F * Ft;
RealTensor Identity;
Identity(0, 0) = 1.0; Identity(1, 1) = 1.0; Identity(2, 2) = 1.0;
RealTensor invC = inv(C);
#if COMPRESSIBLE
//This is the 2nd Piola-Kirchoff stress tensor, see 5.28 in Bonet. (not sure about log(J) term in Bonet)
// S = 0.5 * lambda * (detF * detF - 1) * invC + mu * (identity - invC);
#endif
S = 2.0*K1*pow(I_3,(-1.0/3.0))*Identity + 2.0*K2*I_1*pow(I_3,(-2.0/3.0))*Identity - 2.0*K2*pow(I_3,(-2.0/3.0))*C - K1*(2.0/3.0)*I_1*pow(I_3,(-1.0/3.0))*invC - K2*(4.0/3.0)*I_1*pow(I_3,(-2.0/3.0))*invC;
//std::cout <<"I_3 "<<I_3<<std::endl;
//std::cout <<"S "<<S<<std::endl;
//convert to current configuration using a push forward operation
tau = (F * S) * Ft;
sigma = (1.0)/detF * tau;
}
void MooneyCurrentConfig::get_residual(DenseVector<Real> & residuum, unsigned int & i) {
B_L.resize(3, 6);
DenseVector<Real> sigma_voigt(6);
this->build_b_0_mat(i, B_L);
tensor_to_voigt(sigma, sigma_voigt);
B_L.vector_mult(residuum, sigma_voigt); //should this be B_L^{T} * sigma_voigt ?
// std::cout<< " sigma " << sigma <<std::endl;
}
#if INCOMPRESSIBLE
void MooneyCurrentConfig::get_p_residual(DenseVector<Real> & p_residuum, unsigned int & i) {
Real detF = F.det();
p_residuum.resize(1);
// std::cout<<"neo "<<std::cout;
p_residuum(0)=(1/detF) *psi[i][current_qp]*(detF-1); ///Rp according to chaste fem *psi[i][current_qp] in main code
}
#endif
void MooneyCurrentConfig::tensor_to_voigt(const RealTensor &tensor, DenseVector<Real> &vec) {
vec(0) = tensor(0, 0);
vec(1) = tensor(1, 1);
vec(2) = tensor(2, 2);
vec(3) = tensor(0, 1);
vec(4) = tensor(1, 2);
vec(5) = tensor(0, 2);
}
void MooneyCurrentConfig::tensorOtensor_to_voigt(const RealTensor &tensorA, const RealTensor &tensorB, DenseMatrix<Real> &mat){
//Top left
/*
for (unsigned int i = 0; i < 3; ++i) {
for (unsigned int j = 0; j < 3; ++j) {
mat(i, j) = 2*tensorA(i,i)*tensorB(j,j);
}
}
*/
//Top three rows
for (unsigned int i = 0; i < 3; ++i) {
mat(i,0) = tensorA(i,i)*tensorB(0,0)+tensorA(i,i)*tensorB(0,0);
mat(i,1) = tensorA(i,i)*tensorB(1,1)+tensorA(i,i)*tensorB(1,1);
mat(i,2) = tensorA(i,i)*tensorB(2,2)+tensorA(i,i)*tensorB(2,2);
mat(i,3) = tensorA(i,i)*tensorB(0,1)+tensorA(i,i)*tensorB(1,0);
mat(i,4) = tensorA(i,i)*tensorB(0,2)+tensorA(i,i)*tensorB(2,0);
mat(i,5) = tensorA(i,i)*tensorB(1,2)+tensorA(i,i)*tensorB(2,1);
}
//fourth row
int i=3; int a=0; int b=1;
mat(i,0) = tensorA(a,b)*tensorB(0,0)+tensorA(a,b)*tensorB(0,0);
mat(i,1) = tensorA(a,b)*tensorB(1,1)+tensorA(a,b)*tensorB(1,1);
mat(i,2) = tensorA(a,b)*tensorB(2,2)+tensorA(a,b)*tensorB(2,2);
mat(i,3) = tensorA(a,b)*tensorB(0,1)+tensorA(a,b)*tensorB(1,0);
mat(i,4) = tensorA(a,b)*tensorB(0,2)+tensorA(a,b)*tensorB(2,0);
mat(i,5) = tensorA(a,b)*tensorB(1,2)+tensorA(a,b)*tensorB(2,1);
//fith row
i=4; a=0; b=2;
mat(i,0) = tensorA(a,b)*tensorB(0,0)+tensorA(a,b)*tensorB(0,0);
mat(i,1) = tensorA(a,b)*tensorB(1,1)+tensorA(a,b)*tensorB(1,1);
mat(i,2) = tensorA(a,b)*tensorB(2,2)+tensorA(a,b)*tensorB(2,2);
mat(i,3) = tensorA(a,b)*tensorB(0,1)+tensorA(a,b)*tensorB(1,0);
mat(i,4) = tensorA(a,b)*tensorB(0,2)+tensorA(a,b)*tensorB(2,0);
mat(i,5) = tensorA(a,b)*tensorB(1,2)+tensorA(a,b)*tensorB(2,1);
//sixth row
i=5; a=1; b=2;
mat(i,0) = tensorA(a,b)*tensorB(0,0)+tensorA(a,b)*tensorB(0,0);
mat(i,1) = tensorA(a,b)*tensorB(1,1)+tensorA(a,b)*tensorB(1,1);
mat(i,2) = tensorA(a,b)*tensorB(2,2)+tensorA(a,b)*tensorB(2,2);
mat(i,3) = tensorA(a,b)*tensorB(0,1)+tensorA(a,b)*tensorB(1,0);
mat(i,4) = tensorA(a,b)*tensorB(0,2)+tensorA(a,b)*tensorB(2,0);
mat(i,5) = tensorA(a,b)*tensorB(1,2)+tensorA(a,b)*tensorB(2,1);
}
void MooneyCurrentConfig::z_ref_to_voigt(const RealTensor &tensorA, const RealTensor &tensorB, DenseMatrix<Real> &mat){
//Top left
/*
for (unsigned int i = 0; i < 3; ++i) {
for (unsigned int j = 0; j < 3; ++j) {
mat(i, j) = 2*tensorA(i,i)*tensorB(j,j);
}
}
*/
//Top three rows
for (unsigned int i = 0; i < 3; ++i) {
mat(i,0) = tensorA(i,0)*tensorB(i,0)*2;
mat(i,1) = tensorA(i,1)*tensorB(i,1)*2;
mat(i,2) = tensorA(i,2)*tensorB(i,2)*2;
mat(i,3) = tensorA(i,0)*tensorB(i,1)*2;
mat(i,4) = tensorA(i,0)*tensorB(i,2)*2;
mat(i,5) = tensorA(i,1)*tensorB(i,2)*2;
}
//fourth row
int i=3; int a=0; int b=1;
mat(i,0) = tensorA(a,0)*tensorB(b,0)+tensorA(a,0)*tensorB(0,b);
mat(i,1) = tensorA(a,1)*tensorB(b,1)+tensorA(a,1)*tensorB(1,b);
mat(i,2) = tensorA(a,2)*tensorB(b,2)+tensorA(a,2)*tensorB(2,b);
mat(i,3) = tensorA(a,0)*tensorB(b,1)+tensorA(a,1)*tensorB(0,b);
mat(i,4) = tensorA(a,0)*tensorB(b,2)+tensorA(a,2)*tensorB(0,b);
mat(i,5) = tensorA(a,1)*tensorB(b,2)+tensorA(a,2)*tensorB(1,b);
//fith row
i=4; a=0; b=2;
mat(i,0) = tensorA(a,0)*tensorB(b,0)+tensorA(a,0)*tensorB(0,b);
mat(i,1) = tensorA(a,1)*tensorB(b,1)+tensorA(a,1)*tensorB(1,b);
mat(i,2) = tensorA(a,2)*tensorB(b,2)+tensorA(a,2)*tensorB(2,b);
mat(i,3) = tensorA(a,0)*tensorB(b,1)+tensorA(a,1)*tensorB(0,b);
mat(i,4) = tensorA(a,0)*tensorB(b,2)+tensorA(a,2)*tensorB(0,b);
mat(i,5) = tensorA(a,1)*tensorB(b,2)+tensorA(a,2)*tensorB(1,b);
//sixth row
i=5; a=1; b=2;
mat(i,0) = tensorA(a,0)*tensorB(b,0)+tensorA(a,0)*tensorB(0,b);
mat(i,1) = tensorA(a,1)*tensorB(b,1)+tensorA(a,1)*tensorB(1,b);
mat(i,2) = tensorA(a,2)*tensorB(b,2)+tensorA(a,2)*tensorB(2,b);
mat(i,3) = tensorA(a,0)*tensorB(b,1)+tensorA(a,1)*tensorB(0,b);
mat(i,4) = tensorA(a,0)*tensorB(b,2)+tensorA(a,2)*tensorB(0,b);
mat(i,5) = tensorA(a,1)*tensorB(b,2)+tensorA(a,2)*tensorB(1,b);
}
void MooneyCurrentConfig::get_linearized_stiffness(DenseMatrix<Real> & stiffness, unsigned int & i, unsigned int & j) {
stiffness.resize(3, 3);
double G_IK = (sigma * dphi[i][current_qp]) * dphi[j][current_qp];
stiffness(0, 0) += G_IK;
stiffness(1, 1) += G_IK;
stiffness(2, 2) += G_IK;
B_L.resize(3, 6);
this->build_b_0_mat(i, B_L);
B_K.resize(3, 6);
this->build_b_0_mat(j, B_K);
B_L.right_multiply(C_mat);
B_L.right_multiply_transpose(B_K);
B_L *= 1/F.det();
stiffness += B_L;
}
#if INCOMPRESSIBLE
void MooneyCurrentConfig::get_linearized_uvw_p_stiffness(DenseVector<Real> & p_stiffness, unsigned int & i, unsigned int & j) {
// Find and write down the mathematics for this section.
// eulerian tangent matrix at 6.15 - Bonet
RealTensor Ft = F.transpose();
Real detF = F.det();
RealTensor C = Ft * F;
RealTensor invC = inv(C);
RealTensor A = invC*F;
p_stiffness.resize(3);
RealTensor invF = inv(F);
//Build K_B (differentiate u eqn in p direction).
RealTensor DPHIi;
for (unsigned int z = 0; z < 3; ++z) {
DPHIi(z,0)=dphi[i][current_qp](z);
}
//std::cout<< "DPHIi " << DPHIi <<std::endl;
RealTensor invFt = invF.transpose();
RealTensor uvw_p_stiff=psi[j][current_qp]*invFt*DPHIi;
//std::cout<< "DPHIi " << DPHIi <<std::endl;
//std::cout<< "invFt" << invFt <<std::endl;
//std::cout<< "uvw_p_stiff" << uvw_p_stiff <<std::endl;
p_stiffness(0)=uvw_p_stiff(0,0);
p_stiffness(1)=uvw_p_stiff(1,0);
p_stiffness(2)=uvw_p_stiff(2,0);
////////
p_stiffness.resize(3);
p_stiffness(0)=psi[j][current_qp]*dphi[i][current_qp](0);
p_stiffness(1)=psi[j][current_qp]*dphi[i][current_qp](1);
p_stiffness(2)=psi[j][current_qp]*dphi[i][current_qp](2);
/////////
}
void MooneyCurrentConfig::get_linearized_p_uvw_stiffness(DenseVector<Real> & p_stiffness, unsigned int & i, unsigned int & j) {
//Build K_C (differentiate p eqn in u direction).
RealTensor Ft = F.transpose();
Real detF = F.det();
RealTensor C = Ft * F;
RealTensor invC = inv(C);
RealTensor A = invC*F;
p_stiffness.resize(3);
RealTensor invF = inv(F);
RealTensor invFt = invF.transpose();
RealTensor DPHIj;
for (unsigned int z = 0; z < 3; ++z) {
DPHIj(z,0)=dphi[j][current_qp](z);
}
RealTensor p_uvw_stiff= psi[i][current_qp]*invFt*DPHIj;
p_stiffness(0)=p_uvw_stiff(0,0);
p_stiffness(1)=p_uvw_stiff(1,0);
p_stiffness(2)=p_uvw_stiff(2,0);
p_stiffness.resize(3);
p_stiffness(0)=psi[i][current_qp]*dphi[j][current_qp](0);
p_stiffness(1)=psi[i][current_qp]*dphi[j][current_qp](1);
p_stiffness(2)=psi[i][current_qp]*dphi[j][current_qp](2);
}
#endif
void MooneyCurrentConfig::build_b_0_mat(int i, DenseMatrix<Real>& b_0_mat) {
for (unsigned int ii = 0; ii < 3; ++ii) {
b_0_mat(ii, ii) = dphi[i][current_qp](ii);
}
//See wriggers 4.94
b_0_mat(0, 3) = dphi[i][current_qp](1);
b_0_mat(1, 3) = dphi[i][current_qp](0);
b_0_mat(1, 4) = dphi[i][current_qp](2);
b_0_mat(2, 4) = dphi[i][current_qp](1);
b_0_mat(0, 5) = dphi[i][current_qp](2);
b_0_mat(2, 5) = dphi[i][current_qp](0);
}
void MooneyCurrentConfig::c_update(RealTensor C) {
// Real m=0;
this-> C = C;
this->invC = inv(C);
this->b = F*Ft;
this->Identity(0,0)=1.0;
this->Identity(1,1)=1.0;
this->Identity(2,2)=1.0;
this->I_3 = C.det();
this->I_1 = C(0,0)+C(1,1)+C(2,2);
RealTensor Csqd = C*C;
this->I_2 = 0.5*(pow(I_1,2) - (Csqd(0,0)+Csqd(1,1)+Csqd(2,2))) ;
this->J=pow(I_3,(1.0/2.0));
}
#endif