void
Kinematics<EvalT, Traits>::evaluateFields(typename Traits::EvalData workset)
{
minitensor::Tensor<ScalarT> F(num_dims_), strain(num_dims_), gradu(num_dims_);
minitensor::Tensor<ScalarT> I(minitensor::eye<ScalarT>(num_dims_));
// Compute DefGrad tensor from displacement gradient
if (!def_grad_rc_) {
for (int cell(0); cell < workset.numCells; ++cell) {
for (int pt(0); pt < num_pts_; ++pt) {
gradu.fill(grad_u_, cell, pt, 0, 0);
F = I + gradu;
j_(cell, pt) = minitensor::det(F);
for (int i(0); i < num_dims_; ++i) {
for (int j(0); j < num_dims_; ++j) {
def_grad_(cell, pt, i, j) = F(i, j);
}
}
}
}
} else {
bool first = true;
for (int cell = 0; cell < workset.numCells; ++cell) {
for (int pt = 0; pt < num_pts_; ++pt) {
gradu.fill(grad_u_, cell, pt, 0, 0);
F = I + gradu;
for (int i = 0; i < num_dims_; ++i)
for (int j = 0; j < num_dims_; ++j)
def_grad_(cell, pt, i, j) = F(i, j);
if (first && check_det(workset, cell, pt)) first = false;
// F[n,0] = F[n,n-1] F[n-1,0].
def_grad_rc_.multiplyInto<ScalarT>(def_grad_, cell, pt);
F.fill(def_grad_, cell, pt, 0, 0);
j_(cell, pt) = minitensor::det(F);
}
}
}
if (weighted_average_) {
ScalarT jbar, weighted_jbar, volume;
for (int cell(0); cell < workset.numCells; ++cell) {
jbar = 0.0;
volume = 0.0;
for (int pt(0); pt < num_pts_; ++pt) {
jbar += weights_(cell, pt) * j_(cell, pt);
volume += weights_(cell, pt);
}
jbar /= volume;
for (int pt(0); pt < num_pts_; ++pt) {
weighted_jbar = (1 - alpha_) * jbar + alpha_ * j_(cell, pt);
F.fill(def_grad_, cell, pt, 0, 0);
const ScalarT p = std::pow((weighted_jbar / j_(cell, pt)), 1. / 3.);
F *= p;
j_(cell, pt) = weighted_jbar;
for (int i(0); i < num_dims_; ++i) {
for (int j(0); j < num_dims_; ++j) {
def_grad_(cell, pt, i, j) = F(i, j);
}
}
}
}
}
if (needs_strain_) {
if (!def_grad_rc_) {
for (int cell(0); cell < workset.numCells; ++cell) {
for (int pt(0); pt < num_pts_; ++pt) {
gradu.fill(grad_u_, cell, pt, 0, 0);
strain = 0.5 * (gradu + minitensor::transpose(gradu));
for (int i(0); i < num_dims_; ++i) {
for (int j(0); j < num_dims_; ++j) {
strain_(cell, pt, i, j) = strain(i, j);
}
}
}
}
} else {
for (int cell = 0; cell < workset.numCells; ++cell) {
for (int pt = 0; pt < num_pts_; ++pt) {
F.fill(def_grad_, cell, pt, 0, 0);
gradu = F - I;
// dU/dx[0] = dx[n]/dx[0] - dx[0]/dx[0] = F[n,0] - I.
// strain = 1/2 (dU/dx[0] + dU/dx[0]^T).
strain = 0.5 * (gradu + minitensor::transpose(gradu));
for (int i = 0; i < num_dims_; ++i)
for (int j = 0; j < num_dims_; ++j)
strain_(cell, pt, i, j) = strain(i, j);
}
}
}
}
}
void MechanicsResidual<EvalT, Traits>::
evaluateFields(typename Traits::EvalData workset)
{
std::cout.precision(15);
// initilize Tensors
Intrepid::Tensor<ScalarT> F(num_dims_), P(num_dims_), sig(num_dims_);
Intrepid::Tensor<ScalarT> I(Intrepid::eye<ScalarT>(num_dims_));
if (have_pore_pressure_) {
for (std::size_t cell=0; cell < workset.numCells; ++cell) {
for (std::size_t pt=0; pt < num_pts_; ++pt) {
// Effective Stress theory
sig.fill( &stress_(cell,pt,0,0) );
sig -= biot_coeff_(cell,pt) * pore_pressure_(cell,pt) * I;
for (std::size_t i=0; i<num_dims_; i++) {
for (std::size_t j=0; j<num_dims_; j++) {
stress_(cell,pt,i,j) = sig(i,j);
}
}
}
}
}
// initialize residual
if(have_strain_){
// for small deformation, use Cauchy stress
for (std::size_t cell=0; cell < workset.numCells; ++cell) {
for (std::size_t node=0; node < num_nodes_; ++node) {
for (std::size_t dim=0; dim<num_dims_; ++dim) {
residual_(cell,node,dim)=0.0;
}
}
for (std::size_t pt=0; pt < num_pts_; ++pt) {
//F.fill( &def_grad_(cell,pt,0,0) );
sig.fill( &stress_(cell,pt,0,0) );
for (std::size_t node=0; node < num_nodes_; ++node) {
for (std::size_t i=0; i<num_dims_; ++i) {
for (std::size_t j=0; j<num_dims_; ++j) {
residual_(cell,node,i) +=
sig(i, j) * w_grad_bf_(cell, node, pt, j);
}
}
}
}
}
}
else {
// for large deformation, map Cauchy stress to 1st PK stress
for (std::size_t cell=0; cell < workset.numCells; ++cell) {
for (std::size_t node=0; node < num_nodes_; ++node) {
for (std::size_t dim=0; dim<num_dims_; ++dim) {
residual_(cell,node,dim)=0.0;
}
}
for (std::size_t pt=0; pt < num_pts_; ++pt) {
F.fill( &def_grad_(cell,pt,0,0) );
sig.fill( &stress_(cell,pt,0,0) );
// map Cauchy stress to 1st PK
P = Intrepid::piola(F,sig);
for (std::size_t node=0; node < num_nodes_; ++node) {
for (std::size_t i=0; i<num_dims_; ++i) {
for (std::size_t j=0; j<num_dims_; ++j) {
residual_(cell,node,i) +=
P(i, j) * w_grad_bf_(cell, node, pt, j);
}
}
}
}
}
}
// optional body force
if (have_body_force_) {
for (std::size_t cell=0; cell < workset.numCells; ++cell) {
for (std::size_t node=0; node < num_nodes_; ++node) {
for (std::size_t pt=0; pt < num_pts_; ++pt) {
for (std::size_t dim=0; dim<num_dims_; ++dim) {
residual_(cell,node,dim) +=
w_bf_(cell,node,pt) * body_force_(cell,pt,dim);
}
}
}
}
}
}
