void FormPBJacobian(PetscInt i,PetscInt j,PetscInt k,Field *ex,CoordField *ec,Field *ef,PetscScalar *ej,AppCtx *user)
{
PetscReal vol;
PetscScalar J[9];
PetscScalar invJ[9];
PetscScalar F[9],S[9],dF[9],dS[9],dFS[9],FdS[9],FS[9];
PetscReal scl;
PetscInt l,ll,qi,qj,qk,m;
PetscInt idx = i + j*NB + k*NB*NB;
PetscScalar lgrad[3];
if (ej) for (l = 0; l < 9; l++) ej[l] = 0.;
if (ef) for (l = 0; l < 1; l++) {ef[l][0] = 0.;ef[l][1] = 0.;ef[l][2] = 0.;}
/* loop over quadrature */
for (qk = 0; qk < NQ; qk++) {
for (qj = 0; qj < NQ; qj++) {
for (qi = 0; qi < NQ; qi++) {
PetscInt bidx = NEB*idx + qi + NQ*qj + NQ*NQ*qk;
QuadraturePointGeometricJacobian(ec,qi,qj,qk,J);
InvertTensor(J,invJ,&vol);
TensorVector(invJ,&grad[3*bidx],lgrad);
scl = vol*wts[qi]*wts[qj]*wts[qk];
DeformationGradient(ex,qi,qj,qk,invJ,F);
SaintVenantKirchoff(user->lambda,user->mu,F,S);
/* form the function */
if (ef) {
TensorTensor(F,S,FS);
for (m=0;m<3;m++) {
ef[0][m] += scl*
(lgrad[0]*FS[3*m + 0] + lgrad[1]*FS[3*m + 1] + lgrad[2]*FS[3*m + 2]);
}
ef[0][1] -= scl*user->loading*vals[bidx];
}
/* form the jacobian */
if (ej) {
for (l=0;l<3;l++) {
DeformationGradientJacobian(qi,qj,qk,i,j,k,l,invJ,dF);
SaintVenantKirchoffJacobian(user->lambda,user->mu,F,dF,dS);
TensorTensor(dF,S,dFS);
TensorTensor(F,dS,FdS);
for (m=0;m<9;m++) dFS[m] += FdS[m];
for (ll=0; ll<3;ll++) {
ej[ll + 3*l] += scl*
(lgrad[0]*dFS[3*ll + 0] + lgrad[1]*dFS[3*ll + 1] + lgrad[2]*dFS[3*ll+2]);
}
}
}
}
} /* end of quadrature points */
}
}
//
// Strain displacement operator
//
void FSDielectricElastomer2DT::Set_B_C(const dArray2DT& DNaX, dMatrixT& B_C)
{
const int nsd = NumSD();
const int nen = NumElementNodes();
const int StrainDim = dSymMatrixT::NumValues(nsd);
const int nnd = DNaX.MinorDim();
assert(nen == nnd);
B_C.Dimension(StrainDim, nsd * nen);
const dMatrixT F = DeformationGradient();
for (int ij = 0; ij < StrainDim; ++ij) {
int i;
int j;
dSymMatrixT::ExpandIndex(nsd, ij, i, j);
for (int a = 0; a < nen; ++a) {
for (int k = 0; k < nsd; ++k) {
const int ak = a * nsd + k;
B_C(ij, ak) = DNaX(i, a) * F(k, j) + DNaX(j, a) * F(k, i);
// Shear components doubled to conform with Voigt
// convention - HSP - not sure if this is correct
if (ij >= nsd) {
B_C(ij, ak) *= 2.0;
}
}
}
}
}
void FormElementJacobian(Field *ex,CoordField *ec,Field *ef,PetscScalar *ej,AppCtx *user)
{
PetscReal vol;
PetscScalar J[9];
PetscScalar invJ[9];
PetscScalar F[9],S[9],dF[9],dS[9],dFS[9],FdS[9],FS[9];
PetscReal scl;
PetscInt i,j,k,l,ii,jj,kk,ll,qi,qj,qk,m;
if (ej) for (i = 0; i < NPB*NPB; i++) ej[i] = 0.;
if (ef) for (i = 0; i < NEB; i++) {ef[i][0] = 0.;ef[i][1] = 0.;ef[i][2] = 0.;}
/* loop over quadrature */
for (qk = 0; qk < NQ; qk++) {
for (qj = 0; qj < NQ; qj++) {
for (qi = 0; qi < NQ; qi++) {
QuadraturePointGeometricJacobian(ec,qi,qj,qk,J);
InvertTensor(J,invJ,&vol);
scl = vol*wts[qi]*wts[qj]*wts[qk];
DeformationGradient(ex,qi,qj,qk,invJ,F);
SaintVenantKirchoff(user->lambda,user->mu,F,S);
/* form the function */
if (ef) {
TensorTensor(F,S,FS);
for (kk=0;kk<NB;kk++){
for (jj=0;jj<NB;jj++) {
for (ii=0;ii<NB;ii++) {
PetscInt idx = ii + jj*NB + kk*NB*NB;
PetscInt bidx = NEB*idx + qi + NQ*qj + NQ*NQ*qk;
PetscScalar lgrad[3];
TensorVector(invJ,&grad[3*bidx],lgrad);
/* mu*F : grad phi_{u,v,w} */
for (m=0;m<3;m++) {
ef[idx][m] += scl*
(lgrad[0]*FS[3*m + 0] + lgrad[1]*FS[3*m + 1] + lgrad[2]*FS[3*m + 2]);
}
ef[idx][1] -= scl*user->loading*vals[bidx];
}
}
}
}
/* form the jacobian */
if (ej) {
/* loop over trialfunctions */
for (k=0;k<NB;k++){
for (j=0;j<NB;j++) {
for (i=0;i<NB;i++) {
for (l=0;l<3;l++) {
PetscInt tridx = l + 3*(i + j*NB + k*NB*NB);
DeformationGradientJacobian(qi,qj,qk,i,j,k,l,invJ,dF);
SaintVenantKirchoffJacobian(user->lambda,user->mu,F,dF,dS);
TensorTensor(dF,S,dFS);
TensorTensor(F,dS,FdS);
for (m=0;m<9;m++) dFS[m] += FdS[m];
/* loop over testfunctions */
for (kk=0;kk<NB;kk++){
for (jj=0;jj<NB;jj++) {
for (ii=0;ii<NB;ii++) {
PetscInt idx = ii + jj*NB + kk*NB*NB;
PetscInt bidx = 8*idx + qi + NQ*qj + NQ*NQ*qk;
PetscScalar lgrad[3];
TensorVector(invJ,&grad[3*bidx],lgrad);
for (ll=0; ll<3;ll++) {
PetscInt teidx = ll + 3*(ii + jj*NB + kk*NB*NB);
ej[teidx + NPB*tridx] += scl*
(lgrad[0]*dFS[3*ll + 0] + lgrad[1]*dFS[3*ll + 1] + lgrad[2]*dFS[3*ll+2]);
}
}
}
} /* end of testfunctions */
}
}
}
} /* end of trialfunctions */
}
}
}
} /* end of quadrature points */
}
