void
StructuralInterfaceMaterial :: give2dStiffnessMatrix_Eng_Num(FloatMatrix &answer, GaussPoint *gp, TimeStep *tStep)
{
// Default implementation for computation of the numerical tangent d(sig)/d(jump)
// Computes the material stiffness using a central difference method
StructuralInterfaceMaterialStatus *status = static_cast< StructuralInterfaceMaterialStatus * >( this->giveStatus( gp ) );
double eps = 1.0e-12;
FloatArray t, tPlus, tMinus;
FloatArray tempJump, jumpPlus, jumpMinus, Kcolumn;
FloatArray jump = {status->giveTempJump().at(1), status->giveTempJump().at(3)};
int dim = jump.giveSize();
answer.resize(dim, dim);
answer.zero();
for(int i = 1; i <= dim; i++) {
jumpPlus = jumpMinus = jump;
jumpPlus.at( i ) += eps;
jumpMinus.at( i ) -= eps;
this->giveEngTraction_2d(tPlus, gp, jumpPlus, tStep);
this->giveEngTraction_2d(tMinus, gp, jumpMinus, tStep);
Kcolumn.beDifferenceOf(tPlus, tMinus);
answer.setColumn(Kcolumn, i);
}
answer.times( 1.0 / ( 2 * eps ) );
this->giveEngTraction_2d( t, gp, jump, tStep ); // reset temp values by recomputing the stress
}
void
StructuralInterfaceMaterial :: giveStiffnessMatrix_dTdj_Num(FloatMatrix &answer, MatResponseMode rMode, GaussPoint *gp, TimeStep *tStep)
{
// Default implementation for computation of the numerical tangent
// Computes the material stiffness using a central difference method
StructuralInterfaceMaterialStatus *status = static_cast< StructuralInterfaceMaterialStatus * >( this->giveStatus(gp) );
if ( status ) {
FloatMatrix F;
F = status->giveTempF();
int dim = F.giveNumberOfRows();
answer.resize(dim, dim);
answer.zero();
const double eps = 1.0e-9;
FloatArray T, TPlus, TMinus;
FloatArray jump, jumpPlus, jumpMinus, Kcolumn;
jump = status->giveTempJump();
for ( int i = 1; i <= dim; i++ ) {
jumpPlus = jumpMinus = jump;
jumpPlus.at(i) += eps;
jumpMinus.at(i) -= eps;
this->giveFirstPKTraction_3d(TPlus, gp, jumpPlus, F, tStep);
this->giveFirstPKTraction_3d(TMinus, gp, jumpMinus, F, tStep);
Kcolumn = ( TPlus - TMinus );
answer.setColumn(Kcolumn, i);
}
answer.times( 1.0 / ( 2 * eps ) );
this->giveFirstPKTraction_3d(T, gp, jump, F, tStep); // reset temp values by recomputing the stress
}
}
void
StructuralInterfaceMaterial::giveStiffnessMatrix_Eng_Num( FloatMatrix &answer, MatResponseMode rMode, GaussPoint *gp, TimeStep *tStep,
void( *giveTraction )( FloatArray &answer, GaussPoint *gp, const FloatArray &jump, TimeStep *tStep ) )
{
// Default implementation for computation of the numerical tangent d(sig)/d(jump)
// Computes the material stiffness using a central difference method
StructuralInterfaceMaterialStatus *status = static_cast< StructuralInterfaceMaterialStatus * >( this->giveStatus( gp ) );
if(status) {
const double eps = 1.0e-9;
FloatArray t, tPlus, tMinus;
FloatArray jump, jumpPlus, jumpMinus, Kcolumn;
jump = status->giveTempJump( );
int dim = jump.giveSize();
answer.resize( dim, dim );
answer.zero( );
for(int i = 1; i <= dim; i++) {
jumpPlus = jumpMinus = jump;
jumpPlus.at( i ) += eps;
jumpMinus.at( i ) -= eps;
giveTraction( tPlus, gp, jumpPlus, tStep );
giveTraction( tMinus, gp, jumpMinus, tStep );
Kcolumn = ( tPlus - tMinus );
answer.setColumn( Kcolumn, i );
}
answer.times( 1.0 / ( 2 * eps ) );
giveTraction( t, gp, jump, tStep ); // reset temp values by recomputing the stress
}
}
void
CohesiveInterfaceMaterial :: give3dStiffnessMatrix_Eng(FloatMatrix &answer, MatResponseMode rMode, GaussPoint *gp, TimeStep *tStep)
{
answer.resize(3, 3);
answer.zero();
StructuralInterfaceMaterialStatus *status = static_cast< StructuralInterfaceMaterialStatus * >( this->giveStatus(gp) );
// double normalJump = status->giveTempJump().at(1);
// if (normalJump > 0.) {
// if(normalJump<transitionOpening){ // reduce traction in tension
// double stiffTmp = kn*stiffCoeffKn + (kn - kn*stiffCoeffKn) * (1. - normalJump/transitionOpening);
// answer.at(1, 1) = stiffTmp;
// } else {
// answer.at(1, 1) = kn * stiffCoeffKn;
// }
// } else {
// // standard part of elastic stress-strain law
// answer.at(1, 1) = kn;
// }
//
// if ( rMode == SecantStiffness || rMode == TangentStiffness ) {
// if ( normalJump + transitionOpening <= 0. ) { //local CS
// answer.at(1, 1) = kn; //compression
// } else {
// answer.at(1, 1) = 0*kn*stiffCoeffKn; //tension
// }
// } else {
// answer.at(1, 1) = kn;
// }
double x = status->giveTempJump().at(1) + transitionOpening;
if (stiffCoeffKn == 1.){//tension stiffness = compression stiffness
answer.at(1,1) = kn;
} else {
//TangentStiffness by derivating traction with regards to x (=relative displacement)
answer.at(1,1) = (M_PI/2. + atan(smoothMag*x))/M_PI*kn*stiffCoeffKn + (M_PI/2.-atan(smoothMag*x))/M_PI*kn + smoothMag*kn*stiffCoeffKn*x/M_PI/(smoothMag*smoothMag*x*x+1) - smoothMag*kn*x/M_PI/(smoothMag*smoothMag*x*x+1);
}
//answer.at(1, 1) = kn;
answer.at(2, 2) = ks;
answer.at(3, 3) = ks;
}