tensor DPYieldSurface01::xi_t1( const EPState *EPS) const {
tensor dFoverds( 2, def_dim_2, 0.0);
tensor I2("I", 2, def_dim_2);
stresstensor S = EPS->getStress().deviator();
double p = EPS->getStress().p_hydrostatic();
p = p - Pc;
stresstensor alpha = EPS->getTensorVar( 1 ); // getting alpha_ij from EPState
stresstensor r = S * (1.0 / p); //for p = sig_kk/3
stresstensor r_bar = r - alpha;
stresstensor norm2 = r_bar("ij") * r_bar("ij");
double norm = sqrt( norm2.trace() );
stresstensor n;
if ( norm >= d_macheps() ) {
n = r_bar *(1.0 / norm );
}
else {
opserr << "DPYieldSurface01::dFods |n_ij| = 0, divide by zero! Program exits.\n";
exit(-1);
}
return (-1.0) * n * p;
}
tensor DPYieldSurface01::dFods(const EPState *EPS) const {
tensor dFoverds( 2, def_dim_2, 0.0);
tensor I2("I", 2, def_dim_2);
stresstensor S = EPS->getStress().deviator();
//S.reportshort("S");
double p = EPS->getStress().p_hydrostatic();
p = p - Pc;
//printf("Here we go! p %f\n", p);
stresstensor alpha = EPS->getTensorVar( 1 ); // getting alpha_ij from EPState
//alpha.reportshort("alpha");
//stresstensor n = EPS->getTensorVar( 3 ); // getting n_ij from EPState
//n.reportshort("n");
//-------------------------------------------------
// might be moved to Evolution Law
stresstensor r = S * (1.0 / p);
//r.reportshort("r");
stresstensor r_bar = r - alpha;
//r_bar.reportshort("r_bar");
stresstensor norm2 = r_bar("ij") * r_bar("ij");
double norm = sqrt( norm2.trace() );
//opserr << "d_macheps " << d_macheps() << endlnn;
stresstensor n;
if ( norm >= d_macheps() ) {
n = r_bar*(1.0 / norm );
}
else {
opserr << "DPYieldSurface01::dFods |n_ij| = 0, divide by zero! Program exits.\n";
exit(-1);
}
//EPS->setTensorVar( 3, n); //update n_ij//
//-------------------------------------------------
double m = EPS->getScalarVar( 1 );
//tensorial multiplication produces 1st-order tensor
//tensor temp = n("ij") * n("ij");
//double temp1 = temp.trace();
//printf("==== n_ij*n_ij %e\n", temp1);
//!!Very important: N = n_pq * alpha_pq +sqrt(2/3)*m (always) = n_pq*r_pq(not hold when not on the yield surface)
tensor temp = n("ij") * alpha("ij");
double N = temp.trace() + sqrt(2.0/3.0)*m;
//printf(" N = %e\n", N);
dFoverds = n - N *I2 *(1.0/3.0);
return dFoverds;
}
double XC::MDEvolutionLaw::getKp( EPState *EPS , double dummy) {
//clog << "el-pl EPS: " << *EPS ;
//=========================================================================
//calculate n_ij
XC::stresstensor S = EPS->getStress().deviator();
double p = EPS->getStress().p_hydrostatic();
XC::stresstensor alpha = EPS->getTensorVar( 1 ); // alpha_ij
XC::stresstensor r = S * (1.0 / p);
//r.reportshort("r");
XC::stresstensor r_bar = r - alpha;
XC::stresstensor norm2 = r_bar("ij") * r_bar("ij");
double norm = sqrt( norm2.trace() );
XC::stresstensor n;
if ( norm >= d_macheps() ){
n = ( r - alpha ) *(1.0 / norm );
}
else {
::printf(" \n\n n_ij not defined!!!! Program exits\n");
exit(1);
}
//=========================================================================
//calculating b_ij
//Calculate the state parameters xi
double e = EPS->getScalarVar(3);
double ec = getec_ref() - getLambda() * log( p/getp_ref() );
double xi = e - ec;
//Calculating the lode angle theta
double J2_bar = r_bar.Jinvariant2();
double J3_bar = r_bar.Jinvariant3();
double tempd = 3.0*pow(3.0, 0.5)/2.0*J3_bar/ pow( J2_bar, 1.5);
if (tempd > 1.0 ) tempd = 1.0; //bug. if tempd = 1.00000000003, acos gives nan
if (tempd < -1.0 ) tempd = -1.0;
double theta = acos( tempd ) / 3.0;
//calculate the alpha_theta_b and alpha_theta_d
double m = EPS->getScalarVar(1);
double c = getMe() / getMc();
double cd = getke_d() / getkc_d();
XC::stresstensor alpha_theta_d = n("ij") * (g_WW(theta, c) * Mc + g_WW(theta, cd) * kc_d * xi - m) * pow(2.0/3.0, 0.5);
double cb = getke_b() / getkc_b();
if ( xi > 0.0 ) xi = 0.0; // < -xi >
XC::stresstensor alpha_theta_b = n("ij") * (g_WW(theta, c) * Mc - g_WW(theta, cb) * kc_b * xi - m) * pow(2.0/3.0, 0.5);
alpha_theta_b.null_indices();
//=========================================================================
// calculating h
XC::stresstensor b;
b = alpha_theta_b - alpha;
b.null_indices();
XC::stresstensor d;
d = alpha_theta_d - alpha;
d.null_indices();
double alpha_c_b = g_WW(0.0, c) * Mc + g_WW(0.0, cb) * kc_b * (-xi) - m;
double b_ref = 2.0 * pow(2.0/3.0, 0.5) * alpha_c_b;
BJtensor temp1 = b("ij") * n("ij");
double bn = temp1.trace();
temp1 = d("ij") * n("ij");
double dn = temp1.trace();
// Calculating A
XC::stresstensor F = EPS->getTensorVar( 2 ); // getting F_ij from XC::EPState
temp1 = F("ij") * n("ij");
double temp = temp1.trace();
if (temp < 0) temp = 0;
double A = Ao*(1.0 + temp);
double h = getho() * fabs(bn) / ( b_ref - fabs(bn) );
clog << "ho =" << getho() << " h =" << h << std::endl;
//=========================================================================
double Kp = h * bn + pow(2.0/3.0, 0.5) * getCm() * ( 1.0 + geteo() ) * A * dn;
//double Kp = pow(2.0/3.0, 0.5) * getCm() * ( 1.0 + geteo() ) * A * dn;
Kp = Kp * p;
return Kp;
}
void XC::MDEvolutionLaw::UpdateAllVars( EPState *EPS, double dlamda) {
//=========================================================================
//calculate n_ij
XC::stresstensor S = EPS->getStress().deviator();
double p = EPS->getStress().p_hydrostatic();
XC::stresstensor alpha = EPS->getTensorVar( 1 ); // alpha_ij
// Find the norm of alpha
BJtensor norm_alphat = alpha("ij") * alpha("ij");
double norm_alpha = sqrt( norm_alphat.trace() );
XC::stresstensor r = S * (1.0 / p);
//r.reportshort("r");
XC::stresstensor r_bar = r - alpha;
XC::stresstensor norm2 = r_bar("ij") * r_bar("ij");
double norm = sqrt( norm2.trace() );
XC::stresstensor n;
if ( norm >= d_macheps() ){
n = ( r - alpha ) *(1.0 / norm );
}
else {
::printf(" \n\n n_ij not defined!!!! Program exits\n");
exit(1);
}
//EPS->setTensorVar( 3, n); //update n_ij//
// Update E_Young corresponding to current stress state
double p_atm = 100.0; //Kpa, atmospheric pressure
double E = EPS->getE(); // old E_Young
double E_new = EPS->getEo() * pow( (p/p_atm), geta() );
EPS->setE( E_new );
// Update void ratio
double e = EPS->getScalarVar(3);
double D = EPS->getScalarVar(2);
double elastic_strain_vol = EPS->getdElasticStrain().Iinvariant1();
double plastic_strain_vol = EPS->getdPlasticStrain().Iinvariant1();
double de_p = -( 1.0 + e ) * plastic_strain_vol; // plastic change of void ratio ?? e or eo?
double de_e = -( 1.0 + e ) * elastic_strain_vol; // elastic change of void ratio ????
clog << "get dPlasticStrain-vol" << plastic_strain_vol << std::endl;
clog << "get dElasticStrain-vol" << elastic_strain_vol << std::endl;
clog << "^^^^^^^^^^^ de_e = " << de_e << " de_p = " << de_p << std::endl;
double new_e = e + de_p + de_e;
EPS->setScalarVar( 3, new_e ); // Updating e
//Calculate the state parameters xi
double ec = getec_ref() - getLambda() * log( p/getp_ref() );
double xi = e - ec;
// Update D
double m = EPS->getScalarVar(1);
XC::stresstensor F = EPS->getTensorVar( 2 ); // getting F_ij from XC::EPState
BJtensor temp_tensor = F("ij") * n("ij");
double temp = temp_tensor.trace();
if (temp < 0) temp = 0;
double A = Ao*(1.0 + temp);
//Calculating the lode angle theta
double J2_bar = r_bar.Jinvariant2();
double J3_bar = r_bar.Jinvariant3();
double tempd = 3.0*pow(3.0, 0.5)/2.0*J3_bar/ pow( J2_bar, 1.5);
if (tempd > 1.0 ) tempd = 1.0; //bug. if tempd = 1.00000000003, acos gives nan
if (tempd < -1.0 ) tempd = -1.0;
double theta = acos( tempd ) / 3.0;
//=========================================================================
//calculate the alpha_theta_b and alpha_theta_d
double c = getMe() / getMc();
double cd = getke_d() / getkc_d();
double alpha_theta_dd = (g_WW(theta, c) * Mc + g_WW(theta, cd) * kc_d * xi - m);
XC::stresstensor alpha_theta_d = n("ij") * alpha_theta_dd * pow(2.0/3.0, 0.5);
double cb = getke_b() / getkc_b();
if ( xi > 0 ) xi = 0.0; // < -xi >
double alpha_theta_bd = (g_WW(theta, c) * Mc + g_WW(theta, cb) * kc_b * (-xi) - m);
XC::stresstensor alpha_theta_b = n("ij") *alpha_theta_bd * pow(2.0/3.0, 0.5);
alpha_theta_b.null_indices();
XC::stresstensor b;
b = alpha_theta_b - alpha;
b.null_indices();
XC::stresstensor d;
d = alpha_theta_d - alpha;
d.null_indices();
BJtensor temp1 = d("ij") * n("ij");
temp1.null_indices();
double D_new = temp1.trace() * A;
//Check the restrictions on D
if ( (xi > 0.0) && ( D_new < 0.0) )
D_new = 0.0;
EPS->setScalarVar(2, D_new); // Updating D
//EPS->setScalarVar(2, 0.0); // Updating D
//=========================================================================
// Update m
double dm = dlamda * getCm() * ( 1.0 + e ) * D;
EPS->setScalarVar(1, m + dm); // Updating m
clog << std::endl << "dm = " << dm << std::endl;
//=========================================================================
// Update alpha
//calculate b_ref
double alpha_c_b = g_WW(0.0, c) * Mc + g_WW(0.0, cb) * kc_b * (-xi) - m;
double b_ref = 2.0 * pow(2.0/3.0, 0.5) * alpha_c_b;
temp1 = b("ij") * n("ij");
double bn = temp1.trace();
clog << "xxxxxxxxxxxxxxxxxxx bn " << bn << std::endl;
double h = getho() * fabs(bn) / ( b_ref - fabs(bn) );
//h = h + pow(2.0/3.0, 0.5) * getCm() * ( 1.0 + geteo() ) * A * bn;
clog << " ||b|| " << (alpha_theta_bd - norm_alpha) << std::endl;
clog << " dlamda " << dlamda << " h = " << h << std::endl;
XC::stresstensor dalpha;
dalpha = dlamda * h * b("ij");
//dalpha.null_indices();
clog << "delta alpha =" << dalpha << std::endl;
//dalpha.reportshortpqtheta("\n dalpha ");
alpha = alpha + dalpha;
alpha.null_indices();
//alpha.reportshort("Alpha");
EPS->setTensorVar(1, alpha);
//=========================================================================
// Update F
XC::stresstensor dF;
if ( D > 0.0 ) D = 0.0;
dF = dlamda * getCf() * (-D) * ( getFmax() * n("ij") + F("ij") );
//clog << "dF" << dF;
F = F - dF;
EPS->setTensorVar(2, F);
}
void XC::MDEvolutionLaw::setInitD(EPState *EPS) {
//=========================================================================
//calculate n_ij
XC::stresstensor S = EPS->getStress().deviator();
double p = EPS->getStress().p_hydrostatic();
XC::stresstensor alpha = EPS->getTensorVar( 1 ); // alpha_ij
// Find the norm of alpha
BJtensor norm_alphat = alpha("ij") * alpha("ij");
double norm_alpha = sqrt( norm_alphat.trace() );
XC::stresstensor r = S * (1.0 / p);
//r.reportshort("r");
XC::stresstensor r_bar = r - alpha;
XC::stresstensor norm2 = r_bar("ij") * r_bar("ij");
double norm = sqrt( norm2.trace() );
XC::stresstensor n;
if ( norm >= d_macheps() ){
n = ( r - alpha ) *(1.0 / norm );
}
else {
::printf(" \n\n n_ij not defined!!!! Program exits\n");
exit(1);
}
//Calculate the state parameters xi
double e = EPS->getScalarVar(3);
double ec = getec_ref() - getLambda() * log( p/getp_ref() );
double xi = e - ec;
//calculating A
double m = EPS->getScalarVar(1);
XC::stresstensor F = EPS->getTensorVar( 2 ); // getting F_ij from XC::EPState
BJtensor temp_tensor = F("ij") * n("ij");
double temp = temp_tensor.trace();
if (temp < 0) temp = 0;
double A = Ao*(1.0 + temp);
//Calculating the lode angle theta
double J2_bar = r_bar.Jinvariant2();
double J3_bar = r_bar.Jinvariant3();
double tempd = 3.0*pow(3.0, 0.5)/2.0*J3_bar/ pow( J2_bar, 1.5);
if (tempd > 1.0 ) tempd = 1.0; //bug. if tempd = 1.00000000003, acos gives nan
if (tempd < -1.0 ) tempd = -1.0;
double theta = acos( tempd ) / 3.0;
//=========================================================================
//calculate the alpha_theta_b and alpha_theta_d
double c = getMe() / getMc();
double cd = getke_d() / getkc_d();
double alpha_theta_dd = (g_WW(theta, c) * Mc + g_WW(theta, cd) * kc_d * xi - m);
XC::stresstensor alpha_theta_d = n("ij") * alpha_theta_dd * pow(2.0/3.0, 0.5);
XC::stresstensor d;
d = alpha_theta_d - alpha;
d.null_indices();
BJtensor temp1 = d("ij") * n("ij");
temp1.null_indices();
double D_new = temp1.trace() * A;
//Check the restrictions on D
if ( (xi > 0.0) && ( D_new < 0.0) )
D_new = 0.0;
EPS->setScalarVar(2, D_new); // Updating D
}