tensor MDYieldSurface::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();
stresstensor n = EPS->getTensorVar( 2 );
//stresstensor n;
////-------------------------------------------------
//double m = EPS->getScalarVar( 1 );
//stresstensor alpha = EPS->getTensorVar( 1 ); // getting alpha_ij from EPState
//stresstensor r = S * (1.0 / p);
//stresstensor r_bar = r - alpha;
//stresstensor norm2 = r_bar("ij") * r_bar("ij");
//double norm = sqrt( norm2.trace() );
//
//if ( norm >= d_macheps() ){
// n = r_bar *(1.0 / norm );
//}
//else {
// opserr->fatal("MDYieldSurface::dFods |n_ij| = 0, divide by zero! Program exits.");
// exit(-1);
//}
//n = r_bar *(1.0 / sqrt23rd / m );
////-------------------------------------------------
return n * (-1.0)* p;
}
tensor RMC01YieldSurface::dFods(const EPState *EPS) const
{
tensor dFoverds( 2, def_dim_2, 0.0);
// double p = EPS->getStress().p_hydrostatic();
double q = EPS->getStress().q_deviatoric();
double theta = EPS->getStress().theta();
// double temp_phi = EPS->getScalarVar(1)*3.14159265358979/180.0;
// double temp_cohesive = EPS->getScalarVar(2);
tensor DpoDs = EPS->getStress().dpoverds(); // dp/ds
tensor DqoDs = EPS->getStress().dqoverds(); // dq/ds
tensor DthetaoDs = EPS->getStress().dthetaoverds(); // d(theta)/ds
// double a1 = -6*sin(temp_phi)/(3.0-sin(temp_phi));
// double a2 = -6*temp_cohesive*cos(temp_phi)/(3.0-sin(temp_phi));
double alfa = EPS->getScalarVar(1);
// double k = EPS->getScalarVar(2);
double a1 = (3.0*1.7320508076*alfa) / (2.0+1.7320508076*alfa);
double e = (3.0-a1)/(3.0+a1);
double Frou = g_0(theta, e);
double Frou_prime = g_prime(theta, e);
double dFoverdp = alfa*(-3.0);
// double dFoverdq = Frou;
// double dFoverdtheta = q*Frou_prime;
double dFoverdq = Frou/1.7320508076;
double dFoverdtheta = q*Frou_prime/1.7320508076;
dFoverds = DpoDs * dFoverdp +
DqoDs * dFoverdq +
DthetaoDs * dFoverdtheta; // dF/ds
return dFoverds;
}
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;
}
tensor CAMYieldSurface::dFods(const EPState *EPS) const {
tensor dFoverds( 2, def_dim_2, 0.0);
tensor I2("I", 2, def_dim_2);
double p = EPS->getStress().p_hydrostatic();
double q = EPS->getStress().q_deviatoric();
double po = EPS->getScalarVar( 1 );
tensor DpoDs = EPS->getStress().dpoverds();
tensor DqoDs = EPS->getStress().dqoverds();
double dFoverdp = -1.0*M*M*( po - 2.0*p );
double dFoverdq = 2.0*q;
dFoverds = DpoDs * dFoverdp +
DqoDs * dFoverdq;
return dFoverds;
}
//! @brief BJtensor dF/dsigma_ij (this is the place wher a derivativ over yield function is coded)
XC::BJtensor XC::TriFCYieldSurface::dFods(const XC::EPState *EPS ) const
{
BJtensor dFoverds( 2, def_dim_2, 0.0);
//double xi= EPS->getStress().xi(); // functions to get Haigh-Westergard
double rho= EPS->getStress().rho(); // stress invariants for
double th= EPS->getStress().theta(); // explanation look Jeremic&Sture,1998
BJtensor DpoDs= EPS->getStress().dpoverds(); // functions to get already defined
BJtensor DqoDs= EPS->getStress().dqoverds(); // drivatives of p, q and theta which are defined
BJtensor DtoDs= EPS->getStress().dthetaoverds(); // in stress.cpp file. With method getStress()
// it is made sure that function is filled with curent stress
// some parametres neccecary to define yield function and make calculation more transparent
double el= EPS->getScalarVar(1); // parameters called through
//double c= EPS->getScalarVar(2); // definitions of 'set EPS'
double b1= pow (3.,(1./2.) );
double b2= pow (2.,(1./2.) );
//double b3= pow (1.5,(1./2.) );
double b4= pow (6.,(1./2.) );
double a4= 3.0*((fcomp * fcomp) - (ftens * ftens)); // variables neccecary to define
double a5= (fcomp * ftens); // factor m
double a6= (el/(1.0+ el)); // which is an expresion for
double m= a4*a6/a5; // friction parameter
// William warnke function
double ww1= 4.0*(1.0-el*el)*cos(th)*cos(th) + (2.0*el-1.0)*(2.0*el-1.0);
double ww2= 2.0*(1.0-el*el)*cos(th) +
(2.0*el-1)*pow((4.0*(1.0-el*el)*cos(th)*cos(th) +
5.0*el*el -4.0*el),(1./2.));
double ww= ww1/ww2;
//derivation of the William Warnke fuction over theta
// some factors enabling me to check the function. It might not be
// the example of clearness but it was clear to me at the time I
// wrote this and to be honest function is really ugly
double dWW1= (-1.0 + 2.0 * el) ;
double dWW2= (1.0 - el * el) ;
double dWW3= cos(th);
double dWW4= cos(th) * cos(th);
double dWW5= sin(th);
double dWW6= pow ( ( -4.0 * el + 5.0 * el * el + 4.0 * dWW2 * dWW4 ) , (1.0/2.0 ) );
double dWW7= -8.0 * dWW2 * dWW3 * dWW5;
double dWW8= 2.0 * dWW2 * dWW3;
double dWW9= dWW1 * dWW6;
double dWW10 = dWW1 * dWW1 + 4.0 * dWW2 * dWW4;
double dWW11 = -2.0 * dWW2 * dWW5;
double dWW12 = (4.0 * dWW1 * dWW2 * dWW3 * dWW5) / dWW6;
double dWW13= dWW10 * (dWW11 - dWW12);
double dWW14= (2.0 * dWW2 * dWW3) + (dWW1 * dWW6);
//William Warnke fuction derived over theta
double dWWodth= (dWW7 / (dWW8 + dWW9)) - (dWW13 / (dWW14 * dWW14));
double dFoverdp= ( (3.0/b1) * m/(b1*fcomp) ); // derivation of yield function over xi
double dFoverdq= ((( 3.0*rho/(fcomp*fcomp)) + ( m*ww/(b4*fcomp)))* b2/b1 ); // derivation of yield function over rho
double dFoverdt= ( (m*rho/(b4*fcomp) )*dWWodth ); // derivation of yield function over theta
dFoverds= DpoDs * dFoverdp + // factors are added to this function to take into
DqoDs * dFoverdq + // account small differences between Haigh - Westergard
DtoDs * dFoverdt; // coordinats and defined p an q functions. Vnesel sem jih v vrste 174-175
// ker definica BJ tenzorja ne dopusca deljenje ce ni v tenzoski obliki
return dFoverds;
}
