scalar P_alpha(scalar x,sasfit_param * param)
{
ALPHA = x;
if (EPSILON == 1.0) {
return P_theta(1.0,param)*sin(ALPHA);
} else {
return sasfit_integrate(0.0,M_PI/2.0,&P_theta,param)*2.0/M_PI*sin(ALPHA);
}
}
void umat_plasticity_kin_iso_CCP(const vec &Etot, const vec &DEtot, vec &sigma, mat &Lt, mat &L, vec &sigma_in, const mat &DR, const int &nprops, const vec &props, const int &nstatev, vec &statev, const double &T, const double &DT, const double &Time, const double &DTime, double &Wm, double &Wm_r, double &Wm_ir, double &Wm_d, const int &ndi, const int &nshr, const bool &start, const int &solver_type, double &tnew_dt)
{
UNUSED(nprops);
UNUSED(nstatev);
UNUSED(Time);
UNUSED(DTime);
UNUSED(nshr);
UNUSED(tnew_dt);
//From the props to the material properties
double E = props(0);
double nu= props(1);
double alpha_iso = props(2);
double sigmaY = props(3);
double k=props(4);
double m=props(5);
double kX = props(6);
//definition of the CTE tensor
vec alpha = alpha_iso*Ith();
///@brief Temperature initialization
double T_init = statev(0);
//From the statev to the internal variables
double p = statev(1);
vec EP(6);
EP(0) = statev(2);
EP(1) = statev(3);
EP(2) = statev(4);
EP(3) = statev(5);
EP(4) = statev(6);
EP(5) = statev(7);
///@brief a is the internal variable associated with kinematical hardening
vec a = zeros(6);
a(0) = statev(8);
a(1) = statev(9);
a(2) = statev(10);
a(3) = statev(11);
a(4) = statev(12);
a(5) = statev(13);
//Rotation of internal variables (tensors)
EP = rotate_strain(EP, DR);
a = rotate_strain(a, DR);
///@brief Initialization
if(start)
{
//Elstic stiffness tensor
L = L_iso(E, nu, "Enu");
T_init = T;
vec vide = zeros(6);
sigma = vide;
EP = vide;
a = vide;
p = 0.;
Wm = 0.;
Wm_r = 0.;
Wm_ir = 0.;
Wm_d = 0.;
}
//Additional parameters and variables
vec X = kX*(a%Ir05());
double Hp=0.;
double dHpdp=0.;
if (p > iota) {
dHpdp = m*k*pow(p, m-1);
Hp = k*pow(p, m);
}
else {
dHpdp = 0.;
Hp = 0.;
}
//Variables values at the start of the increment
vec sigma_start = sigma;
vec EP_start = EP;
vec a_start = a;
vec X_start = X;
double A_p_start = -Hp;
vec A_a_start = -X_start;
//Variables required for the loop
vec s_j = zeros(1);
s_j(0) = p;
vec Ds_j = zeros(1);
vec ds_j = zeros(1);
///Elastic prediction - Accounting for the thermal prediction
vec Eel = Etot + DEtot - alpha*(T+DT-T_init) - EP;
sigma = el_pred(L, Eel, ndi);
//Define the plastic function and the stress
vec Phi = zeros(1);
mat B = zeros(1,1);
vec Y_crit = zeros(1);
double dPhidp=0.;
vec dPhida = zeros(6);
vec dPhidsigma = zeros(6);
double dPhidtheta = 0.;
//Compute the explicit flow direction
vec Lambdap = eta_stress(sigma-X);
vec Lambdaa = eta_stress(sigma-X);
std::vector<vec> kappa_j(1);
kappa_j[0] = L*Lambdap;
mat K = zeros(1,1);
//Loop parameters
int compteur = 0;
double error = 1.;
//Loop
for (compteur = 0; ((compteur < maxiter_umat) && (error > precision_umat)); compteur++) {
p = s_j(0);
if (p > iota) {
dHpdp = m*k*pow(p, m-1);
Hp = k*pow(p, m);
}
else {
dHpdp = 0.;
Hp = 0.;
}
dPhidsigma = eta_stress(sigma-X);
dPhidp = -1.*dHpdp;
dPhida = -1.*kX*(eta_stress(sigma - X)%Ir05());
//compute Phi and the derivatives
Phi(0) = Mises_stress(sigma-X) - Hp - sigmaY;
Lambdap = eta_stress(sigma-X);
Lambdaa = eta_stress(sigma-X);
kappa_j[0] = L*Lambdap;
K(0,0) = dPhidp + sum(dPhida%Lambdaa);
B(0, 0) = -1.*sum(dPhidsigma%kappa_j[0]) + K(0,0);
Y_crit(0) = sigmaY;
Fischer_Burmeister_m(Phi, Y_crit, B, Ds_j, ds_j, error);
s_j(0) += ds_j(0);
EP = EP + ds_j(0)*Lambdap;
a = a + ds_j(0)*Lambdaa;
X = kX*(a%Ir05());
//the stress is now computed using the relationship sigma = L(E-Ep)
Eel = Etot + DEtot - alpha*(T + DT - T_init) - EP;
sigma = el_pred(L, Eel, ndi);
}
//Computation of the increments of variables
vec Dsigma = sigma - sigma_start;
vec DEP = EP - EP_start;
double Dp = Ds_j[0];
vec Da = a - a_start;
if (solver_type == 0) {
//Computation of the tangent modulus
mat Bhat = zeros(1, 1);
Bhat(0, 0) = sum(dPhidsigma%kappa_j[0]) - K(0,0);
vec op = zeros(1);
mat delta = eye(1,1);
for (int i=0; i<1; i++) {
if(Ds_j[i] > iota)
op(i) = 1.;
}
mat Bbar = zeros(1,1);
for (int i = 0; i < 1; i++) {
for (int j = 0; j < 1; j++) {
Bbar(i, j) = op(i)*op(j)*Bhat(i, j) + delta(i,j)*(1-op(i)*op(j));
}
}
mat invBbar = zeros(1, 1);
mat invBhat = zeros(1, 1);
invBbar = inv(Bbar);
for (int i = 0; i < 1; i++) {
for (int j = 0; j < 1; j++) {
invBhat(i, j) = op(i)*op(j)*invBbar(i, j);
}
}
std::vector<vec> P_epsilon(1);
P_epsilon[0] = invBhat(0, 0)*(L*dPhidsigma);
std::vector<double> P_theta(1);
P_theta[0] = dPhidtheta - sum(dPhidsigma%(L*alpha));
Lt = L - (kappa_j[0]*P_epsilon[0].t());
}
else if(solver_type == 1) {
sigma_in = -L*EP;
}
double A_p = -Hp;
vec A_a = -X;
double Dgamma_loc = 0.5*sum((sigma_start+sigma)%DEP) + 0.5*(A_p_start + A_p)*Dp + 0.5*sum((A_a_start + A_a)%Da);
//Computation of the mechanical and thermal work quantities
Wm += 0.5*sum((sigma_start+sigma)%DEtot);
Wm_r += 0.5*sum((sigma_start+sigma)%(DEtot-DEP)) - 0.5*sum((A_a_start + A_a)%Da);
Wm_ir += -0.5*(A_p_start + A_p)*Dp;
Wm_d += Dgamma_loc;
///@brief statev evolving variables
//statev
statev(0) = T_init;
statev(1) = p;
statev(2) = EP(0);
statev(3) = EP(1);
statev(4) = EP(2);
statev(5) = EP(3);
statev(6) = EP(4);
statev(7) = EP(5);
statev(8) = a(0);
statev(9) = a(1);
statev(10) = a(2);
statev(11) = a(3);
statev(12) = a(4);
statev(13) = a(5);
}
