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energy_balance.cxx
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void update_stress_energy(const Variables& var, tensor_t& stress, double_vec& stressyy, double_vec& thermal_stress, double_vec& dP,
tensor_t& strain, double_vec& plstrain, double_vec& delta_plstrain, double_vec& dtemp,
tensor_t& strain_rate, double_vec& power, double_vec& tenergy, double_vec& venergy, double_vec& denergy)
{
const int rheol_type = var.mat->rheol_type;
#pragma omp parallel for default(none) \
shared(var, stress, stressyy, power, dP, dtemp, strain, plstrain, delta_plstrain, strain_rate, std::cerr)
for (int e=0; e<var.nelem; ++e) {
// stress, strain and strain_rate of this element
double* s = stress[e];
double& syy = stressyy[e];
double* es = strain[e];
double* edot = strain_rate[e];
// anti-mesh locking correction on strain rate
if(1){
double div = trace(edot);
//double div2 = ((*var.volume)[e] / (*var.volume_old)[e] - 1) / var.dt;
for (int i=0; i<NDIMS; ++i) {
edot[i] += ((*var.edvoldt)[e] - div) / NDIMS; // XXX: should NDIMS -> 3 in plane strain?
}
}
double dT = 0;
const int *conn = (*var.connectivity)[e];
for (int i = 0; i < NODES_PER_ELEM; ++i) {
dT += dtemp[conn[i]];
}
dT /= NODES_PER_ELEM;
double de[NSTR];
double alpha = var.mat->alpha(e);
// double thermal_strain = (alpha * dT)/3;
// normal components
for (int i = 0; i<NDIMS; ++i){
es[i] += (edot[i] * var.dt); // + thermal_strain;
de[i] = (edot[i] * var.dt); // + thermal_strain;
}
// Shear components
for (int i = NDIMS; i<NSTR; ++i) {
es[i] += edot[i] * var.dt;
de[i] = edot[i] * var.dt;
}
switch (rheol_type) {
case MatProps::rh_elastic:
{
double bulkm = var.mat->bulkm(e);
double shearm = var.mat->shearm(e);
#ifdef THREED
double pressure_old=-(s[0] + s[1] + s[2]) / NDIMS;
#else
double pressure_old=-(s[0] + s[1]) / NDIMS;
#endif
elastic(bulkm, shearm, de, s);
#ifdef THREED
double pressure_new = (-(s[0] + s[1] + s[2]) / NDIMS);
#else
double pressure_new=-(s[0] + s[1] + syy) / 3;
#endif
dP[e]=(pressure_new-pressure_old);
}
break;
case MatProps::rh_viscous:
{
double bulkm = var.mat->bulkm(e);
double viscosity = var.mat->visc(e);
double total_dv = trace(es);
viscous(bulkm, viscosity, total_dv, edot, s);
}
break;
case MatProps::rh_maxwell:
{
double bulkm = var.mat->bulkm(e);
double shearm = var.mat->shearm(e);
double viscosity = var.mat->visc(e);
double dv = (*var.volume)[e] / (*var.volume_old)[e] - 1;
maxwell(bulkm, shearm, viscosity, var.dt, dv, de, s);
}
break;
case MatProps::rh_ep:
{
double t_power = 0;
double v_power = 0;
double d_power = 0;
double depls = 0;
double bulkm = var.mat->bulkm(e);
double shearm = var.mat->shearm(e);
double amc, anphi, anpsi, hardn, ten_max;
var.mat->plastic_props(e, plstrain[e],
amc, anphi, anpsi, hardn, ten_max);
int failure_mode;
#ifdef THREED
double pressure_old = -(s[0]+s[1]+s[2])/NDIMS;
#else
double pressure_old = -(s[0]+s[1]+ syy)/3.0; // plane strain
#endif
double thermal_stress = -bulkm * alpha * dT;;
thermal_stress[e] += thermal_stress;
if (var.mat->is_plane_strain) {
elasto_plastic2d(bulkm, shearm, t_power,v_power, d_power, amc, anphi, anpsi, hardn, ten_max, de, depls, s, syy, failure_mode, thermal_stress);
}
else {
elasto_plastic(bulkm, shearm, amc, anphi, anpsi, hardn, ten_max,
de, depls, s, failure_mode);
}
#ifdef THREED
double pressure_new = -(s[0]+s[1]+s[2])/NDIMS;
#else
double pressure_new = -(s[0]+s[1]+syy)/3;
#endif
dP[e] = (pressure_new-pressure_old);
plstrain[e] += depls;
delta_plstrain[e] = depls;
power[e] = t_power;
tenergy[e] += t_power;
venergy[e] += v_power;
denergy[e] += d_power;
}
break;
case MatProps::rh_evp:
{
double t_power = 0;
double v_power = 0;
double d_power = 0;
double depls = 0;
double bulkm = var.mat->bulkm(e);
double shearm = var.mat->shearm(e);
double viscosity = var.mat->visc(e);
double dv = (*var.volume)[e] / (*var.volume_old)[e] - 1;
// stress due to maxwell rheology
double sv[NSTR];
for (int i=0; i<NSTR; ++i) sv[i] = s[i];
maxwell(bulkm, shearm, viscosity, var.dt, dv, de, sv);
double svII = second_invariant2(sv);
double amc, anphi, anpsi, hardn, ten_max;
var.mat->plastic_props(e, plstrain[e],
amc, anphi, anpsi, hardn, ten_max);
// stress due to elasto-plastic rheology
double sp[NSTR], spyy;
for (int i=0; i<NSTR; ++i) sp[i] = s[i];
int failure_mode;
double dT = 0;
const int *conn = (*var.connectivity)[e];
for (int i = 0; i < NODES_PER_ELEM; ++i) {
dT += dtemp[conn[i]];
}
dT /= NODES_PER_ELEM;
if (var.mat->is_plane_strain) {
spyy = syy;
elasto_plastic2d(bulkm, shearm, t_power,v_power, d_power, amc, anphi, anpsi, hardn, ten_max,
de, depls, s, syy, failure_mode, thermal_stress);
}
else {
elasto_plastic(bulkm, shearm, amc, anphi, anpsi, hardn, ten_max,
de, depls, sp, failure_mode);
}
double spII = second_invariant2(sp);
// use the smaller as the final stress
if (svII < spII)
for (int i=0; i<NSTR; ++i) s[i] = sv[i];
else {
for (int i=0; i<NSTR; ++i) s[i] = sp[i];
plstrain[e] += depls;
delta_plstrain[e] = depls;
syy = spyy;
}
}
break;
default:
std::cerr << "Error: unknown rheology type: " << rheol_type << "\n";
std::exit(1);
break;
}
// std::cerr << "stress " << e << ": ";
// print(std::cerr, s, NSTR);
// std::cerr << '\n';
}
}
void update_temperature(const Param ¶m, const Variables &var, double_vec &temperature,
double_vec &temp_power, double_vec &temp_pressure, double_vec &temp_density,
double_vec &dtemp,double_vec &dP, double_vec &tdot, tensor_t &stress,
tensor_t &strain_rate, double_vec &stressyy, double_vec &drho, double_vec &rho,
double_vec &power, double_vec &powerTerm, double_vec &pressureTerm, double_vec &densityTerm)
{
tdot.assign(var.nnode, 0);
powerTerm.assign(powerTerm.size(),0);
pressureTerm.assign(pressureTerm.size(),0);
densityTerm.assign(densityTerm.size(), 0);
class ElemFunc_temperature : public ElemFunc
{
private:
const Variables &var;
const double_vec &temperature;
double_vec &temp_power;
double_vec &temp_pressure;
double_vec &temp_density;
double_vec &dtemp;
double_vec &dP;
double_vec &drho;
double_vec ρ
tensor_t &stress;
tensor_t &strain_rate;
double_vec &stressyy;
double_vec &power;
double_vec &powerTerm;
double_vec &pressureTerm;
double_vec &densityTerm;
double_vec ⃛
public:
ElemFunc_temperature(const Variables &var, const double_vec &temperature, double_vec &temp_power,
double_vec &temp_pressure, double_vec &temp_density, double_vec &dtemp,
double_vec &dP, tensor_t &stress, tensor_t &strain_rate, double_vec &stressyy,
double_vec &drho, double_vec &rho, double_vec &power, double_vec &powerTerm,
double_vec &pressureTerm, double_vec &densityTerm, double_vec &tdot) :
var(var), temperature(temperature), temp_power(temp_power), temp_pressure(temp_pressure),
temp_density(temp_density), dtemp(dtemp), dP(dP), stress(stress), strain_rate(strain_rate),
stressyy(stressyy), drho(drho), rho(rho), power(power),pressureTerm(pressureTerm),
powerTerm(powerTerm), densityTerm(densityTerm),tdot(tdot) {};
void operator()(int e)
{
// diffusion matrix
double D[NODES_PER_ELEM][NODES_PER_ELEM];
const int *conn = (*var.connectivity)[e];
double kv = var.mat->k(e) * (*var.volume)[e]; // thermal conductivity * volumn
double* s = stress[e];
double* edot = strain_rate[e];
const double *shpdx = (*var.shpdx)[e];
#ifdef THREED
const double *shpdy = (*var.shpdy)[e];
#endif
const double *shpdz = (*var.shpdz)[e];
for (int i=0; i<NODES_PER_ELEM; ++i) {
for (int j=0; j<NODES_PER_ELEM; ++j) {
#ifdef THREED
D[i][j] = (shpdx[i] * shpdx[j] +
shpdy[i] * shpdy[j] +
shpdz[i] * shpdz[j]);
#else
D[i][j] = (shpdx[i] * shpdx[j] +
shpdz[i] * shpdz[j]);
#endif
}
}
double temp = 0;
for (int i = 0; i < NODES_PER_ELEM; ++i) {
temp += temperature[conn[i]];
}
double& syy = stressyy[e];
#ifdef THREED
double P = -(s[0] + s[1] + s[2]) / NDIMS;
double vedot = edot[0]+ edot[1] + edot[2];
#else
double P = -(s[0] + s[1] + syy) / 3;
double vedot = edot[0]+ edot[1];
#endif
double alpha = var.mat->alpha(e);
double T = temp / NODES_PER_ELEM;
double plastic = (*var.power)[e] * (*var.volume)[e]/NODES_PER_ELEM;
double pressure = T * alpha * (*var.dP)[e] * (*var.volume)[e] / NODES_PER_ELEM;
double den = P * T * alpha * vedot * (*var.volume)[e] / NODES_PER_ELEM;
for (int i = 0; i < NODES_PER_ELEM; ++i) {
double diffusion = 0;
powerTerm[conn[i]] += plastic;
pressureTerm[conn[i]] += pressure;
densityTerm[conn[i]] += den;
for (int j = 0; j<NODES_PER_ELEM; ++j)
diffusion += D[i][j] * temperature[conn[j]];
tdot[conn[i]] += diffusion * kv;
}
}
} elemf(var, temperature, temp_power, temp_pressure, temp_density, dtemp, dP, stress, strain_rate,
stressyy, drho, rho, power, powerTerm, pressureTerm, densityTerm, tdot);
loop_all_elem(var.egroups, elemf);
// Combining temperature update and bc in the same loop for efficiency,
// since only the top boundary has Dirichlet bc, and all the other boundaries
// have no heat flux bc.
#pragma omp parallel for default(none) \
shared(var, param, tdot, temperature, temp_power, temp_pressure, temp_density, \
dtemp, powerTerm, pressureTerm, densityTerm, std::cout);
for (int n=0; n<var.nnode; ++n) {
double temp_old = temperature[n];
double diffusion_term = -(tdot[n] * var.dt) / (*var.tmass)[n];
double power_term = powerTerm[n] / (*var.tmass)[n];
double pressure_term = pressureTerm[n] / (*var.tmass)[n];
double density_term = densityTerm[n] / (*var.tmass)[n];
double surface_temp = param.bc.surface_temperature;
if ((*var.bcflag)[n] & BOUNDZ1){
temperature[n] = surface_temp;
temp_power[n] = surface_temp;
temp_pressure[n] = surface_temp;
temp_density[n] = surface_temp;
dtemp[n] = temp_old - temperature[n];
}else{
temperature[n] += (diffusion_term) + (power_term) + (pressure_term) + (density_term);
temp_power[n] += power_term;
temp_pressure[n] += pressure_term;
temp_density[n] += density_term;
dtemp[n] = temperature[n] - temp_old;
}
}
}