inline tensor2 add_to_tensor2_elems(const tensor2& m, float_type x) { return tensor2(m.shape(), fplus::transform([x](float_type e) -> float_type { return x + e; }, *m.as_vector())); }
inline tensor2 sub_from_tensor2_elems(const tensor2& m, float_type x) { return tensor2(m.shape(), fplus::transform([x](float_type e) -> float_type { return e - x; }, *m.as_vector())); }
tensor2 transform_tensor2(F f, const tensor2& m) { return tensor2(m.shape(), fplus::transform(f, m.as_vector())); }
//================================================================================ const tensor& DM04_PF::Dm_Dkin(const stresstensor &Stre, const straintensor &Stra, const MaterialParameter &MaterialParameter_in) const { const double oneOver3 = 1.0/3.0; const double rt23 = sqrt(2.0/3.0); tensor I2("I", 2, def_dim_2); tensor I4 = I2("ij")*I2("kl"); tensor I4s = ( I4.transpose0110() + I4.transpose0111() ) *0.5; double e0 = gete0(MaterialParameter_in); double e_r = gete_r(MaterialParameter_in); double lambda_c = getlambda_c(MaterialParameter_in); double xi = getxi(MaterialParameter_in); double Pat = getPat(MaterialParameter_in); //double m = getm(MaterialParameter_in); double M_cal = getM_cal(MaterialParameter_in); double cc = getcc(MaterialParameter_in); double A0 = getA0(MaterialParameter_in); double nd = getnd(MaterialParameter_in); stresstensor alpha = getalpha(MaterialParameter_in); stresstensor z = getz(MaterialParameter_in); stresstensor n; stresstensor alpha_d; stresstensor alpha_d_alpha; double g = 0.0; double ec = e_r; double stateParameter = 0.0; double expnd = 1.0; //double ad = 0.0; double A_d = 0.0; double B = 1.0; double C = 0.0; double D0 = 0.0; stresstensor s_bar; double norm_s = 0.0; double epsilon_v = 0.0; double e = e0; double J3D; double cos3theta = 0.0; double z_n = 0.0; double alpha_n = 0.0; double s_n = 0.0; double p = Stre.p_hydrostatic(); stresstensor s = Stre.deviator(); s_bar = s - (alpha *p); norm_s = sqrt( (s_bar("ij")*s_bar("ij")).trace() ); if (p > 0.0 && norm_s > 0.0) n = s_bar * (1.0/norm_s); J3D = n.Jinvariant3(); cos3theta = -3.0*sqrt(6.0) *J3D; if (cos3theta > 1.0) cos3theta = 1.0; if (cos3theta < -1.0) cos3theta = -1.0; g = getg(cc, cos3theta); if ( (p/Pat) >= 0.0 ) ec = getec(e_r, lambda_c, xi, Pat, p); epsilon_v = Stra.Iinvariant1(); e = e0 + (1.0 + e0) *epsilon_v; stateParameter = e - ec; expnd = exp(nd*stateParameter); alpha_n = (alpha("ij")*n("ij")).trace(); s_n = (s("ij")*n("ij")).trace(); // way 1 //ad = g*M_cal*expnd - m; //D0 = rt23 * ad - alpha_n; // way 2 D0 = rt23*g*M_cal*expnd - s_n /p; z_n = (z("ij")*n("ij")).trace(); if (z_n < 0.0) z_n = 0.0; A_d = A0 * (1.0 + z_n); B = 1.0 + 1.5 *((1.0-cc)/cc) *g *cos3theta; C = 3.0 *sqrt(1.5) *((1.0-cc)/cc) *g; tensor n_n = n("ik")*n("kj"); n_n.null_indices(); tensor nt_nt = n("ij")*n("kl"); nt_nt.null_indices(); tensor alpha_I = alpha("ij")*I2("kl"); alpha_I.null_indices(); tensor n_I = n("ij")*I2("kl"); n_I.null_indices(); // dn_dalpha: tensor dn_da = nt_nt - I4s; dn_da = dn_da *(p/norm_s); // dcos3theta_dalpha: tensor dcos3theta_da = dn_da("ijmn")*n_n("ji"); dcos3theta_da.null_indices(); dcos3theta_da = dcos3theta_da *(-3.0*sqrt(6.0)); // dg_da: tensor dg_da = dcos3theta_da *(g*g*(1.0-cc)/(2.0*cc)); // dB_da: tensor dB_da = (dg_da*cos3theta + dcos3theta_da*g) *(1.5*(1.0-cc)/cc); // dC_ds: tensor dC_da = dg_da *(3.0*sqrt(1.5)*(1.0-cc)/cc); // dR_da: tensor tensor1 = n("ij")*dB_da("mn"); tensor1.null_indices(); tensor tensor2 = n_n - I2 *oneOver3; tensor tensor3 = tensor2("ij")*dC_da("mn"); tensor3.null_indices(); tensor tensor4 = n("kj")*dn_da("ikmn"); tensor4.null_indices(); tensor4.transpose1100(); tensor dR_da = dn_da *B + tensor1 + tensor4 *(2.0*C) + tensor3; // dad_da: tensor dad_da = dg_da *(M_cal*expnd); // dD_da: // way 1 //tensor tensor5 = alpha("pq")*dn_da("pqmn"); // tensor5.null_indices(); //tensor dD_da = (dad_da *rt23 - n - tensor5) *(-A_d); // way 2 tensor tensor5 = s("pq")*dn_da("pqmn"); tensor5.null_indices(); tensor dD_da = (dad_da *rt23 - tensor5 *(1.0/p)) *(-A_d); if (z_n > 0.0) { tensor tensor6 = z("pq")*dn_da("pqmn"); tensor6.null_indices(); dD_da += tensor6 *(-A0*D0); } // dm_da: tensor tensor7 = I2("ij")*dD_da("mn"); tensor7.null_indices(); PlasticFlow::PF_tensorR4 = dR_da + tensor7 *oneOver3; return PlasticFlow::PF_tensorR4; }