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19 Elastic–Plastic Problems epi = elm.str[ip].sEpi; double epi0 = epi; double f1 = yieldFunction(sig, epi); // Elastic point if (f1 < 0.0) return; // Elastic-plastic point double f0 = yieldFunction(sig0, epi); double r; if (f0 < 0.0) { r = -f0/(f1 - f0); for (int i = 0; i < lv; i++) sig[i] = sig0[i] + dsig[i]*r; double f = yieldFunction(sig, epi); derivYieldFunc(sig, a); double c1 = 0.0; for (int i = 0; i < lv; i++) c1 += a[i]*dsig[i]; r = r - f/c1; } else r = 0.0; // Number of subincrements ( = 1 for midpoint method) int nsub = (FE.epIntegrationTANGENT) ? (int) (f1/(beta*sY))+1 : 1; for (int i = 0; i < lv; i++) { sig[i] = sig0[i] + dsig[i]*r; dsig[i] = (1.0 - r)*dsig[i]/nsub; deps[i] = (1.0 - r)*deps[i]/nsub; } // Subincrement loop: tangent or midpoint method for (int isub = 0; isub < nsub; isub++) { if (FE.epIntegrationTANGENT) tangentStressIncrement(); else midpoint.stressIncrement(); } for (int i = 0; i < lv; i++) elm.str[ip].dStress[i] = sig[i] - sig0[i]; elm.str[ip].dEpi = epi - epi0; }
At the beginning of the class, static arrays and scalars are declared, which are necessary during stress-increment computing. The class constructor calls the constructor of superclass ElasticMaterial. Because of certain complications we do not consider implementation of the elastic–plastic material under plane stress conditions. An error message is generated when the user attempts to solve an elastic– plastic problem under plane stress conditions. If integration of elastic–plastic constitutive equations is performed with a midpoint method (see next section) then the constructor of inner class Midpoint is called. The main logic of the final stress increment computation is contained in method strainToStress. The method obtains Element object elm and integration