Efficient return algorithms for associated plasticity with multiple yield planes

TLDR

The paper introduces a new return method for implicit integration of linear isotropic yield criteria. The method operates in principal stress space, providing closed‑form plastic corrector stresses and computing infinitesimal and consistent elastoplastic constitutive matrices for returns to a single yield plane, a line at the intersection of two planes, or a point at the intersection of three or more planes. The closed‑form return formulae eliminate the need for iteration, and the method is demonstrated using the Mohr–Coulomb yield criterion. © 2005 John Wiley & Sons, Ltd.

Abstract

Abstract A new return method for implicit integration of linear isotropic yield criteria is presented. The basic idea is to perform all the manipulations in the principal stress space and thereby achieve very simple formulae for calculating the plastic corrector stresses, based on the constant gradient of such criteria. The return formulae are in closed form and no iteration is required. The method accounts for three types of stress return: return to a single yield plane, to a discontinuity line at the intersection of two yield planes and to a discontinuity point at the intersection between three or more yield planes. The infinitesimal and the consistent elastoplastic constitutive matrix are calculated for each type of stress return, as are the conditions to ascertain which type of return is required. The method is exemplified with the Mohr–Coulomb yield criterion. Copyright © 2005 John Wiley & Sons, Ltd.