A return mapping algorithm for isotropic elastoplasticity

Abstract

Abstract A return mapping algorithm is presented for the numerical time integration of the constitutive equations for elastoplasticity with isotropic yield surfaces, constructed from all three invariants of the stress tensor. Based on the first‐order backward Euler difference formula (BDF), the governing equations for the stresses are solved in the space of the invariants and the discretized persistence parameter. The stresses are recovered afterwards. The solution concept is applied to a pressure‐independent yield function, expressed in terms of the second and third invariant of the stress tensor. The numerical performance of the method is demonstrated with two examples.