Unified stress update algorithms for the numerical simulation of large deformation elasto-plastic and elasto-viscoplastic processes

This paper is concerned with unified stress update algorithms for elastoplastic and elasto-viscoplastic constitutive equations for metals submitted to large deformations. We present here a newly developed time integration algorithm which is, in the case of J2 flow theory material behavior, an extension to the viscoplastic range of the classical radial return algorithm for plasticity. The resulting unified implicit algorithm is both efficient and very inexpensive. Moreover, if there is no viscosity effect (rate-independent material) the presented algorithm degenerates exactly into the classical radial return algorithm for plasticity.