An Extension of the Radial Return Algorithm to Account for Visco-plasticity and Rate-dependent Effects in Frictional Contact

This paper deals with unified elastoplastic and elastic-viscoplastic constitutive equations for metals submitted to large deformations. We present here a newly developed time integration algorithm which is an extension to the viscoplastic range of the classical radial return algorithm for plasticity. The resulting implicit algorithm is both efficient and very inexpensive. This algorithm is also subsequently extended to frictional problems where it allows a generalization of the classical Coulomb dry friction criterion to a criterion depending on the relative slip velocity such as those encountered in hydrodynamic regime. Moreover, a consistent tangent modulus for frictional contact is also presented. Thus, the proposed law can be implemented very efficiently in both explicit and implicit finite element codes.