Finite element implementation of nearly-incompressible rheological models based on multiplicative decompositions

The present work is concerned with the numerical integration of finite viscoelastic or viscoplastic models. A numerical integration scheme based on the definition of a flow direction and a flow amplitude as in elastoplasticity is proposed. The most original feature of this approach resides in a local correction of the direction and amplitude with a sub-stepping strategy. Comparisons with the results obtained using a classical tensorial integrator based on a Runge-Kutta–Fehlberg scheme are provided. The reliability of the present numerical scheme is investigated with three rheological models two are viscoelastic (Zener and Poynting–Thomson) and one is viscoplastic.