An R-Minimum Strategy for Finite Element Modeling of Non-linear Deformation Behaviours of Rate-Dependent Materials

An R-minimum strategy, which was proposed and successfully applied to analyse the non-linear finite deformation behaviours of elasto-plastic materials (e.g. [1] [2]), is extended and applied here to simulate the deformation behaviours of the rate-dependent materials. It involves no iterations, thus belongs to the static-explicit algorithm and avoids the convergence problem resulting from nonlinearities. The R-minimum strategy based adaptive control scheme of the time step size is proposed and applied to the analysis of both time-dependent and -independent viscous materials and verified through the comparison with the others to demonstrate the stability, efficiency and usefulness of this algorithm.