Finite element modelling of non-linear deformation of rate-dependent materials using a R-minimum strategy

A R-minimum strategy, which was proposed and successfully applied to analyse the non-linear rate-independent finite deformation (including the thermal–mechanical coupling and frictional contact) of elasto-plastic materials, is extended and applied here to simulate the deformation of 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 related analysis of the rate-dependent materials with both the time-dependent and the time-independent viscosity. Both the simple benchmark test and the practical application in evaluation of the effect of the Earth materials on its response to the centrifugal force are carried out to demonstrate the stability, efficiency and usefulness of this algorithm.