Implicit algorithm and numeralisation of microscopic constitutive relations

Abstract

Stability, efficiency and precision are key problems in numeralisation of rate dependent microscopic constitutive relations (RDMCR). In order to deal with these problems effectively, a time incremental model is presented in the intermediate configuration, which is simplified into non-linear equations set only containing six unknown scalars. The homotopy autochanging continuation method is adopted for its solution. The studies indicate that the method is stable, efficient and convergent at random initial values, which is then combined with Newton method to ensure high precision. Based on the above algorithm, RDMCR is implemented in Abaqus/Explicit by developing user subroutine Vumat. The reliability of the algorithm is verified. Further studies indicate that anisotropy, rate sensitivity coefficient and loading speed have effects on the deformation of materials. The results are considered reasonable in the light of theoretical analysis, which indicate that the algorithm has a good prospect of application.