A Model for Large Deformations of Elasto-Viscoplastic Solids at Finite Strain: Computational Issues

Abstract

In the context of general isothermal processes, issues related to the constitutive modelling and computational treatment of large deformations of elasto-viscoplastic solids at finite strains are examined employing logarithmic stretches as strain measures. The material is assumed to remain isotropic throughout the process of deformation. A strain-energy function for isotropic elastic materials is utilized, which leads to a linear stress-strain relationship and constant and isotropic elastic modulus in material setting. A computationally effective scheme is proposed based on a fully implicit integration of the constitutive equations, which is exact for elastic processes. It is pointed out that within the proposed framework the small strain integration algorithms and corresponding consistent tangent operators automatically extend to the finite strain regime. The versatility and robustness of the method is illustrated through the numerical analysis of a structural problem typical for the metal forming applications, capturing all silent features of this complex problem and resulting in failure by the strain localisation.