A simplified finite strain plasticity model for metallic applications

Abstract

In this work, a finite strain elastoplastic model is proposed within a total Lagrangian framework based on multiplicative decomposition of the deformation gradient, with several simplifications aimed at facilitating more concise code implementation and enhancing computational efficiency. Pre- and post-processors are utilised for conversion between different stress and strain measures, sandwiching the core plastic flow algorithm which preserves the small strain form. Simplifications focus on the pre- and post-processor components by substituting certain arithmetic operations associated with high computational demands with simpler ones without compromising accuracy. These modifications are based on assumptions, which are valid for most metals, that the elastic strains are small compared to plastic strains, and that the incremental plastic deformations are small for each step. In addition, the consistent tangent modulus matrix is derived in a reduced form, both for the general full model and the new simplified model, facilitating more straightforward computations in both cases. The models are verified against two classical numerical examples where favourable comparisons are achieved. Overall, the simplified model is shown to provide a significant reduction in computational demand for the two considered numerical problems, with negligible deviation in the results compared to the full model, subject to fulfilling the underlying assumptions with the adoption of a sufficiently small step size.