Convergence acceleration by Padé approximants in the ANM algorithm for large strain elasto-plasticity

Abstract

In this work, we show how to introduce improved vectorial Padé approximants in the Asymptotic Numerical Method (ANM) for solving elasto-plasticity problems in finite transformation. In this way, we have proposed an algorithm, based on Taylor series which has shown its efficiency for computing elasto-plastic structures in large deformations. We show, in this paper, how to accelerate the convergence of ANM using a new class of vectorial Padé approximants instead of the Taylor series in the case of finite elasto-plasticity. The efficiency and robustness of the proposed algorithm are tested on 2 D examples. These examples show that some vectorial Padé approximants allow to reduce by 30% the number of tangent matrices. • The paper shows how to introduce improved vectorial Padé approximants in the Asymptotic Numerical Method (ANM) for solving elasto-plasticity problems in finite transformation. • Work shows how to accelerate the convergence of ANM using new Padé approximants. • Two examples show that some vectorial Padé approximants allow to reduce by 30% the number of tangent matrices.