Solving elastoplasticity problems by the Asymptotic Numerical Method: Influence of the parameterizations

In this paper, we will introduce and discuss new parameterizations to solve elastoplasticity problems by using the Asymptotic Numerical Method (ANM). The elastic–plastic transition and the elastic unloading are taken into account by using the regularization technique proposed in Assidi et al. (2009) [1] and Zahrouni et al. (2005) [2]. The ANM is a family of algorithms for path following problems; each ANM step is based on the computation of truncated vectorial series with respect to a path parameter “a” (Cochelin et al., 1994 [3]). We present and discuss different parameterizations in ANM algorithm for solving elastoplasticity problems, namely the definition of the path parameter “a”; two concepts of parameterization are introduced and compared: a Riks type parameterization which is a combination of both load parameter and time and a parameterization based on the minimization of a rest (Mottaqui et al., 2010 [4] and [5]). We will also discuss and compare the definitions of the step length in the case of elastoplasticity. Aiming to analyze the quality of the solutions, we will compute and study the residue of all the equations for different values of tolerance parameters of the ANM continuation. To illustrate the performance of these proposed parameterizations and step length definitions, we will give numerical comparisons on structural elastoplasticity problems with the Newton–Raphson method.