On the efficiency of algorithms for computing a micromechanical constitutive equations coupled with damage

The numerical solution of non-linear constitutive relations problems represents an important topic since it needs relatively an important computational time, especially for micromechanical approaches arising in rate-dependent non-associated elasto-inelasticity coupled with damage. Thus, a recent developed micromechanical model with damage induced anisotropy concept is used [1] to study numerically its responses under different cyclic loading paths. the main goal of this study is based on the formulation and the numerical integration of the model describing the cyclic plasticity behavior. Three well-known algorithms are used comparing their computing times and precisions for different cyclic loadings. These are the algorithms of Runge–Kutta of 2nd and 5th orders with an adaptive step (noted respectively by RK2 and RK5). The algorithm of Burlisch–Stöer (MDP) is also presented and applied. According to the obtained results, it appears that the algorithm MDP gives the best compromise between the computational time and its precision with respect to the used algorithms for such a model especially in the case where the damage is coupled with elasto-inelastic behavior.