13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- New strategy for identification parameters of a micromechanical model coupled with ductile damage Jean-Claude Rakotoarisoaa,c , Donné Razafindramary b,c, Akrum Abdul-Latifb,c,* a Université d’Antsiranana Madagascar b Université Paris 8 c Laboratoire d’Ingénierie des Systèmes Mécaniques et des Matériaux (LISMMA), Supméca, 3, rue Fernand Hainaut - 93407 St Ouen Cedex – France *e-mail: aabdul@iu2t.univ-paris8.fr Abstract A low-cyclic fatigue micromechanical model proposed recently [1] for emphasizing the concept of damage induced anisotropy is used. The solution of these nonlinear constitutive relations is an important topic since it requires an important computational time. With a high nonlinearity due to damage, the identification of model parameters represents consequently an important subject. In fact, a combination of the genetic algorithm (for the global optimization) with pattern search algorithm (for the local optimization) is proposed. A comparative study is conducted under complex cyclic loadings showing the ability of the proposed approach in calibrating model parameters. Keywords Low-cyclic fatigue, parameters identification, global minimum and local minimum optimization 1. Introduction Despite the existence of increasingly powerful computers, the progress in the constitutive equations development is continuous and can be conducted via computational optimization process. Several types of modes like micromechanical approaches are proposed for describing mechanical complex phenomena. Non-linear responses under cyclic loading, for example, make the related resolutions very expensive in computing time and in memory capacity. Numerically, it has been recently reported that the algorithm of Burlisch–Stöer gives the best compromise between computational time and precision compared to other well-known algorithms. For a given model, the identification of parameters is an important issue and should be as accurate as possible to describe efficiently the material behavior. In fact, the use of reliable optimization algorithms is to minimize the difference between the model prediction and experimental behavior. Different methods have been developed to resolve this type of problem. They can, in general, be divided into two major groups: the first one which converges quickly is for local optimization. However, its major disadvantage is the possibility of converging towards local minimums. The Pattern Search algorithm is part of this group. It does not require the gradient calculation of the objective function and accepts parallel computing on different computer processors. The second group is formed by the evolutionary method based on the evolution of individuals. The genetic algorithm is a part of this group which is related to the global minimum convergence. However, it is slow because it requires several evaluations of the objective function. Therefore, this study highlights the concept of damage induced anisotropy via the used model. Numerical solutions of these nonlinear constitutive equations require normally an important computational time. Therefore, a new strategy of model parameters calibration is considered. In fact, a hybrid approach is used, in this paper, to exploit the benefits of these groups of algorithms. Hence, a combination of the genetic algorithm (GA) with pattern search algorithm (PSA) is proposed. The basic idea of this approach is to look for the global minimum with the GA, then move to the local
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