13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- minimum search via the PSA to improve the obtained result. Since the identification of the model parameters is of particular interest in this paper, therefore, several applications are presented. They deal with cyclic plasticity with damage induced anisotropy behavior of polycrystals and its related phenomena under complex history of loading path conditions. To conduct the identification process, the two methods (GA&PSA) are complementary and have different applications. The GA optimizes globally the model parameters leaving the field to the local method, PSA, to determine the final values of these parameters. Then, in order to evaluate the performances of the proposed method, a comparative study is performed under complex cyclic loadings showing the ability of such strategy to identify the model parameters. 2. Employed Micromechanical Model The used micromechanical model utilizes three operating levels which are: microscale (slip system), mesoscale (granular) and macroscale (overall). The theoretical formulation of the developed model is presented in detail in [1]. However, a short description of the main features of the model equations at the overall level is illustrated below. ∑∑ = ⊗ Σ= 3 1 * i i i i p p (1) ∑ = = ⊗ 3 1 i i i Q p p (2) ∑ = + = Σ ⊗ 3 1 * ( ) i i i i Q H p p (3) + + + + + = ia jb ka lb ijkl p Q Q Q Q (4) + =D D p T (5) o T dR I D R: = − (6) o T T d R D p D p R: + = + + & & & (7) R E R E M e d e d & & & & + + Σ= : : (8) e e o e T e e o e T e e o e T R E E E p R E E D E p R E E D E p M D : : : : : : 2 1 : : : 2 1 & & & & ∂ ∂ − ∂ ∂ − ∂ ∂ =− + + + (9)
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