13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- [ ] [ ] [ ] [ ] [ ] [ ] − = = − = − = = = 0 0 1 0 1 0 1 0 0 0 0 1 0 1 0 1 0 0 6 5 4 3 2 1 v v v v v v (14) For a more description of this, see Kolda, Lewis, and Torczon [5]. To accelerate the convergence, we stop the iteration as soon as it finds a mesh point whose fitness value is smaller than that of the current point. After a successful poll, the algorithm multiplies the current mesh size by 2. If none of the mesh points has a smaller objective function value at current point, so the poll is unsuccessful, the algorithm does not change the current point at the next iteration and multiplies the current mesh size by 0.5. In our application the criteria for stopping the pattern search are the number of objective function evaluations. 4. Numerical applications The evaluation of the proposed new strategy for identification is carried out through the description of the elastic-inelastic cyclic behavior of a polycrystal under uniaxial tension-compression (TC), biaxial tension-torsion with 90° out-of-phase angle (TT90). Our polycrystal is a random orientation distribution of 40 grains of a single-phase FCC. Initially, a database for both cyclic loading (TC and TT90) is numerically made up to final damaging of this grains distribution using the coefficients summed up in (Table 1) Table 1 Coefficients used to create the database Elastic-Inelastic parameters Model parameters E (MPa) ν α z K b s Ko (MPa) Qs (MPa) h1=h2=… =h5 h6 Cg (MPa) ag coefficients 215000 0.32 1 20 50 13 240 256 1 2.29 95100 10 Damage parameters Model parameters Ss s o ws d1 d2 0γ coefficients 2 0.95 1 1 1.4 1.25 Such a database is considered as an experimental one. Thereafter, the identification process of model parameters is started by setting the damage parameters changing six key parameters related to the inelastic behavior (bs, ko, Qs, h6, C g and ag). Therefore, the identification process by the global minimum optimization concept is made through the genetic algorithm. After several tests on the population size, a population of 600 individuals is employed to optimize 6 coefficients of the model. Several iterations are made obtaining several families of model parameters followed by a local identification using the pattern search algorithm. The optimized model parameters are summed up
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