Abstract
One of the most widely employed models to evaluate ductile damage and fracture is due to Gurson. An inconvenience of the model is that several material parameters must be determined in order to represent adequately a given experimental behavior. Determination of such parameters is not trivial but can be performed by means of inverse analyses using optimization procedures. In this work, the material parameters are sought by fitting force vs. displacement curves computed using finite element simulation to experimental curves obtained from tensile tests. The resulting optimization problem is non-convex and may present several local minima, thereby posing some difficulties to gradient-based optimization procedures due to the strong dependence on initial estimates of the design variables (the material parameters in this case). An approach based on a genetic algorithm is used in an attempt to avoid this problem. This strategy makes also possible to exploit the parallel nature of evolutionary algorithms as, at each generation, the evaluation of the fitness function of one individual is independent of the fitness of the rest of the population. In this particular implementation, each individual is represented by a gray encoding sequence of genes, the parental selection is performed by means of a tournament selection, the crossover probability is 0.8 and the probability of mutation is 0.05.
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Acknowledgements
The experimental data related to the first example was provided by Prof. Andreas Öchsner and is greatly acknowledged. Prof. Luis Cunda provided the source code of his Gurson damage model implementation. The authors wish to thank the referees for their comments on the manuscript and the financial support provided by FAPESC (Santa Catarina Foundation for Scientific and Technological Research—Project 1775/2006).
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Muñoz-Rojas, P.A., Cardoso, E.L. & Vaz, M. Parameter Identification of Damage Models Using Genetic Algorithms. Exp Mech 50, 627–634 (2010). https://doi.org/10.1007/s11340-009-9321-y
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DOI: https://doi.org/10.1007/s11340-009-9321-y