Multiscale approach with uncertainty for nonlinear inelastic behavior of heterogeneous material and related size effect

Abstract eng:
In this work we address several issues pertaining to efficiency of the computational approach geared towards modeling of inelastic behavior of a heterogeneous materials with microstructure, which is represented by a multiscale model. We elaborate upon both cases, where two-scale computation can be uncoupled and where the scales remain coupled throughout the computations, implying a constant communication between the finite element models employed at each scale. We also discuss different manners of representing a complex multi-phase microstructure within the framework of the finite element model constructed at that scale, selecting a model problem of two-phase material where each phase has potentially different inelastic behavior. We conclude presentation with considerations of microstructure optimization problems. Both computational aspects for coupled nonlinear mechanics-optimization problem and the optimal choice of design variables are addressed. The uncertainty aspects are finally takes into account pertaining to the incomplete information on the material heterogeneities. The latter is presented as an alternative strategy for bridging the scales, which allows to replace the phenomenological model with random fields for parameters. Further details can be found in our recent works [1-7]. References [1] Ibrahimbegovic A., B. Brank (eds.), Multi-physicss and multi-scale computer models in nonlinear analysis and optimal design of engineering structures under extreme conditions, IOS Press, Amsterdam, (ISBN 1-58803-479-0) pp 1-407 (2005) [2] Ibrahimbegovic A., S. Melnyk, ‘Embedded discontinuity finite element method (ED-FEM) versus extended finite element method (X-FEM) for representing the localized failure of heterogeneous materials’, Computational Mechanics, 40, 149-155 (2007) [3] Niekamp R., D. Markovic, A. Ibrahimbegovic, H. G. Matthies, R.L. Taylor, ‘Multi-scale modeling of heterogeneous structures with inelastic constitutive behavior. Part II : Software coupling and implementation aspects‘, International Journal of Engineering Computations, in press (2009) [4] Markovic D., A. Ibrahimbegovic, ‘Complementary energy based FE modeling of coupled elastoplastic and damage behavoir for continuum microstructure computations’, Computer Methods in Applied Mechanics and Engineering, 195, 5077-5093 (2006) [5] Ibrahimbegovic A., I. Gresovnik, D. Markovic, S. Melnyk, T. Rodic, ‘Shape optimizatoin of two-phase material with microstructure‘, International Journal of Engineering Computations, 22, 605-645 (2005) [6] Markovic D., R. Niekamp, A. Ibrahimbegovic, H. G. Matthies, R.L. Taylor, ‘Multi-scale modeling of heterogeneous structures with inelastic constitutive behavior. Part I : Mathematical and physical aspects‘, International Journal of Engineering Computations, 22, 664-683 (2005) [7] Brancherie D., A. Ibrahimbegovic, ‘Fracture of massive structures: a novel approach to constructing an anisotropic damage model combining continuum-type hardening and discretetype softening models’, International Journal of Engineering Computations, in press (2009)

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