Third M.I.T. Conference on Computational Fluid and Solid Mechanics June 14–17, 2005  

Generalized micro-to-macro transitions of microstructures for the first and second order continuum

Ł. Kaczmarczyk*
Institute of Computer Methods in Civil Engineering, Cracow University of Technology, Kraków, Poland

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This paper deals with the first-order and second-order computational homogenization of a heterogeneous material undergoing small displacements. Typically, in this approach a representative volume element (RVE) of nonlinear heterogeneous material is defined. An a priori given discretized microstructure is considered, without focusing on detailed specific discretization techniques. The key contribution of this paper is the formulation of equations coupling micro- and macro-variables and the definition of generalized boundary conditions for the microstructure. The coupling between macroscopic and microscopic level is based on Hill's averaging theorem. We focus on deformation-driven microstructures where overall macroscopic deformation is controlled.

Keywords:  Computational homogenization; Microstructures; Elastic-plastic composite

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