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

A diversity of computer approaches in the homogenization of random composites

M. Kamiński*
Chair of Mechanics of Materials, Technical University of Łódź, Al. Politechniki 6, 93-590, Łódź, Poland

  Full Text
A review of the various numerical techniques relating to the homogenization of composites exhibiting random properties is the main aim of this paper. The simulation, spectral and perturbation-based computational techniques are contrasted below to demonstrate their major as well as minor points in determination of probabilistic moments for effective material tensors in various problems. Special attention is given to the existing and future possible application of symbolic computations and those carried out by the finite element method (FEM) commercial programs. As summarized here, the solution for the homogenization problem of random composites consists of a series of finite element analyses for the analogous boundary value problem on the same periodicity cell instead of a single cell problem analyzed in a deterministic situation. A combined application of symbolic and FEM programs is especially efficient in further numerical simulations of random composites and can be used in probabilistic sensitivity analyses for various homogenized composite structures.

Keywords:  Composite materials; Homogenization technique; Probabilistic analysis; Finite element method

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