Modelling of Nonlinear-Elastic Properties of Composites with Finite Deformations by Asymptotic Homogenization Method

A method for calculating non-linear properties of composites with finite deformations is developed. The method is based on asymptotic homogenization of periodical structures. Universal representations of nonlinear-elastic constitutive relations for materials with finite deformations, earlier proposed by the author, are used in the calculations. Analytical solutions to specific problems for layered composite materials with finite deformations are obtained. A method of nested optimization is proposed for numerical realization of these solutions. Examples of numerical calculations for stress-strain diagrams for layered composite materials with finite deformations are presented.

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