Universal models for effective constitutive relations of laminated composites with finite strains

Abstract

The results of the development of the theory of constructing effective constitutive relations for laminated composites with finite deformations are presented. The theory is based on the application of the method of asymptotic averaging for periodic structures and the use of universal models of constitutive relations for composite layers, proposed by Yu.I. Dimitrienko. Universal models allow us to formulate the constitutive relations simultaneously for all the main conjugated stress – strain tensors pairs. The method of asymptotic averaging makes it possible to obtain a relationship between the effective constitutive relations of the composite and its constituent layers. Cases of incompressible layers and layers with compressibility are considered. A numerical algorithm for constructing effective deformation diagrams of layered composites and calculating the material constants in the effective constitutive relations of an anisotropic composite is proposed. Numerical examples of method implementation and numerical algorithms are given.