Universal models of the constitutive relations for transversely isotropic compressible composites with finite strains

Abstract

A model of a transversely isotropic compressible elastic medium with finite strains is proposed. The model belongs to the class of the so-called universal models, which are formulated in terms of energy (conjugated) pairs of stress and strain tensors - simultaneously for several types of pairs. An algorithm is proposed for calculating the constants included in the constitutive relations of this model, based on a comparative analysis of the results of calculating deformation diagrams under uniaxial loading according to this model and using the asymptotic averaging method. An example of numerical modeling for a layered composite is given.