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.

Modeling of effective elastic-plastic properties of layered composites with a periodic structure in the framework of the anisotropic flow theory

“…With the help of the developed algorithm, averaged strain diagrams ij ij mn F of a layered composite were calculated and built under uniaxial loading in different directions for tension and compression. Also, using the problem of minimizing the functional (38), the constants 3 1. The calculation was carried out according to formula (29), and the unknown constants were preliminarily determined from the strain curve.…”

“…consider a model in which the elastic potential does not depend on the implementation of the invariants(3then relation (6) takes the form:…”

Coupled micro-macroscopic modeling of layered composites with finite deformations

“…The asymptotic averaging method is a rigorous and widely used effective mathematical approach for describing the problems of deformation of structures made of composite materials, it gives an asymptotically correct representation of their solution. AH is also used to predict the effective properties of composites under finite strains [7][8][9][10][11]. Due to the nonlinearity of the problem of mechanics at finite deformations [12][13][14][15], the AH method encounters certain difficulties in implementation.…”