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.

The article considers the modeling results of layered composites with finite strains deformation according to the individual layers characteristics. The article proposes an asymptotic averaging method version for layered composites with finite deformations and periodic structure. The method allows calculating the effective deformation diagrams connecting the averaged Piola-Kirchhoff stress tensors components and the strain gradient.

Abstracts The article is devoted to solving the problem of cylindrical bending of a flat panel made of a transversely isotropic incompressible composite material with finite deformations. The focus of the article is that in this problem the so-called universal model of constitutive relations is considered, which allows one to obtain solutions to problems simultaneously for several classes of models related to different conjugate pairs of stress-strain tensors. This method was proposed earlier in the works of Yu.I. Dimitrienko. Using this method, the difference in the calculation results, which are obtained using various models of composites with finite strains, is shown.

A coupled micro- and macroscopic modeling of an incompressible layered composite material under finite deformations is performed based on the asymptotic homogenization method and universal semi-linear models. The deformation diagrams of the periodicity cell are calculated. A method for searching for effective transversally isotropic properties of LCM based on the obtained diagrams is considered. Cylindrical bending of an LCM plate is simulated using the model of a transversally isotropic medium. The microstresses in the periodicity cell are calculated based on the homogenized stresses.