The model of nonlinear deformation of layered materials

Abstract


 The model of nonlinear deformation of a layered material with physically nonlinear layers is proposed. The laminate is considered a two-component material with random layers. The basis is the stochastic differential equations of the physically nonlinear theory of elasticity by L.P. Khoroshun. The solution to the problem of the stress-strain state and effective properties of the composite material is constructed by the averaging method. An algorithm for determining the effective deformable properties of a layered material with physically nonlinear layers has been developed. The solution of nonlinear equations taking into account their physical nonlinearity is constructed by an iterative method. The law of the relationship between macrostresses and macrostrains in a layered material and the dependence of average strains and stresses in its layers on macrostrains has been established. Curves of material deformation are plotted for different values of the volumetric content of its filler. The dependence of the effective deformative properties of the laminated material on the volumetric content of the filler has been studied. The effect of nonlinearity of layers on the deformation of a layered composite material is investigated. It was found that the nonlinearity of the layers have significant influence on the effective deformative properties and the stress-strain state of laminated materials.