Research into Functional Equations Arising from Mathematical Modeling of Critical States of Heterogeneous Soft Layers

Abstract

We obtained the classification of solutions to a functional equation arising from the research into mathematical models of critical states of the plastic layer. The layer is exposed to a tensile stress under conditions of plane deformation. The function of the layer heterogeneity depends presumably on two variables. We demonstrated how the research into the mentioned mathematical models can be reduced to the solution of some nonlinear systems of ordinary differential equations under the conditions of separating the variables for tangent stress and for the heterogeneity function.