Physically nonlinear deformation of a thin interphase inclusion under antiplane problem conditions

Abstract

The longitudinal shear problem of the bimaterial with thin physically nonlinear inclusion at the interface matrix materials is considered. The solution of the formulated problem is constructed by the method of the conjugation of limit values of analytical functions with the use of the jump function method. A model of thin inclusion with arbitrary nonlinear strain characteristics is constructed. The solution of the problem is reduced to a system of singular integral equations with variable coefficients. A convergent iteration method for solving such a system for different types of physically nonlinear deformation is proposed. An incremental calculation method for calculating stress-strain state under multistep (including cyclic) quasi-static loading is developed. Numerical calculations of the body stress-strain state for various values of the parameters of the nonlinearity of the inclusion material are carried out. Their influence on the mode of deformation of the matrix under loading by a balanced system of concentrated forces is investigated.