Longitudinal shear of the bimaterial with nonlinear elastic thin interfacial inclusion

Abstract

The longitudinal shear problem for the bimaterial with thin nonlinear elastic inclusion at the interface
matrix materials is discussed. Solution of the formulated problem is constructed by applying
the problem linear conjugation of analytic functions and jump functions method. The model of thin
inclusion with nonlinear elastic characteristics is constructed. The solution of problem is reduced
to a system of singular integral equations with variable coefficients. A convergent iterative method
for solving such a system due to the various law of nonlinear deformation, including Ramberg-Osgood law, is proposed. Incremental calculation method for calculating stress-strain state under
the multistep (including cyclic) loading is developed. Numerical calculations of the body stressstrain
state for different values of the inclusion material nonlinearity parameters are made. Their
influence on the mode of deformation of the matrix under the loading by the shift on the infinity
and balanced system of concentrated forces is analyzed.