Open AccessModeling of deformation of the bimaterial with thin Non-linear interface inclusion
Author(s) -
Yosyf Piskozub,
Heorhiy Sulym
Publication year - 2021
Publication title -
doslìdžennâ v matematicì ì mehanìcì
Language(s) - English
Resource type - Journals
ISSN - 2519-206X
DOI - 10.18524/2519-206x.2020.2(36).233748
Subject(s) - jump , nonlinear system , deformation (meteorology) , boundary value problem , inclusion (mineral) , boundary (topology) , mathematical analysis , stress (linguistics) , numerical analysis , state variable , interface (matter) , mechanics , mathematics , materials science , physics , composite material , thermodynamics , linguistics , philosophy , bubble , quantum mechanics , maximum bubble pressure method
An incremental approach to solving the antiplane problem for bimaterial media with a thin, physically nonlinear inclusion placed on the materials interface is discussed. Using the jump functions method and the coupling problem of boundary values of the analytical functions method we reduce the problem to the system of singular integral equations (SSIE) on jump functions with variable coefficients allowing us to describe any quasi-static loads (monotonous or not) and their influence on the stress-strain state in the bulk. To solve the SSIE problem, an iterative analytical-numerical method is offered for various non-linear deformation models. Numerical calculations are carried out for different values of non-linearity characteristic parameters for the inclusion material. Their parameters are analyzed for a deformed body under a load of a balanced concentrated force system.