Antiplane Deformation of a Bimaterial with Thin Interfacial Nonlinear Elastic Inclusion

Abstract

The problem of longitudinal shear of bimaterial with thin nonlinear elastic inclusion at the interface of matrix materials is considered. Solution of the problem is constructed using the boundary value problem of combining analytical functions and jump functions method. The model of the thin inclusion with nonlinear resilient parameters is built. Solution of the problem is reduced to a system of singular integral equations with variable coefficients. The convergent iterative method for solving such a system is offered for various nonlinear strain models, including Ramberg-Osgood law. Numerical calculations are carried out for different values of non-linearity characteristic parameters for the inclusion material. Their parameters are analysed for the tensely-deformed matrix under loading a uniformly distributed shear stresses and for a balanced system of the concentrated forces.

Deformation and Strength Parameters of a Composite Structure with a Thin Multilayer Ribbon-like Inclusion

“…This effect can be useful in designing the modes of operation of structures with such a structure. The solution method and results obtained for the two-layer inclusion have been verified by the coincidence of the numerical results with those known in literature [47,[50][51][52][53] for a homogeneous thin elastic inclusion-the curves 1 in Figures 5 and 7…”

“…The construction of a mathematical model of such a layered thin inclusion-layer (internal problem) should eventually reveal the relation between the stress-strain parameters inside the inclusion and on its external surface as the influence functions σ in yz (x, ±h), w in (x, ±h), which will be used in the further solution of the problem [51][52][53].…”

“…The solution for the matrix as an isotropic bimaterial (external problem) is obtained by the method of the problem of conjugation of analytic functions [51][52][53]:…”

“…The resulting system of Equations ( 26)-( 29) is reduced to a system of linear algebraic equations concerning the unknown coefficients of the decomposition of the desired influence functions [51][52][53] into a series by Jacobi-Chebyshev polynomials, described in [55].…”

“…Due to the brittle nature of ceramics, there is a need for additional research into the applicability limits of such FGM structures [38][39][40]. The complexity of the geometry of structural elements and consideration of imperfections in the contact of their components stimulate the process of improving mathematical models of FGMs to ensure their qualitative design both in terms of mechanical strength [12][13][14][41][42][43][44][45][46][47][48][49][50][51][52][53][54] and in terms of consideration of thermal, magnetic, piezoelectric loading factors [47,48]. The use of the FGMs seems to be one of the most effective materials in the realization of sustainable development in industries.…”