Effect of interfacial stresses in an elastic body with a nanoinclusion

Abstract

The 2-D problem of an infinite elastic solid with a nanoinclusion of a different from circular shape is solved. The interfacial stresses are acting at the interface. Contact of the inclusion with the matrix satisfies the ideal conditions of cohesion. The generalized Laplace – Young law defines conditions at the interface. To solve the problem, Gurtin – Murdoch surface elasticity model, Goursat – Kolosov complex potentials and the boundary perturbation method are used. The problem is reduced to the solution of two independent Riemann – Hilbert’s boundary problems. For the circular inclusion, hypersingular integral equation in an unknown interfacial stress is derived. The algorithm of solving this equation is constructed. The influence of the interfacial stress and the dimension of the circular inclusion on the stress distribution and stress concentration at the interface are analyzed.The 2-D problem of an infinite elastic solid with a nanoinclusion of a different from circular shape is solved. The interfacial stresses are acting at the interface. Contact of the inclusion with the matrix satisfies the ideal conditions of cohesion. The generalized Laplace – Young law defines conditions at the interface. To solve the problem, Gurtin – Murdoch surface elasticity model, Goursat – Kolosov complex potentials and the boundary perturbation method are used. The problem is reduced to the solution of two independent Riemann – Hilbert’s boundary problems. For the circular inclusion, hypersingular integral equation in an unknown interfacial stress is derived. The algorithm of solving this equation is constructed. The influence of the interfacial stress and the dimension of the circular inclusion on the stress distribution and stress concentration at the interface are analyzed.