Anti-plane loading of microstructured materials in the context of couple stress theory of elasticity: half-planes and layers

Abstract

The problem of calculating the displacements and stresses in a layered system often arises in engineering analysis and design, ranging from the field of mechanical engineering, to the field of materials science and soil mechanics. The present work focuses on the anti-plane response of half-planes and layers of finite thickness bonded on rigid substrates, under a point load, in the context of couple stress elasticity. The theory of couple stress elasticity is used to model the material microstructure and incorporate the size effects into the macroscopic response. This problem in plane strain configuration is referred to as Burmister’s problem. The purpose is to derive the pertinent Green’s functions that can be effectively used for the formulation of anti-plane contact problems in the context of couple stress elasticity. Full-field solutions regarding the out-of-plane displacements, the strains and the equivalent stress are presented, and of special importance is the behavior of the new solutions near to the point of application of the force where pathological singularities and discontinuities exist in the classical solutions.