Compression of a semi‐bounded body with a coating layer along the interface sliding zone

Abstract Within the framework of the three‐dimensional linearized theory of stability of deformable bodies, the plane problem on compression of a piecewise‐homogeneous half‐plane along a defect, which is a frictionless sliding zone located at the rectilinear interface between two rigidly connected media, a semi‐bounded homogeneous body (base) and a homogeneous thin coating layer, have been studied. The initial stage of body fracture is associated with the loss of material stability in a local area near the specified defect. The base and coating materials are considered as highly elastic materials described by an elastic potential with different mechanical characteristics. The boundary value problem, formulated in terms of potential harmonic functions, using Fourier integral transforms, is reduced to an eigenvalue problem for the Fredholm integral equation of the first kind, which is studied numerically by employing Bubnov—Galerkin method. For a compressible material with a harmonic potential, critical values of the load parameters that correspond to local instability have been found. The critical load parameters obtained have also been compared with similar values of the critical parameters corresponding to the near‐surface instability of a piecewise‐homogeneous half‐plane (without a defect) compressed along the interface between the media that are rigidly connected or slide without friction against each other.