Two-Parametric Analysis of a Semi-Infinite Three-Layered High-Contrast Elastic Strip Under Antiplane Shear Deformation

Antiplane shear of a symmetric three-layered elastic semi-strip under the self-equilibrated edge load is studied. The arbitrary ratios of thickness and stiffness are considered, with emphasis on high-contrast scenario; in doing so, two aforementioned dimensionless problem parameters are assumed mutually independent. A simple explicit condition, supporting a slowly decaying solution of the equilibrium equations, is derived. Leading order estimates for the decay rate and amplitude of this solution are presented, highlighting its dominant contribution to displacement field. The derivation involves an asymptotic formula ensuring elimination of the boundary layer localised near the edge of the semi-strip. The peculiarities of the latter are also addressed. Numerical results, including comparisons of the derived shortened and full expressions for the sought for slowly decaying solutions, are presented.