Plane deformations of elastic solids with intrinsic boundary elasticity

In this paper, a nonlinear theory of elastic boundary coating (or reinforcement) of an elastic solid is developed for plane strain deformations. The coating consists of a material curve endowed with intrinsic elastic properties associated with extensibility and bending stiffness bonded to part, or all, of the bounding curve of the elastic body. The equations describing the equilibrium of the coated body when subject to finite deformation are derived using a variational method. The incremental equations describing a small departure from an equilibrium configuration are then derived and used to investigate the stability of a deformed configuration and the possibility of bifurcation. The theory is applied to the analysis of the equilibrium of a finitely deformed halfplane consisting of compressible elastic material coated along its edge. The influence of the coating on the bifurcation behaviour of the half-plane is assessed against known results for an uncoated half-plane. Numerical results are used to illustrate the influence of certain material parameters on bifurcation.