Saint-Venant decay rates for a non-homogeneous isotropic mixture of elastic solids in anti-plane shear

The purpose of this research is to investigate the influence of material inhomogeneity on the decay of Saint-Venant end effects in anti-plane shear deformations of linear isotropic mixtures of elastic solids. The work is motivated by the recent research activity on functionally graded materials (FGMs), i.e. materials with spatially varying properties tailored to satisfy particular engineering applications. The spatial decay of solutions of a boundary value problem with variable coefficients on a semi-infinite strip is investigated. The results may be interpreted in terms of a Saint-Venant principle for anti-plane shear deformations of linear isotropic mixtures of elastic solids.