Surface instability of an elastic half space with material properties varying with depth

If a body with a stiffer surface layer is loaded in compression, a surface wrinkling instability may be developed. A bifurcation analysis is presented for determining the critical load for the onset of wrinkling and the associated wavelength for materials in which the elastic modulus is an arbitrary function of depth. The analysis leads to an eigenvalue problem involving a pair of linear ordinary differential equations with variable coefficients which are discretized and solved using the finite element method.The method is validated by comparison with classical results for a uniform layer on a dissimilar substrate. Results are then given for materials with exponential and error-function gradation of elastic modulus and for a homogeneous body with thermoelastically-induced compressive stresses.