On the micro-structure of surface effects and related instabilities

Based on Mindlin's theory for material micro-structure interesting surface effects under conditions of equilibrium are studied in this paper. The governing field equations for uniaxial plane deformations are established; surface instability analysis shows non uniform deformations for a layer of specified distance from the surface. Experimental as well as fracture mechanics based considerations show that this surface-layer is extremely thin for metals while for brittle materials its magnitude is of the order of 1 cm. Material microstructure introduces a singular perturbation to the original Hill and Hutchinson-problem; here we introduce a single perturbation parameter and we obtain a 'dispersion' law for the surface buckling load. It is found that surface degradation and skin effects can be attributed to localized surface buckling instabilities. Experimental information on skin effects can provide an estimation of the internal material length.