SURFACE INSTABILITY IN GRADIENT ELASTICITY WITH SURFACE-ENERGY

Biot's theory of plane strain surface instability of an isotropic elas tic body under initial stress in finite strain is extended to include higher order strain-gradients. Higher order strain-gradients are prope rly introduced in the definition of the strain energy density, leading to an anisotropic gradient elasticity theory with surface energy. Acc ordingly the present theory includes two material lengths characterizi ng the volume strain energy and the surface energy of the elastic body . The consideration of these two material lengths leads to the occurre nce of a boundary layer. This in turn, gives rise to interesting pheno mena related to the stability of the half-space, i.e. extra surface in stability modes, thin skin effects and significant weakening of the ha lf-space. It is also shown that the appearance of surface instability is associated with the vanishing velocity of propagation of Rayleigh w aves. Furthermore, results derived in the context of the present theor y on the dependence of the critical buckling stress of the layer on th e thickness, suggest that it can be used effectively for the homogeniz ation of elastic bodies containing periodic arrays of collinear Griffi th cracks. (C) 1998 Elsevier Science Ltd. All rights reserved.