Surface instability in gradient elasticity with surface energy

Biotʹs theory of plane strain surface instability of an isotropic elastic body ~under initial stress in finite strain is extended to include higher order strain-gradients. Higher order straingradients are properly introduced in the definition of the strain energy density, leading to an anisotropic gradient elasticity theory with surface energy. Accordingly, the present theory includes two material lengths characterizing the volume strain energy and the surface energy of the elastic body. The consideration of these two material lengths leads to the occurrence of a boundary layer. This in turn, gives rise to interesting phenomena related to the stability of the half-space, i.e. extra surface instability modes, thin skin effects and significant weakening of the half-space. It is also shown that the appearance of surface instability is associated with the vanishing velocity of propagation of Rayleigh waves. Furthermore, results derived in the context of the present theory on the dependence of the critical buckling stress of the layer on the thickness, suggest that it can be used effectively for the homogenization of elastic bodies containing periodic arrays of collinear Griffith cracks. © 1998 Elsevier Science Ltd. All rights reserved.