ANTIPLANE SHEAR LAMBS PROBLEM TREATED BY GRADIENT ELASTICITY WITH SURFACE-ENERGY

The consideration of higher-order gradient effects in a classical elas todynamic problem is explored in this paper. The problem is the anti-p lane shear analogue of the well-known Lamb's problem. It involves the time-harmonic loading of a half-space by a single concentrated anti-pl ane shear line force applied on the half-space surface. The classical solution of this problem based on standard linear elasticity was first given by J.D. Achenbach and predicts a logarithmically unbounded disp lacement at the point of application of the load. The latter formulati on involves a Helmholtz equation for the out-of-plane displacement sub jected to a traction boundary condition. Here, the generalized continu um theory of gradient elasticity with surface energy leads to a fourth -order PDE under traction and double-traction boundary conditions. Thi s theory assumes a form of the strain-energy density containing, in ad dition to the standard linear-elasticity terms, strain-gradient and su rface-energy terms. The present solution: in some contrast with the cl assical one, predicts bounded displacements everywhere. This may have important implications for more general contact problems and the Bound ary-Integral-Equation Method. (C) 1998 Elsevier Science B.V. All right s reserved.