Anti-plane shear Lamb's problem treated by gradient elasticity with surface energy

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1998 (EN)
Anti-plane shear Lamb's problem treated by gradient elasticity with surface energy (EN)

Georgiadis, HG (EN)
Vardoulakis, I (EN)

N/A (EN)

The consideration of higher-order gradient effects in a classical elastodynamic problem is explored in this paper. The problem is the anti-plane shear analogue of the well-known Lamb's problem. It involves the time-harmonic loading of a half-space by a single concentrated anti-plane 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 displacement at the point of application of the load. The latter formulation involves a Helmholtz equation for the out-of-plane displacement subjected to a traction boundary condition. Here, the generalized continuum theory of gradient elasticity with surface energy leads to a fourth-order PDE under traction and double-traction boundary conditions. This theory assumes a form of the strain-energy density containing, in addition to the standard linear-elasticity terms, strain-gradient and surface-energy terms. The present solution: in some contrast with the classical one, predicts bounded displacements everywhere. This may have important implications for more general contact problems and the Boundary-Integral-Equation Method. (C) 1998 Elsevier Science B.V. All rights reserved. (EN)


Strain Energy Density (EN)
Contact Problem (EN)
Surface Energy (EN)
Classical Solution (EN)
Linear Elasticity (EN)
Higher Order (EN)
Boundary Integral Equation Method (EN)
Boundary Condition (EN)
Helmholtz Equation (EN)

Εθνικό Μετσόβιο Πολυτεχνείο (EL)
National Technical University of Athens (EN)

Wave Motion (EN)



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