The Cerruti problem in dipolar gradient elasticity

Abstract

The classical three-dimensional Cerruti problem of an isotropic half-space subjected to a concentrated tangential load on its surface is revisited here in the context of dipolar gradient elasticity. This generalized continuum theory encompasses the analytical possibility of size effects, which are absent in the classical theory, and has proven to be very successful in modelling materials with complex microstructure. The dipolar gradient elasticity theory assumes a strain-energy density function, which besides its dependence upon the standard strain terms, depends also on strain gradients. In this way, this theory can be viewed as a first-step extension of classical elasticity. The solution method is based on integral transforms and is exact. Of special importance is the behaviour of the new solution near to the point of application of the load where pathological singularities exist in the classical solution (based on the standard theory). The present results show departure from the ones predicted by the classical elasticity theory. Indeed, continuous and bounded displacements are found at the point of application of the load. Such a behaviour of the displacement field is, of course, more natural than the singular behaviour present in the classical solution.