A Proposition for a "Self-Consistent" Gradient Elasticity

Abstract

The notion of "self-consistent" boundary conditions in gradient elasticity is explored. They are introduced in the place of the "standard" boundary conditions commonly used in the formulation of gradient elasticity problems derived through corresponding variational principles. The case of a perforated membrane under biaxial tension is solved, as an example. The predicted hole size-effect is then compared with the solutions of classical and gradient elasticity and with that obtained by a "quantized elasticity" approach. Only self-consistent gradient elasticity and the quantized approach seem to provide, in a convenient way, fully realistic results in the asymptotic regime.