Causality in strain gradient elasticity: An internal variables approach

Abstract

The absence of higher order time derivatives in equations of motion causes the infinite velocity of wave propagation in strain gradient elasticity models. This issue needs to be avoided from both a theoretical and practical viewpoint. It is shown that dual internal variables approach solves the causality problem. Furthermore, the primary internal variable can be interpreted as the Laplacian of the strain gradient resulting in an Aifantis-type strain gradient model.