Structural analysis of gradient elastic components

The present study investigates the size effects in the problems of cantilever beam bending and cracked bar tension within the gradient elasticity framework. Analytical solutions for metrics that characterize both the normalized stiffness and toughness are derived. It is found that the gradient elastic beam exhibits a significantly stiffer but also more brittle response, while the gradient cracked bar exhibits considerable toughening. These results compare well with respective finite element computations.