Strain-Difference Based Nonlocal Elasticity Theories: Formulations and Obtained Results

The contributions to nonlocal elasticity given by the authors in the last two decades are reported in this article. To better illustrate the above contributions and their pertinence to the nowadays research framework, we start with a scrutiny of the inconsistencies encountered within the Eringen’s purely nonlocal model and the remedies required to overcome shortcomings and paradoxical situations known from the literature. It is shown that the so-called strain-difference based nonlocal theories encompassing the mentioned contributions provide effective methods to address boundary-value problems. Applications to plates by nonlocal finite elements and size effects analysis of beams in bending have been reported as illustrative examples of previously obtained results.