The mechanically based non-local elasticity has been used, recently, in wider and wider engineering applications involving small-size devices and/or materials with marked microstructures. The key feature of the model involves the presence of non-local effects as additional body forces acting on material masses and depending on their relative displacements. An overview of the main results of the theory is reported in this paper
Di Paola, M., Failla, G., Pirrotta, A., Sofi, A., Zingales, M. (2013). The mechanically based non-local elasticity: an overview of main results and future challenges. PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY OF LONDON SERIES A: MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 371(1993) [10.1098/rsta.2012.0433].