A unifying variational framework for stress gradient and strain gradient elasticity theories

作者：Polizzotto Castrenze^*

来源：European Journal of Mechanics - A: Solids , 2015, 49: 430-440.

DOI：10.1016/j.euromechsol.2014.08.013

• Gradient elasticity theories
• Variational principles

Stress gradient elasticity and strain gradient elasticity do constitute distinct continuum theories exhibiting mutual complementary features. This is probed by a few variational principles herein presented and discussed, which include: i) For stress gradient elasticity, a (novel) principle of minimum complementary energy and an (improved-form) principle of stationarity of the Hellinger-Reissner type; ii) For strain gradient elasticity, a (known) principle of minimum total potential energy and a (novel) principle of stationarity of the Hu-Washizu type. Additionally, the higher order boundary conditions for stress gradient elasticity, previously derived by the author (Polizzotto, Int.J. Solids Struct. 51,1809-1818, (2014)) in the form of higher order boundary compatibility equations, are here revisited and reinterpreted with the aid of a discrete model of the body's boundary layer. The reasons why the latter conditions need to be relaxed for beam and plate structural models are explained.

• 出版日期2015-2