A Personal View on Current Generalized Theories of Elasticity and Plastic Flow

Abstract

A brief discussion of some current generalized continuum mechanics theories of elasticity and plasticity is provided. Attention is focused on works directly or indirectly motivated by the initial gradient models proposed by the author which, in turn, rest on ideas pioneered by Maxwell and van der Waals for fluid-like bodies but within a solid mechanics framework in the spirit of the celebrated monograph of brothers Cosserat published a quarter of a century later. The work of Cosserat, being dormant for half a century, ignited in the 1960s a plethora of generalized elasticity theories by the founders of modern continuum mechanics, as described in the treatises of Truesdell and Toupin and Truesdell and Noll. But it was not until another quarter of a century later that the interest in generalized continuum mechanics theories of elasticity and plasticity was revived, partly due to the aforementioned robust gradient models introduced and elaborated upon by the author and his co-workers in relation to some unresolved material mechanics and material physics issues; namely, the elimination of elastic singularities from dislocation lines and crack tips, the interpretation of size effects, and the description of dislocation patterns and spatial features of shear bands. This modest contribution is not aiming at a detailed account and/or critical review of the current state-of-the-art in the field. It only aims at a brief account of selected recent developments with some clarification on difficult points that have not been adequately considered or still remain somewhat obscure (origin and form of gradient terms, boundary conditions, thermodynamic potentials).