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

Part of the Advances in Mechanics and Mathematics book series (AMMA, volume 21)


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).


Gradient Theory Gradient Elasticity Strain Gradient Plasticity Strain Gradient Elasticity Strain Energy Density Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Laboratory of Mechanics and Materials, Polytechnic SchoolAristotle University of ThessalonikiThessalonikiGreece
  2. 2.Center for Mechanics of Material Instabilities and Manufacturing Processes, College of EngineeringMichigan Technological UniversityHoughtonUSA

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