Bifurcation and Stability in Dissipative Media (Plasticity, Friction, Fracture)

[+] Author and Article Information
Quoc Son Nguyen

Laboratoire de Mecanique des Solides, Centre commun X - Mines - Ponts - CNRS Ecole Polytechnique, 91128 - Palaiseau, France

Appl. Mech. Rev 47(1), 1-31 (Jan 01, 1994) (31 pages) doi:10.1115/1.3111068 History: Online April 29, 2009


This paper addresses stability and bifurcation analysis for common systems of solids in the framework of plasticity, of friction and of fracture mechanics. Although physically different, usual time-independent laws adopted in these domains lead to a certain mathematical similarity concerning the quasi-static behaviour of materials and structures. These mechanical systems can be described practically in the same mathematical manner concerning their quasi-static evolution and in particular concerning the stability of their response. Our objective is to present within this framework a review of principal results of the recent literature on these subjects in relation with some energy-related considerations and with an unified description based upon energy and dissipation analysis.

Copyright © 1994 by American Society of Mechanical Engineers
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