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Entropy 2011, 13(2), 332-366; doi:10.3390/e13020332

Article

Analysis of Stability and Bifurcation in Nonlinear Mechanics with Dissipation

Claude Stolz

Lab. Mécanique des Solides, CNRS UMR 7649, Ecole polytechnique, 91128 Palaiseau Cedex France LAMSID CNRS UMR2832, EdF Clamart, France

Received: 12 January 2011; in revised form: 25 January 2011 / Accepted: 25 January 2011 / Published: 31 January 2011

(This article belongs to the Special Issue Advances in Thermodynamics)

Download PDF Full-Text [227 KB, uploaded 31 January 2011 10:45 CET]

Abstract: The analysis of stability and bifurcation is studied in nonlinear mechanics with dissipative mechanisms: plasticity, damage, fracture. The description is based on introduction of a set of internal variables. This framework allows a systematic description of the material behaviour via two potentials: the free energy and the potential of dissipation. In the framework of standard generalized materials the internal state evolution is governed by a variational inequality which depends on the mechanism of dissipation. This inequality is obtained through energetic considerations in an unified description based upon energy and driving forces associated to the dissipative process. This formulation provides criterion for existence and uniqueness of the system evolution. Examples are presented for plasticity, fracture and for damaged materials.

Keywords: stability; bifurcation; plasticity; damage; fracture; normality law

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