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

Analysis of Stability and Bifurcation in Nonlinear Mechanics with Dissipation

Lab. Mécanique des Solides, CNRS UMR 7649, Ecole polytechnique, 91128 Palaiseau Cedex France LAMSID CNRS UMR2832, EdF Clamart, France
Received: 12 January 2011 / Revised: 25 January 2011 / Accepted: 25 January 2011 / Published: 31 January 2011
(This article belongs to the Special Issue Advances in Thermodynamics)
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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 stability; bifurcation; plasticity; damage; fracture; normality law
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Stolz, C. Analysis of Stability and Bifurcation in Nonlinear Mechanics with Dissipation. Entropy 2011, 13, 332-366.

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