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analysis of stability and bifurcation in nonlinear mechanics with dissipation分析的稳定性和分岔与耗散非线性力学
Entropy 2011, 13, 332-366; doi:10.3390/
OPEN ACCESS
entropy
ISSN 1099-4300
/journal/entropy
Article
Analysis of Stability and Bifurcation in Nonlinear Mechanics
with Dissipation
Claude Stolz
´
Lab. Mecanique des Solides, CNRS UMR 7649, Ecole polytechnique, 91128 Palaiseau Cedex France
LAMSID CNRS UMR2832, EdF Clamart, France; E-Mail: stolz-lms@polytechnique.fr;
Tel.: +33-0-169-335-805
Received: 12 January 2011; in revised form: 25 January 2011 / Accepted: 25 January 2011 /
Published: 31 January 2011
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
1. Introduction
Thermody
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