Journal
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
Volume 59, Issue 6, Pages 1163-1190Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jmps.2011.03.010
Keywords
Damage mechanics; Gradient damage model; Variational methods; Stability; Bifurcation
Funding
- French research network MoMaS (Mo delisations Ma thematiques et S imulations numeriques liees aux problemes de gestion des dechets nucleaires)
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We consider a wide class of gradient damage models which are characterized by two constitutive functions after a normalization of the scalar damage parameter. The evolution problem is formulated following a variational approach based on the principles of irreversibility, stability and energy balance. Applied to a monotonically increasing traction test of a one-dimensional bar, we consider the homogeneous response where both the strain and the damage fields are uniform in space. In the case of a softening behavior, we show that the homogeneous state of the bar at a given time is stable provided that the length of the bar is less than a state dependent critical value and unstable otherwise. However, we also show that bifurcations can appear even if the homogeneous state is stable. All these results are obtained in a closed form. Finally, we propose a practical method to identify the two constitutive functions. This method is based on the measure of the homogeneous response in a situation where this response is stable without possibility of bifurcation, and on a procedure which gives the opportunity to detect its loss of stability. All the theoretical analyses are illustrated by examples. (C) 2011 Elsevier Ltd. All rights reserved.
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