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Construction et analyse de modèles d'endommagement à gradient

Abstract : This work is concerned with the modeling of softening material by regularized damage models. First we propose a rigorous construction of the underlying local model by justifying its formulation within the framework of Generalized Standard Materials. Accordingly, the strain work becomes a state function whose convexity properties are directly related to the hardening or softening properties and the quasi-static evolution problem admits a variational form. As the modeling of softening material can deal with non-uniqueness and time discontinuities, we propose to reinforce the classical evolution problem by integrating stability concepts and energy conservation principle. The local model is then enhanced by inserting gradient of damage into the energy expression. The merits of this new approach are emphasized throughout the study of homogeneous damage states. Secondly, a bifurcation and stability analysis is carried out for a bar submitted to a tensile test. It permits us to construct homogeneous as well as localized damage solutions in closed form and to illustrate the concepts of loss of uniqueness and stability, of damage localization and structural failure. Additionally, by enforcing the energy balance, we provide an explicit construction to overcome the issue of time discontinuities. Finally we proceed to the identification of the model parameters in the case of concrete. On the one hand, by an energetic analogy with fracture mechanics, the internal length of the model is linked to the surface energy density of a crack. On the other hand, the laws of rigidity and dissipation of the underlying local damage model are identified by using stress-strain and stability diagrams of homogeneous states. As the PIED experiment allows to stabilize these states in a tensile test, we carry on analytical and numerical calculations on this experimental procedure and show under which conditions the homogeneous states can really gain stability.
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Contributor : Kim Pham Connect in order to contact the contributor
Submitted on : Tuesday, January 25, 2011 - 2:53:23 PM
Last modification on : Tuesday, November 16, 2021 - 5:04:54 AM
Long-term archiving on: : Tuesday, November 6, 2012 - 12:20:42 PM

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  • HAL Id : tel-00559405, version 1

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Kim Pham. Construction et analyse de modèles d'endommagement à gradient. Mécanique [physics.med-ph]. Université Pierre et Marie Curie - Paris VI, 2010. Français. ⟨tel-00559405⟩

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