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Lois de comportement à gradients de variables internes : construction, formulation variationnelle et mise en œuvre numérique

Abstract : Experimental observations show that local theories fail to describe the behavior of materials submitted to strong gradients of mechanical fields, due to strain localization for instance. In that way, a general framework is proposed to take into account these gradient effects by extending the local generalized standard constitutive relations. It relies on two features : first, a homogenization method to derive constitutive relations with internal variable gradients at the scale of the material point, then a generalization of these constitutive laws at the structural scale, based on the internal variable fields. This variational framework is well-suited to examine such questions as existency conditions for the law of evolution, appropriate functional spaces for the internal variable fields or the relations between local and gradient models. Moreover, a time-discretization leads to express the global constitutive relation as the minimization of an energy. This problem is solved through an augmented lagrangian algorithm, which places the treatment of strong nonlinearities (among which the non differentiability of the energy) at the integration point level, and therefore allows an easy implementation in the software we used, namely the Code_Aster®. Three applications highlight the capabilities of this method. First, its efficiency is shown when applied to a brittle damage model, from the derivation of the constitutive law up to numerical simulations. Then, the widely used theory of gradient plasticity is cast into our framework, thus proving its degree of generality. Finally, its application to Rousselier's law for ductile fracture of steels points out the interaction between large plastic strains and nonlocal behavior.
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https://tel.archives-ouvertes.fr/tel-00474024
Contributor : Eric Lorentz <>
Submitted on : Sunday, April 18, 2010 - 4:52:12 PM
Last modification on : Wednesday, December 9, 2020 - 3:17:16 PM
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  • HAL Id : tel-00474024, version 1

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Eric Lorentz. Lois de comportement à gradients de variables internes : construction, formulation variationnelle et mise en œuvre numérique. Mécanique [physics.med-ph]. Université Pierre et Marie Curie - Paris VI, 1999. Français. ⟨tel-00474024⟩

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