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Comportement macroscopique et statistiques des champs dans les composites viscoplastiques.

Abstract : We have developed nonlinear homogenization methods capable of delivering estimates not only for the macroscopic behavior but also for the field statistics in viscoplastic composites. These methods are based on suitably designed variational principles, which make use of an optimally chosen 'linear comparison composite', allowing direct conversion of linear estimates into corresponding estimates for the effective potentials of nonlinear composites. In order to extract estimates for the field statistics from these methods, a novel procedure is proposed, ! making use of suitably perturbed effective potentials. By means of this procedure, we obtain estimates for the first moments of the local fields in each phase that are entirely consistent with the corresponding estimates for the effective behavior. In addition, unlike earlier approaches, this procedure is not limited to first and second moments, and can be used to estimate higher-order moments as well as the phase average of more general convex functions of the fields. Sample results are given for two-phase composites with random 'particulate' microstructures exhibiting overall transversely isotropic and isotropic symmetry. Their accuracy is assessed by confronting them with corresponding exact results for nonlinear sequential laminates. Homogenization estimates are found to be in good agreement with the exact results, even for high nonlinearities, when the strain-rate fields are found to become strongly heterogeneous.
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Submitted on : Thursday, July 29, 2010 - 2:22:15 PM
Last modification on : Wednesday, November 17, 2021 - 12:28:04 PM
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  • HAL Id : pastel-00002202, version 1


Martin Idiart. Comportement macroscopique et statistiques des champs dans les composites viscoplastiques.. Mécanique des matériaux [physics.class-ph]. Ecole Polytechnique X, 2006. Français. ⟨pastel-00002202⟩



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