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Mathematical and numerical analysis in thermo-gradient-dependent theory of plasticity

Type
Articles dans des revues avec comité de lecture
Author
AOUADI, Moncef
232921 Université de Carthage - University of Carthage
BEN BETTAIEB, Mohamed
243747 Labex DAMAS
178323 Laboratoire d'Etude des Microstructures et de Mécanique des Matériaux [LEM3]
ABED-MERAIM, Farid
178323 Laboratoire d'Etude des Microstructures et de Mécanique des Matériaux [LEM3]
243747 Labex DAMAS

URI
http://hdl.handle.net/10985/13555
DOI
10.1002/zamm.201700131
Date
2018
Journal
Journal of Applied Mathematics and Mechanics (ZAMM)

Abstract

In this paper, we develop new governing equations for thermo-gradient-dependent theory of plasticity. They include the coupled effects of thermal elastic-plastic theory, including balance and constitutive equations. To demonstrate the salient feature of the gradient-dependent model of plasticity, particular attention is addressed to isotropic hardening with second sound effects to eliminate the paradox of infinite speed of thermal signals. The resulting system of partial differential equations formally describes the coupled thermomechanical behavior of the gradient-dependent elasto-plastic system. Then, we develop an appropriate state-space form and, by using the semigroup theory, we prove the well-posedness and the exponential stability of the thermo-gradient-dependent elasto-plastic one-dimensional problem. Finally, we perform numerical simulations to validate the proposed model and to show its capability.

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