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Two stable-by-homogenization models in simple shearing of rate-dependent non-homogeneous materials

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TLDR
In this article, the viscoplastic model and the thermoviscous model of rate-dependent non-homogeneous materials with non-oscillating strain-rate sensitivity submitted to simple quasistatic shearing are studied.
Abstract
In this paper we study two models, the viscoplastic model and the thermoviscous model, of rate-dependent non-homogeneous materials with non-oscillating strain-rate sensitivity submitted to simple quasistatic shearing. We prove that the two models are stable by homogenization, i.e. that the equations in both the heterogeneous problems and the homogenized one have the same form, and we give explicit formulas for the homogenized (effective) coefficients. These formulas depend on the initial conditions, but not on the boundary conditions. Our theoretical results are illustrated by a numerical example.

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Mathematical homogenization of inelastic dissipative materials: a survey and recent progress

TL;DR: In this paper, a review of mathematical homogenization of dissipative composites under small strains and the interplay between homogenisation procedure and dissipation due to mechanical work is presented.

Plasticité et homogénéisation de poutres hétérogènes périodiques : analyse limite et adaptation

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Plastic deformation modes in perforated sheets and their relation to yield and limit surfaces

TL;DR: In this paper, the authors employ an efficient homogenization theory to identify deformation modes in plates under plane stress with hexagonal arrays of circular holes at small and intermmediate pore volume fractions, and establish their relation to the branches of initial and subsequent yield and limit surfaces.
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Stability by homogenization of thermoviscoplastic problems

TL;DR: In this article, the authors study the homogenization of the system of partial differential equations describing the quasistatic shearing of heterogeneous thermoviscoplastic materials.
Journal ArticleDOI

The role of gradation on the improvement of effective properties of highly heterogeneous multilayered thermoviscoplastic materials under simple shearing

TL;DR: In this article, the role of the gradation on the effective properties of heterogeneous multilayered thermoviscoplastic materials with discontinuous properties under simple shearing was studied.
References
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Book

Asymptotic analysis for periodic structures

TL;DR: In this article, the authors give a systematic introduction of multiple scale methods for partial differential equations, including their original use for rigorous mathematical analysis in elliptic, parabolic, and hyperbolic problems, and with the use of probabilistic methods when appropriate.
Book

Non-Homogeneous Media and Vibration Theory

TL;DR: In this article, a spectral perturbation of spectral families and applications to self-adjoint eigenvalue problems are discussed, as well as the Trotter-Kato theorem and related topics.
Journal ArticleDOI

Analysis of Composite Materials—A Survey

TL;DR: In this paper, the authors review the analysis of composite materials from the applied mechanics and engineering science point of view, including elasticity, thermal expansion, moisture swelling, viscoelasticity, conductivity, static strength, and fatigue failure.
Book

Mécanique des matériaux solides

TL;DR: In this paper, Rheologie, Milieux continus continus, Plasticite, and Fissuration Reference Record created on 2004-09-07, modified on 2016-08-08
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