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

Charalambakis, Nicolas; Murat, François

doi:10.1090/S0033-569X-10-01199-9

Authors: Nicolas Charalambakis and François Murat
Journal: Quart. Appl. Math. 68 (2010), 395-419
MSC (2000): Primary 74Q15, 74Q10, 35B27
DOI: https://doi.org/10.1090/S0033-569X-10-01199-9
Published electronically: June 8, 2010
MathSciNet review: 2676968
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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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