Asymptotic Analysis of Periodic Structures
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This article is published in Journal of Applied Mechanics.The article was published on 1979-06-01 and is currently open access. It has received 5038 citations till now. The article focuses on the topics: Asymptotic analysis.read more
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Homogenization with corrector term for periodic elliptic differential operators
TL;DR: In this paper, the problem of homogenization in the small period limit is considered for matrix periodic elliptic differential operators with coefficients oscillating rapidly (i.e., depending on x/ε).
Journal ArticleDOI
Nonlinear mechanical behaviour and analysis of wood and fibre materials
TL;DR: In this article, the mechanical properties of the cellular structure of wood are characterized and modelled, the irregular cell shape, the anisotropic layered structure of the cell walls and the periodic variations in density being taken into account.
Journal ArticleDOI
Finite difference heterogeneous multi-scale method for homogenization problems
Assyr Abdulle,Weinan E +1 more
TL;DR: A numerical method for solving multi-scale parabolic problems based on the use of two different schemes for the original equation, at different grid level which allows to give numerical results at a much lower cost than solving the original equations.
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Multiscale asymptotic homogenization for multiphysics problems with multiple spatial and temporal scales: a coupled thermo-viscoelastic example problem
Qing Yu,Jacob Fish +1 more
TL;DR: In this paper, a systematic approach for analyzing multiple physical processes interacting at multiple spatial and temporal scales is developed, which is applied to coupled thermo-viscoelastic composites with microscopically periodic mechanical and thermal properties.
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A nonstandard method of modelling of thermoelastic periodic composites
TL;DR: In this paper, the authors derive from the equations of the nonlinear thermoelasticity a certain class of homogenized models of periodic composite materials, based on the methods of nonstandard analysis.
References
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An Introduction To Probability Theory And Its Applications
TL;DR: A First Course in Probability (8th ed.) by S. Ross is a lively text that covers the basic ideas of probability theory including those needed in statistics.
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Théorie des distributions
TL;DR: The merite as discussed by the authors is a date marque une date dans le progres des mathematiques and de la physique en levant l'ambiguite que constituait le succes des methodes de calcul symbolique aupres des physiciens and l'inacceptabilite de leurs formules au regard de la rigueur mathematiques.