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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Design of materials with extreme thermal expansion using a three-phase topology optimization method
Ole Sigmund,Salvatore Torquato +1 more
TL;DR: In this article, a three-phase topology optimization method was proposed to find the distribution of material phases that optimizes an objective function (e.g. thermoelastic properties) subject to certain constraints, such as elastic symmetry or volume fractions of the constituent phases, within a periodic base cell.
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Materials with prescribed constitutive parameters: An inverse homogenization problem
TL;DR: In this article, the construction of materials with arbitrary prescribed positive semi-definite constitutive tensors is formulated as an inverse problem of finding a material with given homogenized coefficients.
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Heterogeneous multiscale methods: A review
TL;DR: This paper gives a systematic introduction to HMM, the heterogeneous multiscale methods, including the fundamental design principles behind the HMM philosophy and the main obstacles that have to be overcome.
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Multi-scale constitutive modelling of heterogeneous materials with a gradient-enhanced computational homogenization scheme
TL;DR: In this article, a gradient-enhanced computational homogenization procedure is proposed for the modeling of microstructural size effects, within a general non-linear framework, where the macroscopic deformation gradient tensor and its gradient are imposed on a micro-structural representative volume element (RVE).
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A unified periodical boundary conditions for representative volume elements of composites and applications
TL;DR: In this paper, an explicit unified boundary condition for a periodic representative volume element (RVE) is presented which satisfies the periodicity conditions, and is suitable for any combination of multiaxial loads.
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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.