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Scaling to RVE in Random Media
University of Illinois at Urbana-Champaign, USA.
University of Illinois at Urbana-Champaign, USA.
University of Illinois at Urbana-Champaign, USA.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (MAM)ORCID iD: 0000-0002-0139-0747
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2016 (English)In: Advances in Applied Mechanics / [ed] Stephane P. A. Bordas and Daniel S. Balint, Academic Press, 2016, 111-211 p.Chapter in book (Refereed)
Abstract [en]

The problem of effective properties of material microstructures has received considerableattention over the past half a century. By effective (or overall, macroscopic, global) ismeant the response assuming the existence of a representative volume element (RVE)on which a homogeneous continuum is being set up. Since the efforts over the pastquarter century have been shifting to the problem of the size of RVE, this chapterreviews the results and challenges in this broad field for a wide range of materials.For the most part, the approach employed to assess the scaling to the RVE is basedon the Hill–Mandel macrohomogeneity condition. This leads to bounds that explicitlyinvolve the size of a mesoscale domain—this domain also being called a statisticalvolume element (SVE)—relative to the microscale and the type of boundary conditionsapplied to this domain. In general, the trend to pass from the SVE to RVE depends onrandom geometry and mechanical properties of the microstructure, and displayscertain, possibly universal tendencies. This chapter discusses that issue first for linearelastic materials, where a scaling function plays a key role to concisely grasp theSVE-to-RVE scaling. This sets the stage for treatment of nonlinear and or/inelastic randommaterials, including elasto-plastic, viscoelastic, permeable, and thermoelasticclasses. This methodology can be extended to homogenization of random media bymicropolar (Cosserat) rather than by classical (Cauchy) continua as well as to homogenizationunder stationary (standing wave) or transient (wavefront) loading conditions.The final topic treated in this chapter is the formulation of continuum mechanicsaccounting for the violations of second law of thermodynamics, which have been studied on a molecular level in statistical physics over the past two decades. We end with anoverview of open directions and challenges of this research field.

Place, publisher, year, edition, pages
Academic Press, 2016. 111-211 p.
Series
Advances in Applied Mechanics, ISSN 0065-2156 ; 49
National Category
Other Mathematics Computational Mathematics
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-33454DOI: 10.1016/bs.aams.2016.07.001ISBN: 978-0-12-804779-8 (print)OAI: oai:DiVA.org:mdh-33454DiVA: diva2:1039380
Available from: 2016-10-24 Created: 2016-10-24 Last updated: 2016-12-05Bibliographically approved

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Publisher's full texthttp://www.sciencedirect.com/science/bookseries/00652156

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CiteExportLink to record
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Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
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Language
  • de-DE
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