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The Representative Volume Size in Static and Dynamic Micro-Macro Transitions

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Abstract

Two homogenisation schemes (first-order or local, and second-order or non-local) are employed in this paper. In case second-order homogenisation is applied, it turns out that elastic behaviour at the micro-scale implies the appearance of second-order space and time derivatives of macroscopic strain in an otherwise elastic constitutive equation for the macroscopic stress. The coefficients of the second-order terms scale with the size of the Representative Volume Element (RVE) employed in the homogenisation scheme.

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Authors and Affiliations

  1. School of Mechanical, Aerospace & Civil Engineering, University of Manchester, Sackville Street, Manchester, M60 1QD, United Kingdom

    Inna M. Gitman

  2. Department of Civil and Structural Engineering, University of Sheffield, Mappin Street, Sheffield, S1 3JD, United Kingdom

    Harm Askes

  3. Polytechnic School, Laboratory of Mechanics and Materials, Aristotle University of Thessaloniki, 54006, Thessaloniki, Greece

    Elias C. Aifantis

  4. Center for Mechanics of Materials and Instabilities, Michigan Technological University, Houghton, MI, 49931, USA

    Elias C. Aifantis

Authors
  1. Inna M. Gitman
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  2. Harm Askes
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  3. Elias C. Aifantis
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Correspondence to Inna M. Gitman.

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Gitman, I.M., Askes, H. & Aifantis, E.C. The Representative Volume Size in Static and Dynamic Micro-Macro Transitions. Int J Fract 135, L3–L9 (2005). https://doi.org/10.1007/s10704-005-4389-6

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  • DOI: https://doi.org/10.1007/s10704-005-4389-6

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