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Scale-Dependent Homogenization of Random Hyperbolic Thermoelastic Solids

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Abstract

The scale-dependent homogenization is applied to a hyperbolic thermoelastic material with two relaxation times, where conductivity and stiffness are wide-sense stationary ergodic random fields. The previously established scaling functions for the Fourier-type conductivity and linear elastic responses are used to describe the trends to scale from the mesoscale statistical volume element level (SVE) to the (representative volume element) RVE level of a deterministic homogeneous continuum. In the case of white-noise type random fields, this finite-size scaling can be quantified via universally appearing stretched exponentials for conductivity and elasticity problems.

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Acknowledgements

Comments of two anonymous reviewers helped improve this note. The work was supported by the RDECOM-AMSAA: Army Materiel Systems Analysis Activity (William Davis) under the auspices of the US Army Research Office Scientific Services Program administered by Battelle (W911NF-11-D-0001 DO# 0169; TCN 12-078).

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Authors and Affiliations

  1. Department of Mechanical Science & Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA

    Martin Ostoja-Starzewski

  2. Institute for Condensed Matter Theory and Beckman Institute, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA

    Martin Ostoja-Starzewski

  3. Institute for Multiscale Reactive Modeling, Energetics and Warheads Research and Development, RDAR-MEE-W, Building 3022, Room 44, Picatinny, NJ, 07806-5000, USA

    Luis Costa

  4. Department of Mechanical Engineering, American University of Sharjah, P.O. Box 26666, Sharjah, UAE

    Shivakumar I. Ranganathan

Authors
  1. Martin Ostoja-Starzewski
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  2. Luis Costa
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  3. Shivakumar I. Ranganathan
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Correspondence to Martin Ostoja-Starzewski.

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Ostoja-Starzewski, M., Costa, L. & Ranganathan, S.I. Scale-Dependent Homogenization of Random Hyperbolic Thermoelastic Solids. J Elast 118, 243–250 (2015). https://doi.org/10.1007/s10659-014-9483-4

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  • DOI: https://doi.org/10.1007/s10659-014-9483-4

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