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Nonconventional thermodynamics, indeterminate couple stress elasticity and heat conduction

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Abstract

We present a phenomenological thermodynamic framework for continuum systems exhibiting responses which may be nonlocal in space and for which short time scales may be important. Nonlocality in space is engendered by state variables of gradient type, while nonlocalities over time can be modelled, e.g. by assuming the rate of the heat flux vector to enter into the heat conduction law. The central idea is to restate the energy budget of the system by postulating further balance laws of energy, besides the classical one. This allows for the proposed theory to deal with nonequilibrium state variables, which are excluded by the second law in conventional thermodynamics. The main features of our approach are explained by discussing micropolar indeterminate couple stress elasticity and heat conduction theories.

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Authors and Affiliations

  1. Department of Analysis, Faculty of Mathematics, TU Darmstadt, Schlossgartenstraße 7, 64289, Darmstadt, Germany

    H.-D. Alber

  2. Department of Continuum Mechanics, Institute for Mechanics and Civil Engineering, TU Darmstadt, Franziska-Braun-Str. 7, 64287, Darmstadt, Germany

    K. Hutter & Ch. Tsakmakis

Authors
  1. H.-D. Alber
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  2. K. Hutter
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  3. Ch. Tsakmakis
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Correspondence to Ch. Tsakmakis.

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Communicated by Andreas Öchsner.

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Alber, HD., Hutter, K. & Tsakmakis, C. Nonconventional thermodynamics, indeterminate couple stress elasticity and heat conduction. Continuum Mech. Thermodyn. 28, 699–719 (2016). https://doi.org/10.1007/s00161-014-0406-1

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  • DOI: https://doi.org/10.1007/s00161-014-0406-1

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