This article is cited in 5 papers

Thermodynamically consistent gradient elasticity with an internal variable

Peter Ván<sup>abc

a</sup> Wigner Research Centre for Physics, Department of Theoretical Physics, Budapest, Hungary
^b Budapest University of Technology and Economics, Faculty of Mechanical Engineering, Department of Energy Engineering, Budapest, Hungary
^c Montavid Thermodynamic Research Group, Budapest, Hungary

Abstract: The role of thermodynamics in continuum mechanics and the derivation of proper constitutive relations is a topic discussed in Rational Mechanics. The classical literature did not use the accumulated knowledge of thermostatics and was very critical of the heuristic methods of irreversible thermodynamics. In this paper, a small strain gradient elasticity theory is constructed with memory effects and dissipation. The method is nonequilibrium thermodynamics with internal variables; therefore, the constitutive relations are compatible with thermodynamics by construction. The thermostatic Gibbs relation is introduced for elastic bodies with a single tensorial internal variable. The thermodynamic potentials are first-order weakly nonlocal, and the entropy production is calculated. The constitutive functions and the evolution equation of the internal variable are then constructed. The second law analysis has shown a contribution of gradient terms to the stress, also without dissipation.

Keywords: nonequilibrium thermodynamics, generalised continua, gradient elasticity.

MSC: 74A15, 74A60

Received: 04.02.2020
Revised: 27.05.2020

Language: English

DOI: 10.2298/TAM200204006V

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