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Entropy 2018, 20(3), 179; https://doi.org/10.3390/e20030179

Non-Conventional Thermodynamics and Models of Gradient Elasticity

1
Faculty of Mathematics, Technische Universität Darmstadt, Schlossgartenstraße 7, D-64289 Darmstadt, Germany
2
Department of Continuum Mechanics, Faculty of Civil Engineering, Technische Universität Darmstadt, Franziska-Braun-Str. 7, D-64287 Darmstadt, Germany
3
Department of Civil Engineering, University of Patras, 26500 Patras, Greece
*
Author to whom correspondence should be addressed.
Received: 29 December 2017 / Revised: 28 February 2018 / Accepted: 2 March 2018 / Published: 8 March 2018
(This article belongs to the Special Issue Phenomenological Thermodynamics of Irreversible Processes)
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Abstract

We consider material bodies exhibiting a response function for free energy, which depends on both the strain and its gradient. Toupin–Mindlin’s gradient elasticity is characterized by Cauchy stress tensors, which are given by space-like Euler–Lagrange derivative of the free energy with respect to the strain. The present paper aims at developing a first version of gradient elasticity of non-Toupin–Mindlin’s type, i.e., a theory employing Cauchy stress tensors, which are not necessarily expressed as Euler–Lagrange derivatives. This is accomplished in the framework of non-conventional thermodynamics. A one-dimensional boundary value problem is solved in detail in order to illustrate the differences of the present theory with Toupin–Mindlin’s gradient elasticity theory. View Full-Text
Keywords: gradient elasticity; non-equilibrium thermodynamics; interstitial working; boundary conditions; energy transfer law gradient elasticity; non-equilibrium thermodynamics; interstitial working; boundary conditions; energy transfer law
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Alber, H.-D.; Broese, C.; Tsakmakis, C.; Beskos, D.E. Non-Conventional Thermodynamics and Models of Gradient Elasticity. Entropy 2018, 20, 179.

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