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Non-Conventional Thermodynamics and Models of Gradient Elasticity

Alber, Hans-Dieter ; Broese, Carsten ; Tsakmakis, Charalampos ; Beskos, Dimitri (2018):
Non-Conventional Thermodynamics and Models of Gradient Elasticity.
20, In: Entropy, (3), MDPI, ISSN 1099-4300,

Copyright Information: CC BY 4.0 International - Creative Commons, Attribution.

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Item Type: Article
Origin: Secondary publication via sponsored Golden Open Access
Title: Non-Conventional Thermodynamics and Models of Gradient Elasticity
Language: English

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.

Journal or Publication Title: Entropy
Series Volume: 20
Issue Number: 3
Place of Publication: Darmstadt
Publisher: MDPI
Classification DDC: 600 Technik, Medizin, angewandte Wissenschaften > 600 Technik
Divisions: 13 Department of Civil and Environmental Engineering Sciences > Mechanics > Continuum Mechanics
Date Deposited: 14 Mar 2018 14:48
Last Modified: 13 Dec 2022 10:17
Corresponding Links:
URN: urn:nbn:de:tuda-tuprints-72954
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/7295
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