Thermodynamically consistent gradient elasticity with an internal variable

• Published in: arXiv.org
• Main Author: Ván, Peter
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 27.05.2020
• Subjects: Constitutive relationships; Continuum mechanics; Elastic bodies; Elasticity; Heuristic methods; Mathematical analysis; Nonequilibrium thermodynamics; Physics - Soft Condensed Matter; Physics - Statistical Mechanics; Strain; Thermodynamics
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2005.13662

The role of thermodynamics in continuum mechanics and the derivation of the proper constitutive relations is a discussed subject of Rational Mechanics. The classical literature did not use the accumulated knowledge of thermostatics and was very critical with 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. 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. Then the constitutive functions and the evolution equation of the internal variable is constructed. The second law analysis has shown a contribution of gradient terms to the stress, also without dissipation.