What are internal variables? A. Berezovski answers

Jüri Engelbrecht
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Jüri Engelbrecht: Tallinn University of Technology Institute of Cybernetics, Centre for Nonlinear Studies (CENS)

Chapter Chapter 4 in Questions About Elastic Waves, 2015, pp 43-69 from Springer

Abstract: Abstract Internal structures (microstructures) appear in solids at different length scales. Generally speaking, their influence on the macromotion can be understood and measured on the macrolevel. However, “there is no unique answer to the question how the microstructure influence can be accounted for in a continuum mechanical model” [132]. In addition, thermodynamical constraints should be taken into account, which is not obvious in many theories. In the previous section, heterogeneity is linked to the real microstructure, like “cells” in the Mindlin theory. One possibility to bring thermodynamics directly into modelling of dynamical phenomena is provided by the concept of internal variables. The idea of internal variables can be traced back to P. Duhem, P. Bridgman and J. Kestin (see historical overview in [161]). A contemporary presentation of the formalism of internal variables is presented by Maugin [154] and Maugin and Muschik [163].

Keywords: Internal Variable; Energy Conservation Equation; Free Energy Function; Dissipation Inequality; Eshelby Stress (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/978-3-319-14791-8_4

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