One-dimensional nonlinear motions in electroelastic solids: Characteristics and shock waves
type: Item
instance of: scholarly article
title: One-dimensional nonlinear motions in electroelastic solids: Characteristics and shock waves
zbMATH Open document ID: 0653.73016
DOI: 10.1007/BF00945051
author: Wafa Ani
author: Gérard A. Maugin
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 1988-01-01T00:00:00Z
review text: The paper is mainly concerned with the propagation of one-dimensional longitudinal shocks in nonlinear elastic dielectries. The magnetic effects are totally disregarded and quasistatic electric field approximation is employed to facilitate the analysis a great deal. After having recapitulated appropriate field equations, constitutive relations and jump conditions on a surface of discontinuity, the authors first obtain expressions corresponding to one-dimensional longitudinal motion and to a quartic internal energy density. Then they obtain the linearized forms of the governing equations and they determine the speed of propagation of infinitesimal disturbances through the method of characteristics. Finally they study the propagation of longitudinal shocks by employing dynamical, kinematical and geometrical compatibility conditions on the field quantities across the shock plane. They prove for weak shocks that entropy jump across the shock wave is again of the third order in shock strength. It is also shown that if the internal energy is a quadratic polynomial and if the electroelastic coupling is represented solely by piezoelectricity, only compressive shocks are thermodynamically admissible. Finally electroelastic shocks are classified and the existence of compressive switch-on and switch-off shocks are shown. Although the analysis can be extended in principle to three-dimensional curved shocks the algebra involved would probably prove to be prohibitive.
Mathematics Subject Classification ID: 74H45
Mathematics Subject Classification ID: 74F15
Mathematics Subject Classification ID: 35L67
Mathematics Subject Classification ID: 74M20
Mathematics Subject Classification ID: 78A40
zbMATH DE Number: 4066457
zbMATH Keywords: one-dimensional longitudinal shocks
zbMATH Keywords: nonlinear elastic dielectries
zbMATH Keywords: quasistatic electric field approximation
zbMATH Keywords: quartic internal energy density
zbMATH Keywords: linearized forms of the governing equations
zbMATH Keywords: speed of propagation
zbMATH Keywords: infinitesimal disturbances
zbMATH Keywords: method of characteristics
zbMATH Keywords: dynamical
zbMATH Keywords: kinematical
zbMATH Keywords: geometrical compatibility conditions
zbMATH Keywords: entropy jump
zbMATH Keywords: third order
reviewed by: Erdoğan S. Şuhubi
MaRDI profile type: Publication
cites work: Q3701019
cites work: Q5646485
cites work: Q5555602
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cites work: Thermodynamic influences on the behavior of one-dimensional shock waves in elastic dielectrics
cites work: On the behavior of shock waves in deformable dielectric materials
full work available at URL: https://doi.org/10.1007/bf00945051
OpenAlex ID: W2419591744
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description: scientific article; zbMATH DE number 4066457