One-dimensional nonlinear motions in electroelastic solids: Characteristics and shock waves
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.
quasistatic electric field approximation
linearized forms of the governing equations
scientific article; zbMATH DE number 4066457
scientific article