SOME STRONG WAVE PROBLEMS IN AN ELASTIC MATERIAL WITH MICROSTRUCTURE
Final technical rept. 18 May 1967-17 Jun 1968
GENERAL RESEARCH CORP SANTA BARBARA CA
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The historical development of the foundations of thermomechanics is reviewed, with emphasis placed upon the critical contribution of each investigator. The theories are discussed in terms of their relevance to real materials in the important high-velocity regime which lies between the low and intermediate velocity regime which involves essentially isothermal elastic and plastic wave propagation on one hand and the ultrahigh-velocity regime in which a hydrodynamic description of the material behavior is adequate on the other. Various facets of high-velocity wave propagation in various materials involve elastic, plastic, viscous, and thermal effects on a macroscopic scale and perhaps on a microscopic scale. Evaluations are made from the standpoint of thermodynamics as well as classical mechanics. Using fundamental principles of thermodynamics and mechanics, thermomechanically coupled linear energy and constitutive equations are derived for the elastic solid with micro unit cells discussed by Mindlin. Equations of motion for the microstructure are found for the large amplitude case where Eulerian and Lagrangian formulations are not identical.