Modeling bodies that can only undergo isochoric motions subject to mechanical stimuli but are compressible or expansible with respect to thermal stimuli
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In this short note, we discuss a new constitutive approach to describing the response of bodies, both solid and fluid, that can only undergo isochoric motions in isothermal processes but which can undergo non-isochoric motions in arbitrary processes. Within this new framework, one finds that conditions that were perceived as constraints on the response of the body now arise naturally within the frame work of the constitutive definition of these bodies. For instance, a central approximation in fluid mechanics that is of great utility in the analysis of fluid flow problems in geophysics and astrophysics is that due to Oberbeck (Ann Phys Chem 1:271-292, 1879; Uber die bewengungsercheinungen der Atmosphare, Sitz Ber K Preuss Akad Miss, pp 383-395, 1129-1138, 1888) and Boussinesq (Theorie Analytique de la Chaleur. Gauthier-Villas, Paris, 1903) for describing the flow of fluids, which can undergo only isochoric motions in isothermal processes but which are otherwise capable of non-isochoric motions. A similar demand can be made concerning the response of solid bodies wherein one could carry out an approximation similar to that of the Oberbeck-Boussinesq equations, and such an approach might be of great value in the study of technologically relevant problems. © 2012 Springer Basel AG.
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