In this paper we derive necessary and sufficient conditions for strong ellipticity in several classes of anisotropic linearly elastic materials. Our results cover all classes in the rhombic system (nine elasticities), four classes of the tetragonal system (six elasticities) and all classes in the cubic system (three elasticities). As a special case we recover necessary and sufficient conditions for strong ellipticity in transversely isotropic materials. The central result shows that for the rhombic system strong ellipticity restricts some appropriate combinations of elasticities to take values inside a domain whose boundary is the third order algebraic surface defined by x^2 + y^2 + z^2 − 2xyz − 1 = 0 situated in the cube |x| < 1, |y| < 1, |z| < 1. For more symmetric situations, the general analysis restricts combinations of elasticities to
range inside either a plane domain (for four classes in the tetragonal system) or in an one-dimensional interval (for the hexagonal systems, transverse isotropy and cubic system). The proof involves only the basic statement of the strong ellipticity condition
A model for coupled elasto-acoustic waves, thermal waves, and waves associated with the voids, in a
porous medium is investigated. Due to the use of lighter materials in modern buildings and noise concerns
in the environment such models for thermo-poroacoustic waves are of much interest to the building industry.
Analysis of such waves is also of interest in acoustic microscopy where the identification of material defects
is of paramount importance to industry and medicine. We present a model for acoustic wave propagation in
a porous material which also allows for propagation of a thermal wave. The thermodynamics is based on
an entropy inequality of A.E. Green, F.R.S. and N. Laws and is presented for a modification of the theory
of elastic materials with voids due to J.W. Nunziato and S.C. Cowin. A fully nonlinear acceleration wave
analysis is initiated
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.