On an elastodynamic classification of orthorhombic media

Abstract

Sets of elastic constants for crystalline media are normally presented with reference to the axes of the unit cell defined by structural crystallographers (Landolt & Bdrnstein 1979). In orthorhombic materials, the magnitudes of the nine elastic stiffnesses, in general, show little or no consistent correspondence with the suffixes (related to crystal axes) of the physical constants. A classification scheme for orthorhombic media, based on an ordering of the elastodynamically important principal stiffnesses of extension ( c 11 , c 22 , c 33 ) and of shear ( c 44 , c 55 , c 66 ), is described and illustrated. The classification facilitates meaningful comparisons of elastodynamic properties since it offers the following advantages: (i) It is amenable to cyclic interchange. (ii) It permits concise expression of basic homogeneous plane wave theory (Musgrave 1970). (iii) It affords rapid appreciation of the possible essential configurations of homogeneous plane wave slowness in each coordinate plane. (iv) It allows known criteria for the existence of hyperbolic regions in elastic slowness and wave surfaces (Musgrave 1957,1979) and some further developments, to be succinctly expressed. Application of the scheme to the theory of bulk waves is exemplified in detail for three media, diverse in their properties, a-uranium, spruce (wood) and a hypothetical medium discussed by Al’shits & Lothe (19796); specification of exceptional, limiting bulk waves (Chadwick & Smith 1977) is included.