These results depend only weakly on the crack density and on the matrix material. Finally, media containing dry inclusions of any aspect ratio cannot be modelled by thin isotropic layering. The limiting aspect ratio decreases for a decreasing ratio of theīulk modulus of the fluid to the shear modulus of the matrix material. Inclusions can be represented by sequences of stable isotropic layers if the inclusions haveĪspect ratios less than 0.1. This expression (which is a good approximationįor several crack models) and numerical calculations show that media containing water-filled The constraints are satisfied can be derived. An analytical expression describing the range of aspect ratios for which Important parameters determining whether theseĬcrlditions are satisfied are the aspect ratio of the inclusions and the material filling the several stability conditions are satisfied. These transversely isotropic media can be modelled by such sequences if - and only if
However, the transversely isotropic media which are equivalent to media containingĪligned inclusions do not necessarily have to be representable by sequences of stable isotropic Sequences of isotropic layers show transverse isotropy with respect to elastic wave propagation. Media containing aligned cracks or ellipsoidal inclusions as well as media consisting of The representability of cracked media by periodically layered media.
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