Journal
QUARTERLY JOURNAL OF MECHANICS AND APPLIED MATHEMATICS
Volume 67, Issue 2, Pages 311-342Publisher
OXFORD UNIV PRESS
DOI: 10.1093/qjmam/hbu008
Keywords
-
Categories
Funding
- Engineering and Physical Sciences Research Council [EP/H010114/1]
- New Zealand Foundation of Research, Science and Technology [RW9019]
- EPSRC [EP/H010114/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/H010114/1] Funding Source: researchfish
Ask authors/readers for more resources
Using the method of asymptotic homogenization in the low-frequency wave propagation regime we derive the effective antiplane elastic properties of a cracked solid which in the absence of cracks would be orthotropic. The solid is a periodic medium defined by a periodic cell containing N cracks of infinite extent in the z direction but with arbitrary shape and orientation in the xy plane. Effective properties are defined in terms of the solution to a so-called cell problem. We propose two convenient schemes by which the cell problem can be solved, one based on a nearly periodic Green's function, the other based on doubly periodic multipole expansions. Using these methods we compare results with existing approximate expressions for periodic arrays of straight cracks and discuss their regimes of validity by assessing their departure from the exact results obtained by the present method. We go on to consider more complex distributions such as elliptical cavities, non-straight cracks and effects of an orthotropic host phase. In particular we show that specific types of regular arrays of cracks in an orthotropic host medium can induce a macroscopically isotropic response to antiplane shear waves propagating in the xy plane.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available