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Overall properties of a cracked solid

Published online by Cambridge University Press:  24 October 2008

J. A. Hudson
J. A. Hudson
Affiliation:
University of Cambridge
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Abstract

The differential-integral equation of motion for the mean wave in a solid material containing embedded cavities or inclusions is derived. It consists of a series of terms of ascending powers of the scattering operator, and is here truncated after the third term. This implies the second-order interactions between scatterers are included but those of the third order are not.

The formulae are specialized to the case of thin cracks, either aligned in a single direction or randomly oriented. Expressions for the overall elastic constants are derived for the case of long wavelengths. These expressions are accurate to the second order in the number density of scatterers.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 88 , Issue 2 , September 1980 , pp. 371 - 384
Copyright
Copyright © Cambridge Philosophical Society 1980

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