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SIMULATION OF A MIXTURE MODEL FOR ULTRASOUND PROPAGATION THROUGH CANCELLOUS BONE USING STAGGERED-GRID FINITE DIFFERENCES

ROBERT P. GILBERT

Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA

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PHILIPPE GUYENNE

Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA

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, and

JING LI

Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA

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https://doi.org/10.1142/S0218396X12500178Cited by:6 (Source: Crossref)

Abstract

In this paper we treat the cancellous bone as is done in mixture theory, i.e. each point in the material has both a fluid and a solid phase co-existing there. Each phase is weighted by the volume fraction of material in the composite structure. It is seen that in such a material attenuation of amplitude as frequency increases occurs as is observed in laboratory experiments^33,34 and as was observed in the finite element homogenization approach used by Hackl, Ilic and Gilbert.

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