Improved Hashin–Shtrikman Bounds for Elastic Moment Tensors and an Application

Improved Hashin–Shtrikman Bounds for Elastic Moment Tensors and an Application This paper is devoted to the derivation of trace bounds for elastic moment tensors. Starting from the integral equation formulation of the elastic moment tensor, we establish that its trace can be obtained as a sum of minimal energies. We then recover the so-called Hashin–Shtrikman bounds, and show that these bounds can be tightened for inclusions which have some local thickness. As an application, we show that the volume of the inclusion can be estimated by the elastic moment tensor. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Improved Hashin–Shtrikman Bounds for Elastic Moment Tensors and an Application

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Publisher
Springer-Verlag
Copyright
Copyright © 2008 by Springer Science+Business Media, LLC
Subject
Mathematics; Numerical and Computational Methods ; Mathematical Methods in Physics; Mathematical and Computational Physics; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-007-9022-9
Publisher site
See Article on Publisher Site

Abstract

This paper is devoted to the derivation of trace bounds for elastic moment tensors. Starting from the integral equation formulation of the elastic moment tensor, we establish that its trace can be obtained as a sum of minimal energies. We then recover the so-called Hashin–Shtrikman bounds, and show that these bounds can be tightened for inclusions which have some local thickness. As an application, we show that the volume of the inclusion can be estimated by the elastic moment tensor.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Apr 1, 2008

References

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