Jump to ContentJump to Main Navigation
Mathematical Methods in Elasticity Imaging$
Users without a subscription are not able to see the full content.

Habib Ammari, Elie Bretin, Josselin Garnier, Hyeonbae Kang, Hyundae Lee, and Abdul Wahab

Print publication date: 2015

Print ISBN-13: 9780691165318

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691165318.001.0001

Show Summary Details
Page of

PRINTED FROM PRINCETON SCHOLARSHIP ONLINE (www.princeton.universitypressscholarship.com). (c) Copyright Princeton University Press, 2022. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in PRSO for personal use.date: 02 July 2022

Elasticity Equations with High Contrast Parameters

Elasticity Equations with High Contrast Parameters

(p.33) Chapter Two Elasticity Equations with High Contrast Parameters
Mathematical Methods in Elasticity Imaging

Habib Ammari

Elie Bretin

Josselin Garnier

Hyeonbae Kang

Hyundae Lee

Abdul Wahab

Princeton University Press

This chapter presents some recent results on the elasticity equations with high contrast coefficients. It first sets up the problems for finite and extreme moduli before discussing the incompressible limit of elasticity equations. It then provides a complete asymptotic expansion with respect to the compressional modulus and considers the limiting cases of holes and hard inclusions. It proves that the energy functional is uniformly bounded and demonstrates that the potentials on the boundary of the inclusion are also uniformly bounded. It also shows that these potentials converge as the bulk and shear moduli tend to their extreme values and that similar boundedness and convergence result holds true for the boundary value problem.

Keywords:   elasticity equation, high contrast coefficient, incompressible limit, asymptotic expansion, compressional modulus, hole, hard inclusion, energy functional, boundary value problem, boundedness

Princeton Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us.