Advanced Search

Journal Navigation

Journal Home

Subscriptions

Archive

Contact Us

Table of Contents

CiteULike is a free service for managing and discovering scholarly references - click here to get started.

Sign In to gain access to subscriptions and/or personal tools.
Mathematics and Mechanics of Solids
This Article
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
1081286505059748v1
1081286505059748v2
12/4/363    most recent
Right arrow References
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in Web of Science
Right arrow Alert me to new issues of the journal
Right arrow Add to Saved Citations
Right arrow Download to citation manager
Right arrowRequest Permissions
Right arrow Request Reprints
Right arrow Add to My Marked Citations
Citing Articles
Right arrow Citing Articles via Web of Science (3)
Right arrow Citing Articles via Google Scholar
Right arrow Citing Articles via Scopus
Google Scholar
Right arrow Articles by Emmrich, E.
Right arrow Articles by Weckner, O.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Complore   Add to Connotea   Add to Del.icio.us   Add to Digg   Add to Reddit   Add to Technorati   Add to Twitter  
What's this?

Analysis and Numerical Approximation of an Integro-differential Equation Modeling Non-local Effects in Linear Elasticity

Etienne Emmrich

Technische Universität Berlin, Institut für Mathematik, Strasse des 17. Juni 136, 10623 Berlin, Germany

Olaf Weckner

Massachusetts Institute of Technology, Department of Mechanical Engineering, Cambridge, MA 02139, USA

Long-range interactions for linearly elastic media resulting in nonlinear dispersion relations are modeled by an initial-value problem for an integro-differential equation (IDE) that incorporates non-local effects. Interpreting this IDE as an evolutionary equation of second order, well-posedness in L {infty}(R) as well as jump relations are proved. Moreover, the construction of the micromodulus function from the dispersion relation is studied. A numerical approximation based upon quadrature is suggested and carried out for two examples, one involving jump discontinuities in the initial data corresponding to a Riemann-like problem.

Key Words: Long-range interactions • peridynamic theory • nonlinear dispersion relations • integro-differential equation • existence and uniqueness • jump discontinuity • numerical approximation

This version was published on August 1, 2007

Mathematics and Mechanics of Solids, Vol. 12, No. 4, 363-384 (2007)
DOI: 10.1177/1081286505059748
Add to CiteULike CiteULike   Add to Complore Complore   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us   Add to Digg Digg   Add to Reddit Reddit   Add to Technorati Technorati   Add to Twitter Twitter    What's this?