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Main Title: Analysis and Numerical Approximation of an Integro-differential Equation Modeling Non-local Effects in Linear Elasticity
Author(s): Emmrich, Etienne
Weckner, Olaf
Type: Article
Language Code: en
Abstract: 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 ∞(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.
Issue Date: 2007
Date Available: 8-Jan-2019
DDC Class: 510 Mathematik
620 Ingenieurwissenschaften und zugeordnete Tätigkeiten
Subject(s): long-range interactions
peridynamic theory
nonlinear dispersion relations
integro-differential equation
existence and uniqueness
jump discontinuity
numerical approximation
Journal Title: Mathematics and Mechanics of Solids
Publisher: SAGE Publications
Publisher Place: Washington, DC
Volume: 12
Issue: 4
Publisher DOI: 10.1177/1081286505059748
Page Start: 363
Page End: 384
EISSN: 1741-3028
ISSN: 1081-2865
Notes: Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.
This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.
Appears in Collections:Inst. Mathematik » Publications

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