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Mathematical analysis for the peridynamicnonlocal continuum theory*

Published online by Cambridge University Press:  02 August 2010

Qiang Du  and
Kun Zhou
Qiang Du
Affiliation:
Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA. qdu@math.psu.edu; zhou@math.psu.edu
Kun Zhou
Affiliation:
Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA. qdu@math.psu.edu; zhou@math.psu.edu

Abstract

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We develop a functional analytical framework for a linearperidynamic model of a spring network system in any space dimension.Various properties of the peridynamic operators are examined forgeneral micromodulus functions. These properties are utilized toestablish the well-posedness of both the stationary peridynamicmodel and the Cauchy problem of the time dependent peridynamicmodel. The connections to the classical elastic models are alsoprovided.

Keywords

Peridynamic modelnonlocal continuum theorywell-posednessNavier equation

Information

Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 45 , Issue 2 , March 2011 , pp. 217 - 234
Copyright
© EDP Sciences, SMAI, 2010

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