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Mathematical analysis for the peridynamic nonlocal 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
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Abstract

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

Keywords

Peridynamic modelnonlocal continuum theorywell-posednessNavier equation
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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