| Issue |
ESAIM: M2AN
Volume 45, Number 2, March-April 2011
|
|
|---|---|---|
| Page(s) | 217 - 234 | |
| DOI | https://doi.org/10.1051/m2an/2010040 | |
| Published online | 02 August 2010 | |
Mathematical analysis for the peridynamic nonlocal continuum theory*
Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA. qdu@math.psu.edu; zhou@math.psu.edu
Received:
3
September
2009
Revised:
21
March
2010
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.
Mathematics Subject Classification: 45A05 / 46N20 / 74B99
Key words: Peridynamic model / nonlocal continuum theory / well-posedness / Navier equation
© EDP Sciences, SMAI, 2010
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