Mathematical analysis for the peridynamic nonlocal continuum theory

Qiang Du; Kun Zhou

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2011)

  • Volume: 45, Issue: 2, page 217-234
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Du, Qiang, and Zhou, Kun. "Mathematical analysis for the peridynamic nonlocal continuum theory." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 45.2 (2011): 217-234. <http://eudml.org/doc/273242>.

@article{Du2011,
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.},
author = {Du, Qiang, Zhou, Kun},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {peridynamic model; nonlocal continuum theory; well-posedness; Navier equation; spring network system; Cauchy problem; classical elastic models},
language = {eng},
number = {2},
pages = {217-234},
publisher = {EDP-Sciences},
title = {Mathematical analysis for the peridynamic nonlocal continuum theory},
url = {http://eudml.org/doc/273242},
volume = {45},
year = {2011},
}

TY - JOUR
AU - Du, Qiang
AU - Zhou, Kun
TI - Mathematical analysis for the peridynamic nonlocal continuum theory
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2011
PB - EDP-Sciences
VL - 45
IS - 2
SP - 217
EP - 234
AB - 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.
LA - eng
KW - peridynamic model; nonlocal continuum theory; well-posedness; Navier equation; spring network system; Cauchy problem; classical elastic models
UR - http://eudml.org/doc/273242
ER -

References

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