Mathematical analysis for the peridynamic nonlocal continuum theory
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 45 (2011) no. 2, p. 217-234

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.

DOI : https://doi.org/10.1051/m2an/2010040
Classification:  45A05,  46N20,  74B99
Keywords: peridynamic model, nonlocal continuum theory, well-posedness, Navier equation
@article{M2AN_2011__45_2_217_0,
author = {Du, Qiang and Zhou, Kun},
title = {Mathematical analysis for the peridynamic nonlocal continuum theory},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {45},
number = {2},
year = {2011},
pages = {217-234},
doi = {10.1051/m2an/2010040},
zbl = {1269.45005},
mrnumber = {2804637},
language = {en},
url = {http://www.numdam.org/item/M2AN_2011__45_2_217_0}
}

Du, Qiang; Zhou, Kun. Mathematical analysis for the peridynamic nonlocal continuum theory. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 45 (2011) no. 2, pp. 217-234. doi : 10.1051/m2an/2010040. http://www.numdam.org/item/M2AN_2011__45_2_217_0/

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