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.
Mots-clés : 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 },
pages = {217--234},
publisher = {EDP-Sciences},
volume = {45},
number = {2},
year = {2011},
doi = {10.1051/m2an/2010040},
mrnumber = {2804637},
zbl = {1269.45005},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2010040/}
}
TY - JOUR AU - Du, Qiang AU - Zhou, Kun TI - Mathematical analysis for the peridynamic nonlocal continuum theory JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2011 SP - 217 EP - 234 VL - 45 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2010040/ DO - 10.1051/m2an/2010040 LA - en ID - M2AN_2011__45_2_217_0 ER -
%0 Journal Article %A Du, Qiang %A Zhou, Kun %T Mathematical analysis for the peridynamic nonlocal continuum theory %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2011 %P 217-234 %V 45 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2010040/ %R 10.1051/m2an/2010040 %G en %F M2AN_2011__45_2_217_0
Du, Qiang; Zhou, Kun. Mathematical analysis for the peridynamic nonlocal continuum theory. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 45 (2011) no. 2, pp. 217-234. doi : 10.1051/m2an/2010040. http://www.numdam.org/articles/10.1051/m2an/2010040/
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