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nonlocal continuum theory

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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Mathematical analysis for the peridynamic nonlocal continuum theory *
Qiang Du, Kun Zhou
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 45 / Issue 2 / March 2011

Published online by Cambridge University Press:

02 August 2010, pp. 217-234

Print publication:

March 2011
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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.