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Type: Journal article
Title: Four simplified gradient elasticity models for the simulation of dispersive wave propagation
Author: Askes, H.
Metrikine, A.
Pichugin, A.
Bennett, T.
Citation: Philosophical Magazine, 2008; 88(28-29):3415-3443
Publisher: Taylor & Francis
Issue Date: 2008
ISSN: 1478-6435
Statement of
H. Askes, A.V. Metrikine, A.V. Pichugin and T. Bennett
Abstract: Gradient elasticity theories can be used to simulate dispersive wave propagation as it occurs in heterogeneous materials. Compared to the second-order partial differential equations of classical elasticity, in its most general format gradient elasticity also contains fourth-order spatial, temporal as well as mixed spatial-temporal derivatives. The inclusion of the various higher-order terms has been motivated through arguments of causality and asymptotic accuracy, but for numerical implementations it is also important that standard discretization tools can be used for the interpolation in space and the integration in time. In this paper, we will formulate four different simplifications of the general gradient elasticity theory. We will study the dispersive properties of the models, their causality according to Einstein and their behavior in simple initial/boundary value problems.
Keywords: generalized continuum; gradient elasticity; length scale; dispersion; wave propogation
Rights: © 2008 Taylor & Francis
RMID: 0020132264
DOI: 10.1080/14786430802524108
Appears in Collections:Civil and Environmental Engineering publications

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