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Title: Lumped mass finite element implementation of continuum theories with micro-inertia
Authors: Lombardo, Mariateresa
Askes, Harm
Keywords: Explicit dynamics
Lumped mass
Critical time step
Length scale
Neumann expansion
Issue Date: 2013
Publisher: © John Wiley & Sons, Ltd.
Citation: LOMBARDO, M. and ASKES, H., 2013. Lumped mass finite element implementation of continuum theories with micro-inertia. International Journal for Numerical Methods in Engineering, 96 (7), pp. 448 - 466
Abstract: Continuum theories can be equipped with additional inertia terms to make them capable of capturing wave dispersion effects observed in micro-structured materials. Such terms, often called micro-inertia, are convenient and straightforward extensions of classical continuum theories. Furthermore, the critical time step is usually increased via the inclusion of micro-inertia. However, the drawback exists that standard finite element discretisation leads to mass matrices that cannot be lumped without losing the micro-inertia terms. In this paper, we will develop a solution algorithm based on Neumann expansions by which this disadvantage is avoided altogether. The micro-inertia terms are translated into modifications of the residual force vector, so that the system matrix is the usual lumped mass matrix and all advantages of explicit time integration are maintained. The numerical stability of the algorithm and its effect on the dispersive properties of the model are studied in detail. Numerical examples are used to illustrate the various aspects of the algorithm.
Description: This article is closed access, it was published in the serial International Journal for Numerical Methods in Engineering [© John Wiley & Sons, Ltd]. The definitive version is available at: http://dx.doi.org/10.1002/nme.4570
Version: Accepted for publication
DOI: 10.1002/nme.4570
URI: https://dspace.lboro.ac.uk/2134/13580
Publisher Link: http://dx.doi.org/10.1002/nme.4570
ISSN: 0029-5981
Appears in Collections:Closed Access (Architecture, Building and Civil Engineering)

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