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A multiscale quasicontinuum method for dissipative lattice models and discrete networks

Beex, Lars, Peerlings, R. H. J. and Geers, M. G. D. 2014. A multiscale quasicontinuum method for dissipative lattice models and discrete networks. Journal of the Mechanics and Physics of Solids 64 , pp. 154-169. 10.1016/j.jmps.2013.11.010

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Abstract

Lattice models and discrete networks naturally describe mechanical phenomena at the mesoscale of fibrous materials. A disadvantage of lattice models is their computational cost. The quasicontinuum (QC) method is a suitable multiscale approach that reduces the computational cost of lattice models and allows the incorporation of local lattice defects in large-scale problems. So far, all QC methods are formulated for conservative (mostly atomistic) lattice models. Lattice models of fibrous materials however, often require non-conservative interactions. In this paper, a QC formulation is derived based on the virtual-power of a non-conservative lattice model. By using the virtual-power statement instead of force-equilibrium, errors in the governing equations of the force-based QC formulations are avoided. Nevertheless, the non-conservative interaction forces can still be directly inserted in the virtual-power QC framework. The summation rules for energy-based QC methods can still be used in the proposed framework as shown by two multiscale examples.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Engineering
Subjects: T Technology > T Technology (General)
T Technology > TJ Mechanical engineering and machinery
T Technology > TS Manufactures
Uncontrolled Keywords: Multiscale; Quasicontinuum method; Lattice model; Virtual power; Dissipation
Publisher: Elsevier
ISSN: 0022-5096
Last Modified: 21 Feb 2019 09:52
URI: http://orca-mwe.cf.ac.uk/id/eprint/56956

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