A multiscale quasicontinuum method for dissipative lattice models and discrete networks

Beex, Lars ORCID: https://orcid.org/0000-0002-0486-6624, 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:	25 Oct 2022 09:03
URI:	https://orca.cardiff.ac.uk/id/eprint/56956

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