A multiscale quasicontinuum method for dissipative lattice models and discrete networks

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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. Crown Copyright © 2013 Published by Elsevier Ltd.
Original languageEnglish
Pages (from-to)154-169
JournalJournal of the Mechanics and Physics of Solids
Volume64
Issue number1
DOIs
Publication statusPublished - 2014

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Crystal defects
costs
formulations
fibers
Crystal lattices
Costs
interactions
defects
energy

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title = "A multiscale quasicontinuum method for dissipative lattice models and discrete networks",
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. Crown Copyright {\circledC} 2013 Published by Elsevier Ltd.",
author = "L.A.A. Beex and R.H.J. Peerlings and M.G.D. Geers",
year = "2014",
doi = "10.1016/j.jmps.2013.11.010",
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A multiscale quasicontinuum method for dissipative lattice models and discrete networks. / Beex, L.A.A.; Peerlings, R.H.J.; Geers, M.G.D.

In: Journal of the Mechanics and Physics of Solids, Vol. 64, No. 1, 2014, p. 154-169.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

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AU - Beex, L.A.A.

AU - Peerlings, R.H.J.

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PY - 2014

Y1 - 2014

N2 - 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. Crown Copyright © 2013 Published by Elsevier Ltd.

AB - 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. Crown Copyright © 2013 Published by Elsevier Ltd.

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