A multiscale quasicontinuum method for dissipative lattice models and discrete networks

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...

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Bibliographic Details
Published in:Journal of the mechanics and physics of solids 2014-03, Vol.64, p.154-169
Main Authors: Beex, L.A.A., Peerlings, R.H.J., Geers, M.G.D.
Format: Article
Language:English
Subjects:
Computational efficiency
Crystal defects
Dissipation
Lattice model
Lattices
Mathematical analysis
Mathematical models
Multiscale
Networks
Quality control
Quasicontinuum method
Virtual power
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Summary: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.
ISSN:0022-5096
DOI:10.1016/j.jmps.2013.11.010