A variational formulation of dissipative quasicontinuum methods
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F16%3A00303913" target="_blank" >RIV/68407700:21110/16:00303913 - isvavai.cz</a>
Result on the web
<a href="https://arxiv.org/abs/1601.00625" target="_blank" >https://arxiv.org/abs/1601.00625</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.ijsolstr.2016.10.003" target="_blank" >10.1016/j.ijsolstr.2016.10.003</a>
Alternative languages
Result language
angličtina
Original language name
A variational formulation of dissipative quasicontinuum methods
Original language description
Lattice systems and discrete networks with dissipative interactions are successfully employed as meso-scale models of heterogeneous solids. As the application scale generally is much larger than that of the discrete links, physically relevant simulations are computationally expensive. The QuasiContinuum (QC) method is a multiscale approach that reduces the computational cost of direct numerical simulations by fully resolving complex phenomena only in regions of interest while coarsening elsewhere. In previous work (Beex et al., J. Mech. Phys. Solids 64, 154–169, 2014), the originally conservative QC methodology was generalized to a virtual-power-based QC approach that includes local dissipative mechanisms. In this contribution, the virtual-power-based QC method is reformulated from a variational point of view, by employing the energy-based variational framework for rate-independent processes (Mielke and Roubíček, Rate-Independent Systems: Theory and Application, Springer-Verlag, 2015). By construction it is shown that the QC method with dissipative interactions can be expressed as a minimization problem of a properly built energy potential, providing solutions equivalent to those of the virtual-power-based QC formulation. The theoretical considerations are demonstrated on three simple examples. For them we verify energy consistency, quantify relative errors in energies, and discuss errors in internal variables obtained for different meshes and two summation rules.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
JJ - Other materials
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GA14-00420S" target="_blank" >GA14-00420S: Quasicontinuum methods for discrete dissipative systems</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
International Journal of Solids and Structures
ISSN
0020-7683
e-ISSN
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Volume of the periodical
102-103
Issue of the periodical within the volume
December
Country of publishing house
GB - UNITED KINGDOM
Number of pages
16
Pages from-to
214-229
UT code for WoS article
000389390200020
EID of the result in the Scopus database
2-s2.0-84995605680