Reference : A variational formulation of dissipative quasicontinuum methods

	Document type :	Scientific journals : Article
	Discipline(s) :	Engineering, computing & technology : Aerospace & aeronautics engineering Engineering, computing & technology : Civil engineering Engineering, computing & technology : Materials science & engineering Engineering, computing & technology : Mechanical engineering Engineering, computing & technology : Multidisciplinary, general & others
	Focus Areas :	Computational Sciences
	To cite this reference:	http://hdl.handle.net/10993/28912

Title :	A variational formulation of dissipative quasicontinuum methods
Language :	English
Author, co-author :	Rokos, Ondrej [Eindhoven University of Technology > Mechanical Engineering]
	Beex, Lars [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit >]
	Peerlings, Ron [Eindhoven University of Technology > Mechanical Engineering]
	Zeman, Jan [Czech Technical University in Prague > Civil Engineering]
Publication date :	15-Dec-2016
Journal title :	International Journal of Solids and Structures
Publisher :	Pergamon Press (part of Elsevier Science)
Volume :	102-103
Pages :	214-229
Peer reviewed :	Yes (verified by ORBilu)
Audience :	International
ISSN :	0020-7683
e-ISSN :	1879-2146
City :	Oxford
Country :	United Kingdom
Keywords :	[en] quasicontinuum method ; lattice model ; variational formulation ; plasticity ; multiscale modelling
Abstract :	[en] 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 Roub cek, 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.
Target :	Researchers ; Professionals
Permalink :	http://hdl.handle.net/10993/28912
DOI :	10.1016/j.ijsolstr.2016.10.003
Other URL :	http://www.sciencedirect.com/science/article/pii/S0020768316302943

	File(s) associated to this reference
	Fulltext file(s): File Commentary Version Size Access Open access PlasticityQC.pdf Author postprint 1.47 MB View/Open

All documents in ORBi^lu are protected by a user license.

 

University of Luxembourg Library |  Feedback |  Legal notices Site Map