Reference : A variational formulation of dissipative quasicontinuum methods |
Scientific journals : Article | |||
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 | |||
Computational Sciences | |||
http://hdl.handle.net/10993/28912 | |||
A variational formulation of dissipative quasicontinuum methods | |
English | |
Rokos, Ondrej [Eindhoven University of Technology > Mechanical Engineering] | |
Beex, Lars ![]() | |
Peerlings, Ron [Eindhoven University of Technology > Mechanical Engineering] | |
Zeman, Jan [Czech Technical University in Prague > Civil Engineering] | |
15-Dec-2016 | |
International Journal of Solids and Structures | |
Pergamon Press (part of Elsevier Science) | |
102-103 | |
214-229 | |
Yes (verified by ORBilu) | |
International | |
0020-7683 | |
1879-2146 | |
Oxford | |
United Kingdom | |
[en] quasicontinuum method ; lattice model ; variational formulation ; plasticity ; multiscale modelling | |
[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. | |
Researchers ; Professionals | |
http://hdl.handle.net/10993/28912 | |
10.1016/j.ijsolstr.2016.10.003 | |
http://www.sciencedirect.com/science/article/pii/S0020768316302943 |
File(s) associated to this reference | ||||||||||||||
Fulltext file(s):
| ||||||||||||||
All documents in ORBilu are protected by a user license.