A comparison of staggered solution schemes for coupled particle-continuum systems modeled with the Arlequin method

Pfaller S, Possart G, Steinmann P, Rahimi M, Müller-Plathe F, Böhm MC (2011)

Publication Type: Journal article

Publication year: 2011

Journal

Computational Mechanics Springer Verlag (Germany)

Publisher: Springer Verlag (Germany)

Book Volume: 49

Pages Range: 565

URI: https://doi.org/10.25593/opus4-fau-17828

DOI: 10.1007/s00466-011-0657-7

Abstract

This contribution aims at a systematic investigation of staggered solution schemes for the computation of coupled domains having different resolutions in space, a problem frequently arising in multi-scale modeling of materials. To couple a standard finite element domain with a high resolution atomistic or coarse-grained, i.e. particle-based domain, a so-called bridging domain is considered. In this handshake region a total energy, which is the sum of the
weighted energies of both domains, needs to be formulated. Interactions in the particle domain are modeled by potential functions, e.g. a harmonic potential in the simplest case or the Lennard-Jones potential to consider also anharmonic interactions between the particles. The main goal is to separate the computation of finite element and particle domains as much as possible, amongst others to calculate the different domains on several CPUs. In the present work, the governing equations of the coupling method are presented. The energy functions of continuum, particle domain and bridging domain are recapitulated and the coupling constraint is set up. For the sake of simplicity, these relations are reformulated for the case of a one dimensional system. On the one hand, this system is computed monolithically without any
separation of domains. On the other hand, various staggered solution schemes are derived systematically. The relevant equations of each scheme are given in detail together with
the sequent iteration steps. All staggered schemes are investigated qualitatively, e.g. by their convergence behavior, as well as quantitatively by comparing the staggered solutions
with the monolithic solution.

Authors with CRIS profile

Sebastian Pfaller Lehrstuhl für Technische Mechanik (LTM) Gunnar Possart Lehrstuhl für Technische Mechanik (LTM) Paul Steinmann Lehrstuhl für Technische Mechanik (LTM)

Involved external institutions

Technische Universität Darmstadt

Germany (DE) University of Chicago

United States (USA) (US)

How to cite

APA:

Pfaller, S., Possart, G., Steinmann, P., Rahimi, M., Müller-Plathe, F., & Böhm, M.C. (2011). A comparison of staggered solution schemes for coupled particle-continuum systems modeled with the Arlequin method. Computational Mechanics, 49, 565. https://doi.org/10.1007/s00466-011-0657-7

MLA:

Pfaller, Sebastian, et al. "A comparison of staggered solution schemes for coupled particle-continuum systems modeled with the Arlequin method." Computational Mechanics 49 (2011): 565.

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