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A refinement indicator for adaptive quasicontinuum approaches for structural lattices
Author(s) -
Chen Li,
Berke Péter Z.,
Massart Thierry J.,
Beex Lars A.A.,
Magliulo Marco,
Bordas Stéphane P.A.
Publication year - 2021
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6629
Subject(s) - homogenization (climate) , computer science , lattice (music) , adaptive mesh refinement , statistical physics , algorithm , generalization , computational science , theoretical computer science , mathematics , physics , mathematical analysis , biodiversity , ecology , acoustics , biology
The quasicontinuum (QC) method is a concurrent multiscale approach in which lattice models are fully resolved in small regions of interest and coarse‐grained elsewhere. Since the method was originally proposed to accelerate atomistic lattice simulations, its refinement criteria—that drive refining coarse‐grained regions and/or increasing fully‐resolved regions—are generally associated with quantities relevant to the atomistic scale. In this contribution, a new refinement indicator is presented, based on the energies of dedicated cells at coarse‐grained domain surfaces. This indicator is incorporated in an adaptive scheme of a generalization of the QC method able to consider periodic representative volume elements, like the ones employed in most computational homogenization approaches. However, this indicator can also be used for conventional QC frameworks. Illustrative numerical examples of elastic indentation and scratch of different lattices demonstrate the capabilities of the refinement indicator and its impact on adaptive QC simulations.