A refinement indicator for adaptive quasicontinuum approaches for structural lattices. (18th February 2021)

• Record Type: Journal Article
• Authors: Chen, Li; Berke, Péter Z.; Massart, Thierry J.; Beex, Lars A.A.; Magliulo, Marco; Bordas, Stéphane P.A.
• Is Part Of: International journal for numerical methods in engineering. Volume 122:Number 10(2021)
• Page Start: 2498
• Page End: 2527
• Publication Date: 2021-02-18
• Subjects: 3D co‐rotational beam -- adaptivity -- generalized quasicontinuum method -- refinement indicator -- structural lattices; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.6629
• Languages: English
• ISSNs: 0029-5981

Abstract

Abstract: 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.