A refinement indicator for adaptive quasicontinuum approaches for structural lattices

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.

Comparative study of multiscale computational strategies for materials with discrete microstructures

“…Available options for the refinement criteria have been recently discussed in [22]. From the presented options, only a few studies presented concepts suitable for applications to structural lattices [46,62,61,51,22]. In this work, the following mesh error indicator, employed also in [62], is adopted for mesh refinement as well as for mesh coarsening.…”

“…see also Eq. (22). Due to the symmetry of the considered problem, the tangential component ∆ t vanishes, i.e., u…”

“…The area of high interest, i.e., the fully-resolved region, is allowed to evolve adaptively throughout the simulation. Available options for the refinement criteria have been recently discussed in [22]. From the presented options, only a few studies presented concepts suitable for applications to structural lattices [46,62,61,51,22].…”

An adaptive multiscale quasicontinuum approach for mechanical simulations of elastoplastic periodic lattices

“…the evolution of the spatial reduction of the QC method based on the deformation) is crucial if the (local) deformation spatially evolves during the course of a simulation. In [8], Li et al proposed an adaptive version of GQC (termed as AGQC), which exploits a novel refinement indicator to refine CGDs and transform CGDs into FRDs. It was proposed and critically assessed for elastic beams with geometrical nonlinearities.…”

“…The main focus of present work is therefore the extension of the adaptive GQC (AGQC) framework of [8] towards elastoplasticity. This extension significantly widens the applicability of AGQC.…”