The Quasicontinuum Method: Theory and Applications

Kochmann, Dennis M.; Amelang, Jeffrey S.

doi:10.1007/978-3-319-33480-6_5

Cited by 19 publications

(11 citation statements)

References 88 publications

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“…This method was originally proposed in 1996 [1] for regular atomistic lattices with long-range interactions. Since that time, the QC method has been widely used and extended to applications for a variety of materials represented by regular lattices [2]. An extension of the QC method to irregular lattices has recently been developed by the authors [3].…”

Section: Qc Methodsmentioning

confidence: 99%

Adaptive Quasicontinuum Simulation of Elastic-Brittle Disordered Lattices

Mikeš

Jirásek

2017

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Abstract. The quasicontinuum (QC) method is a computational technique that can efficiently handle atomistic lattices by combining continuum and atomistic approaches. In this work, the QC method is combined with an adaptive algorithm, to obtain correct predictions of crack trajectories in failure simulations. Numerical simulations of crack propagation in elastic-brittle disordered lattices are performed for a two-dimensional example. The obtained results are compared with the fully resolved particle model. It is shown that the adaptive QC simulation provides a significant reduction of the computational demand. At the same time, the macroscopic crack trajectories and the shape of the force-displacement diagram are very well captured.

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Section: Qc Methodsmentioning

confidence: 99%

Adaptive Quasicontinuum Simulation of Elastic-Brittle Disordered Lattices

Mikeš

Jirásek

2017

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“…In order to test the full nonlinear capabilities of truss QC, we perform adaptive indentation simulations on 2D and 3D multi-lattices. Indentation is chosen because it features highly localized deformation, buckling of beams in compression, a non-trivial onset of localization, and it has been used as a standard benchmark in classical QC (Kochmann and Amelang, 2016). We use the nonlinear corotational beams described in Section 2.4.…”

Section: Indentation Testsmentioning

confidence: 99%

“…More recently, the QC method has been extended to model simple truss lattices (Beex et al, 2011). Initial studies assumed the truss members to behave as linear elastic springs; later extensions included inelasticity and failure of truss members (Beex et al, 2014d,c;Kochmann and Amelang, 2016;Rokoš et al, 2016) as well as Euler-Bernoulli beam connections to model stretching and bending of truss members (Beex et al, 2014a). Concepts were further paired with the eXtended Finite Element Method (XFEM) to track the propagation of cracks in the lattice (Rokoš et al, 2017).…”

Section: Introductionmentioning

confidence: 99%

A quasicontinuum theory for the nonlinear mechanical response of general periodic truss lattices

Phlipot

Kochmann

2019

Journal of the Mechanics and Physics of Solids

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We present a framework for the efficient, yet accurate description of general periodic truss networks based on concepts of the quasicontinuum (QC) method. Previous research in coarse-grained truss models has focused either on simple bar trusses or on two-dimensional beam lattices undergoing small deformations. Here we extend the truss QC methodology to nonlinear deformations, general periodic beam lattices, and three dimensions. We introduce geometric nonlinearity into the model by using a corotational beam description at the level of individual truss members. Coarse-graining is achieved by the introduction of representative unit cells and an affine interpolation analogous to traditional QC. General periodic lattices defined by the periodic assembly of a single unit cell are modeled by retaining all unique degrees of freedom of the unit cell (identified by a lattice decomposition into simple Bravais lattices) at each macroscopic point in the simulation, and interpolating each degree of freedom individually. We show that this interpolation scheme accurately captures the homogenized properties of periodic truss lattices for uniform deformations. In order to showcase the efficiency and accuracy of the method, we perform simulations to predict the brittle fracture toughness of multiple lattice architectures and compare them to results obtained from significantly more expensive discrete truss simulations. Finally, we demonstrate the applicability of the method for nonlinear elastic truss lattices undergoing finite deformations. Overall, the new technique shows convincing agreement with exact, discrete results for most lattice architectures, and offers opportunities to reduce computational expenses in structural lattice simulations and thus to efficiently extract the effective mechanical performance of discrete networks.

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“…The QC method was originally proposed to decrease the computational expenses of atomistic lattices simulation—characterized by conservative interactions 1‐11 . Later, it was reformulated by Beex et al 12‐14 using a virtual‐power‐statement to incorporate dissipative phenomena.…”

Section: Introductionmentioning

confidence: 99%

A refinement indicator for adaptive quasicontinuum approaches for structural lattices

Chen

Berke

Massart

et al. 2021

Numerical Meth Engineering

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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.

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The Quasicontinuum Method: Theory and Applications

Cited by 19 publications

References 88 publications

Adaptive Quasicontinuum Simulation of Elastic-Brittle Disordered Lattices

Adaptive Quasicontinuum Simulation of Elastic-Brittle Disordered Lattices

A quasicontinuum theory for the nonlinear mechanical response of general periodic truss lattices

A refinement indicator for adaptive quasicontinuum approaches for structural lattices

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