Quasicontinuum-based multiscale approaches for plate-like beam lattices experiencing in-plane and out-of-plane deformation

Beex, Lars; Kerfriden, Pierre; Rabczuk, Timon; Bordas, Stéphane

doi:10.1016/j.cma.2014.06.018

Cited by 30 publications

(27 citation statements)

References 51 publications

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“…A simple remedy to avoid this numerical issue, also exploited in this contribution, is to use relatively large triangles in the coarse-grained domain and couple them kinematically in a non-conforming manner to the fully resolved lattice model in the domain of interest [28]. Hence, in this work no transition regime is present at all.…”

Section: Interpolationmentioning

confidence: 99%

“…In [28] it was observed that the triangles in the transition zone in QC approaches with higher-order interpolation have too many triangle nodes, i.e. too many degrees of freedom, than are governed by underlying lattice.…”

Section: Interpolationmentioning

confidence: 99%

“…Obviously, this is also the case for the triangles in the fully resolved domain, but as the size and dimensions of those triangles are known, this numerical issue can straightforwardly be overcome by locally reducing the order of the interpolation. However, this cannot be done, a priori, for the triangles in the transition zone [28].…”

Section: Interpolationmentioning

confidence: 99%

“…This has for instance been shown for a lattice model that includes bond failure and subsequent fibre sliding [20] and an elastoplastic lattice model for an electronic textile [21]. In light of applying QC approaches to structural lattice models, recently a QC approach was also formulated for planar beam lattices undergoing in-plane and out-of-plane deformation [28]. It was shown that for these planar beam lattices higher-order interpolation is required, whereas normally linear interpolation is used in QC approaches.…”

Section: Introductionmentioning

confidence: 99%

“…The aim of the current contribution is to investigate the use of higher-order interpolation for lattices in which the interactions use an internally linear interpolation, whereas the beam interactions of the beam lattices in [28] use an internally higher-order interpolation (Hermite interpolation to be exact). The study of [29] also deals with higher-order interpolation for (conservative atomistic) lattices with interactions using internally linear interactions, but focuses on remeshing.…”

Section: Introductionmentioning

confidence: 99%

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Higher‐order quasicontinuum methods for elastic and dissipative lattice models: uniaxial deformation and pure bending

et al. 2015

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The quasicontinuum (QC) method is a numerical strategy to reduce the computational cost of direct lattice computations -in this study we achieve a speed up of a factor of 40. It has successfully been applied to (conservative) atomistic lattices in the past, but using a virtualpower statement it was recently shown that QC approaches can also be used for spring and beam lattice models that include dissipation. Recent results have shown that QC approaches for planar beam lattices experiencing in-plane and out-of-plane deformation require higherorder interpolation. Higher-order QC frameworks are scarce nevertheless. In this contribution, the possibilities of a second-order and third-order QC framework are investigated for an elastoplastic spring lattice. The higher-order QC frameworks are compared to the results of the direct lattice computations and to those of a linear QC scheme. Examples are chosen so that both a macroscale and a microscale quantity influences the results. The two multiscale examples focused on are (i) macroscopically prescribed uniaxial deformation and (ii) macroscopically prescribed pure bending. Furthermore, the examples include an individual inclusion in a large lattice and hence, are concurrent in nature.

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Section: Interpolationmentioning

confidence: 99%

Section: Interpolationmentioning

confidence: 99%

Section: Interpolationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Higher‐order quasicontinuum methods for elastic and dissipative lattice models: uniaxial deformation and pure bending

et al. 2015

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An adaptive variational Quasicontinuum methodology for lattice networks with localized damage

Rokoš

Peerlings

Zeman

et al. 2017

Numerical Meth Engineering

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Lattice networks with dissipative interactions can be used to describe the mechanics of discrete mesostructures of materials such as 3D-printed structures and foams. This contribution deals with the crack initiation and propagation in such materials and focuses on an adaptive multiscale approach that captures the spatially evolving fracture. Lattice networks naturally incorporate non-locality, large deformations and dissipative mechanisms taking place inside fracture zones. Because the physically relevant length scales are significantly larger than those of individual interactions, discrete models are computationally expensive. The Quasicontinuum (QC) method is a multiscale approach specifically constructed for discrete models. This method reduces the computational cost by fully resolving the underlying lattice only in regions of interest, while coarsening elsewhere. In this contribution, the (variational) QC is applied to damageable lattices for engineering-scale predictions. To deal with the spatially evolving fracture zone, an adaptive scheme is proposed. Implications induced by the adaptive procedure are discussed from the energy-consistency point of view, and theoretical considerations are demonstrated on two examples. The first one serves as a proof of concept, illustrates the consistency of the adaptive schemes and presents errors in energies. The second one demonstrates the performance of the adaptive QC scheme for a more complex problem. AN ADAPTIVE VARIATIONAL QUASICONTINUUM METHODOLOGY FOR LATTICE 175 beam (fibre or yarn) versus that of the network. Second, the formulation and implementation of lattice models is generally significantly easier compared with that of alternative continuum models. Large deformations, large yarn reorientations and fracture are easier to formulate and implement (cf. e.g. the continuum model of Peng and Cao [5] that deals with large yarn reorientations). Thanks to the simplicity and versatility of lattice networks, they are furthermore used for the description of heterogeneous cohesive-frictional materials such as concrete. The reason is that discrete models can realistically represent distributed microcracking with gradual softening, implement material structure with inhomogeneities, capture non-locality of damage processes and reflect deterministic or stochastic size effects. Examples of the successful use of lattice models for such materials are given in [6][7][8][9].As lattice models are typically constructed at the meso-scale, micro-scale or nano-scale, they require reduced-model techniques to allow for application-scale simulations. A prominent example is the Quasicontinuum (QC) method, which specifically aims at discrete lattice models. The QC method was originally introduced for conservative atomistic systems by Tadmor et al. [10] and extended in numerous aspects later on, see for example [11][12][13]. Subsequent generalizations for lattices with dissipative interactions (e.g. plasticity and bond sliding) were provided in [14,15]. In principle, the QC is a numerical p...

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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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Quasicontinuum-based multiscale approaches for plate-like beam lattices experiencing in-plane and out-of-plane deformation

Cited by 30 publications

References 51 publications

Higher‐order quasicontinuum methods for elastic and dissipative lattice models: uniaxial deformation and pure bending

Higher‐order quasicontinuum methods for elastic and dissipative lattice models: uniaxial deformation and pure bending

An adaptive variational Quasicontinuum methodology for lattice networks with localized damage

A refinement indicator for adaptive quasicontinuum approaches for structural lattices

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