The damage tolerance of elastic–brittle, two-dimensional isotropic lattices

Fleck, N.A.; Qiu, Xinming

doi:10.1016/j.jmps.2006.08.004

Cited by 199 publications

(148 citation statements)

References 22 publications

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“…Kagome honeycomb has been revealed to have pronounced higher fracture toughness [30] and better thermal-mechanical performance than the triangular honeycombs [54]. Therefore, in this section, we will consider the third topology of the MHH, namely, substituting the ORHH cell walls with their equal-mass Kagome sub-structure (Fig.…”

Section: Basic Theorymentioning

confidence: 99%

See 1 more Smart Citation

Elastic and transport properties of the tailorable multifunctional hierarchical honeycombs

Sun

Chen

Pugno

2014

Composite Structures

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Compared with triangular, square and Kagome honeycombs, hexagonal honeycombs have lower inplane stiffness, which restricts their multifunctional applications. Focusing on this problem, in this paper, we analytically study the in-plane elastic and transport properties of a kind of hexagonal honeycombs, i.e., the multifunctional hierarchical honeycomb (MHH). The MHH structure is developed by replacing the solid cell walls of the original regular hexagonal honeycomb (ORHH) with three kinds of equal mass isotropic honeycomb sub-structures possessing hexagonal, triangular and Kagome lattices. Formulas to derive the effective in-plane elastic properties of the regular hexagonal honeycombs at all densities are developed for analyzing the MHH structure. Resultsshow that the hexagonal sub-structure does not improve much the elastic properties of the MHH structure. However, the triangular and Kagome sub-structures result in a substantial improvement by 1 magnitude or even 3 orders of magnitude on the Young's and shear moduli of the MHH structure, depending on the cell-wall thickness-to-length ratio of the ORHH. Besides, the effective in-plane conductivities (or dielectric constants) of the three different MHH structures are also studied. The presented theory could be used in designing new tailorable hierarchical honeycomb structures for multifunctional applications. Keywords:In-plane effective moduli; In-plane effective conductivity (or dielectric constants);Original regular hexagonal honeycomb (ORHH); Multifunctional hierarchical honeycomb (MHH).

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Section: Basic Theorymentioning

confidence: 99%

“…Fleck and Qiu [30] analyzed the damage tolerance property of 2D elastic-brittle isotropic honeycombs and reported that Kagome cells have much higher fracture toughness than those of the hexagonal and triangular cells.…”

Section: Introductionmentioning

confidence: 99%

Elastic and transport properties of the tailorable multifunctional hierarchical honeycombs

Sun

Chen

Pugno

2014

Composite Structures

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“…27 Both these phenomena are intimately connected with Saint Venant type locations around a free edge, which facilitates transition from stress free state from the free edge to a uniform value in the interior. The quadratic eigenvalue problem (or the equivalent linear eigenvalue problem) can be used to predict the scaling of the boundary layer depth with relative density as was done in.…”

Section: B Saint Venant's Edge Effectsmentioning

confidence: 99%

On elastic waves and related phenomena in lattice materials and structures

Phani

2011

AIP Advances

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Lattice materials possessing a spatially periodic microstructure are suitable in weight sensitive multifunctional structural applications such as sandwich panels. They not only possess high specific stiffness but also provide opportunities to tailor acoustic and thermal properties through designing their unit cell topology. This paper seeks to understand their mechanical response under static and dynamic loads from a structural mechanics perspective combining Bloch wave theory with Finite Element Method (FEM). Bringing together results from earlier works, it is shown that three eigenvalue problems, containing the frequency and wave vector as the unknowns, can be used to analyze bulk and surface wave phenomena. The application of eigenvalue problems to band-gaps (spatially extended response), edge effects of Saint Venant type (spatially localised response), and buckling of long cellular structures is shown

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“…1) are often used to numerically predict the mechanical behavior of materials with a discrete microstructure (Ostoja-Starzewski, 2002;Fleck and Qiu, 2007;Ryvkin and Slepyan, 2010). They are often used to investigate the mechanics of atomistic crystals (Tadmor et al, 1996a,b;Miller et al, 1998;Shimokawa et al, 2004), fibrous materials, such as textiles (Ben Boubaker et al, 2007;Lomov et al, 2007;Beex et al, 2013a), paper (Heyden, 2000;Bronkhorst, 2003;Kulachenko and Uesaka, 2012;Persson and Isaksson, 2013;Wilbrink et al, 2013), collagen networks (Chandran and Barocas, 2006;Stylianopoulos and Barocas, 2007;Argento et al, 2012) and glass-fiber networks (Ridruejo et al, 2010(Ridruejo et al, , 2012, and heterogeneous materials, such as concrete (Ince et al, 2002;Karihaloo et al, 2003;Lilliu and Van Mier, 2007).…”

Section: Introductionmentioning

confidence: 99%

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

Beex

Kerfriden

Rabczuk

et al. 2014

Computer Methods in Applied Mechanics and Engineering

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The quasicontinuum (QC) method is a multiscale approach that aims to reduce the computational cost of discrete lattice computations. The method incorporates smallscale local lattice phenomena (e.g. a single lattice defect) in macroscale simulations. Since the method works directly and only on the beam lattice, QC frameworks do not require the construction and calibration of an accompanying continuum model (e.g. a cosserat/micropolar description). Furthermore, no coupling procedures are required between the regions of interest in which the beam lattice is fully resolved and coarse domains in which the lattice is effectively homogenized. Hence, the method is relatively straightforward to implement and calibrate. In this contribution, four variants of the QC method are investigated for their use for planar beam lattices which can also experience out-of-plane deformation. The different frameworks are compared to the direct lattice computations for three truly multiscale test cases in which a single lattice defect is present in an otherwise perfectly regular beam lattice.

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The damage tolerance of elastic–brittle, two-dimensional isotropic lattices

Cited by 199 publications

References 22 publications

Elastic and transport properties of the tailorable multifunctional hierarchical honeycombs

Elastic and transport properties of the tailorable multifunctional hierarchical honeycombs

On elastic waves and related phenomena in lattice materials and structures

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

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