Quasi-periodic lattices: Pattern matters too

Somera, Audrey; Poncelet, Martin; Auffray, Nicolas; Réthoré, Julien

doi:10.1016/j.scriptamat.2021.114378

Cited by 13 publications

(13 citation statements)

References 22 publications

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“…This also accounts for the low computational cost of such a VIC strategy. Besides, one can notice that, contrary to DIC, the cost function in (5) will not decrease, in general, towards values as low as the magnitude of the camera noise since the virtual and real images are different. However, as long as the virtual image is even in the 𝜂-direction, this has almost no effect on the accuracy thanks to the least square nature of minimization (5).…”

Section: Image Correlation Cost Functionmentioning

confidence: 93%

“…This is achieved be linearizing the graylevel residual. Starting with initial guess 𝝀 (0) c , at iteration k + 1, an estimate 𝝀 (k) c being known, we look for 𝝀 (k+1) c = 𝝀 (k) c + 𝛿𝝀 (k) c that minimizes the cost function in (5) where:…”

Section: Algorithmmentioning

confidence: 99%

“…We only have to ensure that 𝛿𝝀 (k) c constitutes a descent direction, 50 which has been the case in all the numerical experiments performed in this article. Moreover, it has to be underlined that 𝝀 c is voluntary chosen of small dimension, that is, that only few control variables are considered for the beam centerline, which helps regularizing the inverse problem (5). The last important ingredient concerns the initialization of the algorithm with 𝝀 (0) c .…”

Section: Algorithmmentioning

confidence: 99%

“…In order to measure the varying beam thickness in addition to the beam centerline, one may act either on the mapping (2) or on the virtual image (1). Although modifying the mapping (2) may be the most natural, it may complexify the solution stage since both the beam centerline and thickness variables will be involved in the real image term in the minimization (5). In particular, this would lead to the product of the beam centerline and thickness variables when performing the linearization (6).…”

Section: Taking Into Account a Varying Beam Thicknessmentioning

confidence: 99%

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Image‐based isogeometric twins of lattices with virtual image correlation for varying cross‐section beams

Passieux

Bouclier

Weeger

2023

Numerical Meth Engineering

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Cellular materials, in particular metal or polymer foams and beam lattices, are characterized by a complex architecture where the material is concentrated in slender struts. This study is concerned with the construction of numerically efficient sample-specific digital twin for the analysis and characterization of the mechanical behavior of such meta-materials. A method to build an explicit, light, and analysis-suitable isogeometric beam model directly from digital images is proposed. More precisely, as a main contribution, the virtual image correlation method is extended to the case of multiple interconnected beams with varying cross-sections. Special care is also given to the initialization for better efficiency and robustness. Synthetic and real examples of increasing complexity, that is, curved beams, lattices, and foams, are presented to account for the performance of the developed workflow from digital images to an isogeometric twin for mechanical modeling and simulation. K E Y W O R D Scellular materials, digital twin, image-based models, isogeometric analysis, lattices INTRODUCTIONCellular materials are currently gathering an important momentum in both the scientific and industrial communities. 1 They rely upon a simple idea: mimicking nature, such as bones and wood, which allows to achieve, in particular, unprecedented stiffness-to-weight ratios. 2 In practice, cellular materials are characterized by a complex micro-architecture. Most of times, the material is concentrated in small struts connected in different ways, at an intermediate scale between the constituents and the structure. Originally consisting of foams, 3,4 that is, exhibiting a random distribution of cells, the advent of additive manufacturing (AM) now pushes these materials to a new stage: it becomes possible to produce so-called lattices where well-designed unit-cells are periodically (or quasi-periodically 5 ) repeated all over a macro shape to obtain exceptional specific performances. Among others, lattices can be made highly stretchable, 6 auxetic, 7 and multi-functional, and therefore, besides being attractive for lightweight components, they appear of crucial interest for energy absorption, thermal management, design of medical implants, to name a few. [8][9][10][11] However, due to the coexistence of two very different scales, the prediction of the mechanical behavior of such materials remains an issue, especially in non-linear regimes. [12][13][14][15] Their global response is actually intimately related to the local architecture, which may not be perfectly known a priori, either because of the random aspect in foams, or because of the strut-level process-induced defects and uncertainties in lattices. [16][17][18] In view of characterizing the mechanical behavior of such materials, it thus appears of paramount importance to build a digital mechanical twin for each individual tested

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Section: Image Correlation Cost Functionmentioning

confidence: 93%

Section: Algorithmmentioning

confidence: 99%

Section: Algorithmmentioning

confidence: 99%

Section: Taking Into Account a Varying Beam Thicknessmentioning

confidence: 99%

See 2 more Smart Citations

Image‐based isogeometric twins of lattices with virtual image correlation for varying cross‐section beams

Passieux

Bouclier

Weeger

2023

Numerical Meth Engineering

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“…38,39 As a consequence, the concept of aperiodicity is often taken congruous to the idea of quasi-periodicity. 40,41 Due to their unusual structure, metallic quasicrystals show remarkable micromechanics, more akin to ceramics than metals and they can be considerably more isotropic than periodic crystals -giving nearly uniform mechanical properties in all directions. 42 As such, mimicking the form of quasicrystals at the mesoscopic scale offers an interesting possibility for cellular structures, and their linear elastic properties are worthy of investigation, but difficult to simulate and analyze using methods that take advantage of periodically repeating geometry.…”

Section: Introductionmentioning

confidence: 99%

A computational method for determining the linear elastic properties of 2D aperiodic lattice structures

Imediegwu

Grimm

Moat

et al. 2023

The Journal of Strain Analysis for Engineering Design

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This paper develops a framework for determining the linear elastic properties of non-periodic lattice structures. An element-based material assignment methodology is implemented that facilitates the generation and analyses of arbitrary patterns on a structured mesh. An adapted numerical homogenization strategy features the inclusion of a homogenized region in the neighbourhood of the domain boundary that validates the implementation of periodic boundary conditions for an arbitrary finite patch of a periodic or non-periodic lattice structure. To demonstrate the method, the linear elastic properties of an aperiodic lattice pattern based on the Penrose (P3) pattern is evaluated. Such a structure exhibits order without translational symmetry and consequently lacks a repeating unit cell. The isotropic performance of the aperiodic lattice structure is investigated and compared to that of the well-known square periodic lattice. The framework opens the door to the investigation and analyses of other novel cellular structures which are not based on a repeating unit cell. Additive manufacturing facilitates the physical realization of such lattice structures, presenting them as viable alternatives to conventional periodic structures in the aerospace and bio-engineering industries.

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Architecture-Driven Digital Volume Correlation: Application to the Analysis of In-Situ Crushing of a Polyurethane Foam

et al. 2023

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Background Digital Volume correlation (DVC) consists in identifying the displacement fields that allow for the best possible registration of volume images of a sample captured at various loading stages. With cellular materials, the use of DVC faces an intrinsic limit: in the absence of an exploitable texture on (or in) the struts or cell walls, the available speckle pattern will unavoidably be formed by the material architecture itself. This leads to the inability of classical DVC techniques to measure kinematics below the cellular scale, i.e. at the sub-cellular or micro scales. Objective Here, we extend a newly developed architecture-driven DIC technique [1] for the measurement of 3D displacement fields in real cellular materials at the scale of the architecture. Methods The proposed solution consists in assisting DVC by a weak elastic regularization using, as support, an automatic finite-element image-based mechanical model. Results Complex (locally buckling) kinematics of a polyurethane foam under compression are accurately measured during an in-situ test. The method is essential to evidence the class of dominance (stretching versus bending) of the foam. Conclusions The proposed method allows to confirm that the foam used is bending-dominated, which is not possible with a classical mesoscopic DVC approach. This method is a good candidate for the analysis of complex local deformation mechanisms at the architecture scale.

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Quasi-periodic lattices: Pattern matters too

Cited by 13 publications

References 22 publications

Image‐based isogeometric twins of lattices with virtual image correlation for varying cross‐section beams

Image‐based isogeometric twins of lattices with virtual image correlation for varying cross‐section beams

A computational method for determining the linear elastic properties of 2D aperiodic lattice structures

Architecture-Driven Digital Volume Correlation: Application to the Analysis of In-Situ Crushing of a Polyurethane Foam

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