Star-shaped metrics for mechanical metamaterial design

Martínez, Jonàs; Skouras, Mélina; Schumacher, Christian; Hornus, Samuel; Lefèbvre, Sylvain; Thomaszewski, Bernhard

doi:10.1145/3306346.3322989

Cited by 41 publications

(25 citation statements)

References 61 publications

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“…A good parametrization can significantly facilitate the solution of high-dimensional non-convex problems [Bharaj et al 2015] or even cast them to convex subspaces [Piovarči et al 2017]. Additionally, it may influence the durability of the manufactured objects and improve the expressiveness of the design space [Martínez et al 2019]. Similarly, in this work, our problem leads to a non-trivial optimization procedure, where good parametrization becomes critical for capturing a sufficient range of haptic feedback produced by stylus-surface interaction.…”

Section: Goal-based Computational Fabricationmentioning

confidence: 99%

Fabrication-in-the-loop co-optimization of surfaces and styli for drawing haptics

et al. 2020

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Digital drawing tools are now standard in art and design workflows. These tools offer comfort, portability, and precision as well as native integration with digital-art workflows, software, and tools. At the same time, artists continue to work with long-standing, traditional drawing tools. One feature of traditional tools, well-appreciated by many artists and lacking in digital tools, is the specific and diverse range of haptic responses provided by them. Haptic feedback in traditional drawing tools provides unique, per-tool responses that help determine the precision and character of individual strokes. In this work, we address the problem of fabricating digital drawing tools that closely match the haptic feedback of their traditional counterparts. This requires the formulation and solution of a complex, co-optimization of both digital styli and the drawing surfaces they move upon. Here, a potentially direct formulation of this optimization with numerical simulation-in-the-loop is not yet viable. As in many complex design tasks, state-of-the-art methods do not currently offer predictive modeling at rates and scales that can account for the numerous, coupled, physical behaviors governing the haptics of styli and surfaces, nor for the limitations and uncertainties inherent in their fabrication processes. To address these challenges, we propose fabrication-in-the-loop optimization. Critical to making this strategy practical we construct our objective via a Gaussian Process that does not require computing derivatives with respect to design parameters. Our Gaussian Process surrogate model then provides both function estimates and confidence intervals that guide the efficient sampling of our design space. In turn, this sampling critically reduces the numbers of fabricated examples during exploration and automatically handles exploration-exploitation trade-offs. We apply our method to fabricate drawing tools that provide a wide range of haptic feedback, and demonstrate that they are often hard for users to distinguish from their traditional drawing-tool analogs.

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Section: Goal-based Computational Fabricationmentioning

confidence: 99%

Fabrication-in-the-loop co-optimization of surfaces and styli for drawing haptics

et al. 2020

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“…We build from the work of Martínez et al [42] that introduces the notion of combining a star-shaped distance with an underlying lattice in 2D. We explore the much wider space of symmetries offered by the three-dimensional case and design dedicated 3D star-shaped parameterizations offering a good expressivenesscompactness trade-off.…”

Section: Families Of Tilesmentioning

confidence: 99%

“…The algorithmic growth process is analogous to the 2D version proposed in [42]. Let us recall that the growth process operates on a 3D grid G of integer labels.…”

Section: Algorithmic Growth Processmentioning

confidence: 99%

3D Periodic Cellular Materials with Tailored Symmetry and Implicit Grading

Efremov

Martínez

Lefèbvre

2021

Computer-Aided Design

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Periodic cellular materials allow triggering complex elastic behaviors within the volume of a part. In this work, we study a novel type of 3D periodic cellular materials that emerge from a growth process in a lattice. The growth is parameterized by a 3D star-shaped set at each lattice point, defining the geometry that will appear around it. Individual tiles may be computed and used in a periodic lattice, or a global structure may be produced under spatial gradations, changing the parametric star-shaped set at each lattice location.Beyond free spatial gradation, an important advantage of our approach is that elastic symmetries can easily be enforced. We show how shared symmetries between the lattice and the star-shaped set directly translate into symmetries of the periodic structures' elastic response. Thus, our approach enables restricting the symmetry of the elastic responses -monoclinic, orthorhombic, trigonal, and so on -while freely exploring a wide space of possible geometries and topologies. We make a comprehensive study of the space of symmetries and broad combinations that our method spans and demonstrate through numerical and experimental results the elastic responses triggered by our structures.

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“…Since the many cells play together to exhibit a desired property, their design is difficult. Inverse design tools for structured sheets of materials [27,47] help users design such materials, by optimizing the parameters (e. g., edge lengths) of a structure family as to find the best-fitting material for users definition.…”

Section: Related Workmentioning

confidence: 99%