Computational Design of Laser-Cut Bending-Active Structures☆
Graphical abstract
Introduction
Bending-active structures are curved structures made of initially planar components that have been elastically bent so that they assume a 3D shape [1]. This construction technique offers several advantages: flat panels are easy to manufacture, store and transport, and can be used to create objects of multiple scales, from models to large-scale structures. These multiple benefits explain the popularity of active bending for design applications as well as in architecture [2], [3], [4].
In this work, we are interested in controlling the shapes of the silhouettes of bent planar strips of plywood. More specifically, we want the profile of the deformed structure, subject to external loads, to match a given target curve when at equilibrium. While this can be achieved by playing with the width of the strips (see e.g. the recent work by Hafner and Bickel [5]) or their thickness (at the expense of a more involved fabrication process), we do not want to alter the outer shape of our ribbons. Instead, drawing inspiration from the design of living hinges and from kerfing techniques used in lute-making, we propose to modulate the curvature of our structures by patterning their interior according to a parameterized rectangular motif that is regularly laser-cut. Inserting such cuts to the initially flat panel through laser-cutting is no more difficult than cutting its external layout. Our objects can thus be fabricated using a widespread, scalable and affordable technique.
On the computational side, relying on a parametric cut pattern allows us to treat the cut fiberboard as a metamaterial with programmable bending capabilities and to turn towards two-scale methods when solving the inverse design problem of finding cut parameters that will produce a bending-active structure with the desired target profile. To our knowledge, such an approach, leveraging explicit bending control and building on recent results in bending homogenization [6], has not yet been proposed in the context of computational fabrication.
While we focus on the particular setting of 2D structures and rectangular cuts, we believe that our technique, that decouples macro-scale geometry from material inner structure paves the way to generalization. Indeed, beyond the mechanics of the final object, the shapes of the cuts also impact its appearance. Therefore, playing with the cut patterns also allows to play with the aesthetics of the structure. Our methodology, which does not explicitly rely on a specific pattern geometry should be extendable to other motifs, as long as they form a parametric family and exhibit a wide range of mechanical behaviors.
In summary, the main contributions of our work are the following:
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We propose a novel “living-hinge”-inspired parametric family of laser-cut metamaterials with tunable bending capabilities.
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We characterize the bending properties of these metamaterials using a recent bending homogenization method “with a twist”.
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We present a two-scale algorithm for the inverse design of bending-active structures of custom deformed shape.
Section snippets
Related works
Fabrication-aware computational design has gained increasing interest in computer graphics for a decade. For a broad overview of the field, we refer the reader to the surveys by Bickel et al. [7] and Bermano et al. [8], which cover a wide variety of techniques. In the following section, we focus the discussion on previous work on inverse design of deployables and slender structures, metamaterials and Kirigami-inspired research.
Overview
Given a planar target curve, external planar forces and boundary conditions (Fig. 1, top-left), our method produces a bending-active structure made of a rectangular piece of wood panel in which holes are laser-cut (Fig. 1, right). The silhouette of the structure in physical equilibrium is aimed to match the target under the given loading conditions. The actual output of our process are the geometric parameters (Fig. 1, curve-plots) defining the cut layout (Fig. 1, bottom) which locally
Laser-cut metamaterial
Metamaterials are engineered materials designed to exhibit superior mechanical properties to those of the constituent material. They are structured with periodically arranged or spatially varying building blocks which either define a homogeneous, resp. heterogeneous metamaterial. Tailor-made geometry of the building blocks is the key for gaining extraordinary properties.
Designing a metamaterial, and characterizing its mechanical behavior, is not only a matter of geometry, but also of scale. In
Inverse design algorithm
We now address an inverse design problem for laser-cut MDF panels. Remember our initial problem: given a 2D target profile shape and user-defined external forces and boundary conditions, we are searching for a cut layout of a planar panel of fixed length and width, such that the silhouette of the deformed panel matches the target under physical equilibrium.
The approach for solving this inverse modeling problem consists of two main steps. First, a constrained optimization problem is solved to
Results
We have used our design system to create a diverse set of bending-active structures whose silhouettes at equilibrium match different target shapes. We demonstrate the versatility of our system by combining the target shapes with various sets of boundary conditions and external loads. In addition to computing numerous results, we have fabricated four structures in order to validate the presented design system as well as the choices and hypothesis made in Sections 4 Laser-cut metamaterial, 5
Conclusion
We presented a computational method to design bending-active structures whose silhouette at equilibrium matched a desired target curve. To this end, we programmed the curvature of the structure thanks to laser-cut rectangular patterns whose sizes were automatically determined using a two-scale algorithm. Our approach, based on the homogenization of the bending properties of the cut MDF wood allowed us to directly play with macro-scale stiffnesses, which in turn allowed us to dramatically reduce
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This work was supported by the European Union’s Horizon 2020 programme under grant agreement No 862025 (FETOpen ADAM). The authors are grateful to Stan Borkowsky and the Amiqual4Home platform for giving us access to their laser-cut machine.
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This paper has been recommended for acceptance by Dr. Morad Behandish & Professor Jianmin Zheng.