Procedural and stochastic microstructures for functional fabrication – MuFFin

Inspired by procedural solids in computer graphics, MuFFin proposed to go beyond periodic tilings by studying procedural, stochastic, and manufacturable foams with a controlled macroscopic elastic behavior. A procedural geometry is defined as an implicit function evaluated at every point in space at the desired resolution. It does not require explicitly storing the geometry in the memory. Stochastic geometry enables an easier grading of material properties and conforming to a surface. Compared to periodic structures, the lack of global organization and periodicity allows for better gradation of stochastic geometry. The absence of regularity affords a simple approach to grade their geometry -- and thus their mechanical properties -- within a target object and its surface. Moreover, MuFFin aimed at controlling the macroscopic elastic behavior by connecting the parameters driving the procedural foam to the elastic properties. Finally, MuFFin aimed to discover microstructures that can be manufactured with a broad spectrum of technologies (SLS, FDM, SLA, etc.) without requiring supporting structures.

To the best of their knowledge, the project team has introduced the first class of foams that can be manufactured by filament deposition modeling. To achieve this, the Euclidean distance was replaced by a class of polyhedral distances to ensure that the 3D Voronoi diagram faces of any set of points define a geometrically self-supporting structure. Its usefulness has also been demonstrated to radically modify the kinematics of a soft robot, with the introduction of 2D/3D materials based on a growth process driven by a new star distance class. Remarkably, the geometry gradation is implicitly controlled by distance, unlike most existing methods that treat gradation explicitly. Finally, procedural noise was introduced for high-contrast anisotropic patterns, well-suited to the production of mechanical foams. This technique has been integrated by rendering software (e.g., Pixar's RenderMan) and used in some renderings of Star Wars Episode IX.

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MuFFin aims at contributing a unified pipeline for the efficient and scalable synthesis, visualization, and modeling of additively manufactured microstructures with tailored macroscopic physical behavior. In an interdisciplinary effort, MuFFin will blend together computer and material science perspectives to deliver an integrated approach that is both computationally and physically sound.

Additive Manufacturing (AM) technologies are now capable of fabricating microstructures at the scale of microns, therefore enabling to precise control of the macroscopic physical behavior. This control empowers a wide range of industrial applications by bringing high-performance customized materials. In particular, a promising venue lies in the optimization of material properties such as rigidity or impact absorption.

Microstructures for AM will play a decisive role in the factory of the future, but several challenges remain aside. The dimension of the objects being printed increases, and concurrently, the available printing resolution becomes finer. Thus, the geometry size of microstructures is drastically escalating. From a computational viewpoint, explicitly storing the microstructure geometry (e.g in an STL file), will eventually render infeasible the whole computational pipeline (numerical simulation, visualization, and computational design of microstructures). From a material science viewpoint, it remains a challenge to properly embed and grade microstructures within an object, and to ensure that they can be directly fabricated with AM processes.

State of the art methods consider periodic microstructures, offering compact storage, efficient display, and simulation of the macroscopic physical behavior. However, due to their constrained global structure, periodic microstructures exhibit a poor grading behavior, specially when targeting anisotropic material properties that follow an arbitrary orientation field.

MuFFin seeks to answer the aforementioned interdisciplinary challenges by considering procedural, stochastic, and fabricable microstructures, with a controlled macroscopic physical behavior. Thanks to its procedural formulation, MuFFin will computationally scale with future technologies. As a result of its stochastic nature MuFFin will afford for free grading and embedding of microstructures into objects, hence avoiding the limitations imposed by periodic structures.