# Robust Elastic Metamaterial Design for Additive Fabrication

#### Séminaire Modèles et Algorithmes Déterministes: EDP-MOISE-MGMI

8/03/2018 - 11:00
Mr Julian Panetta *(Ecole Polytechnique Fédérale de Lausanne (EPFL))*
Salle 106 - Batiment IMAG

Modern additive fabrication technologies like 3D printing have made manufacturing special-purpose, customized objects easy, quick, and affordable. Their widespread availability has spurred the development of computational tools for designing objects to meet specific performance goals--for instance, designing an object that performs a particular deformation when subject to forces. However, these design goals typically require controlling the fabrication material's elastic properties more precisely than is possible with even the most advanced multi-material 3D printers. Furthermore, many goals require material behaviors outside the range of properties offered by ordinary fabrication materials (e.g., negative Poisson's ratios). In this talk, I will present my work on designing elastic metamaterials for 3D printing: periodic microstructures that are tuned to emulate a large space of elastic materials. This approach to tailoring material properties is a perfect fit for additive fabrication, which can produce parts of arbitrary complexity at a cost proportional to only the material consumed. I will also present a design tool to optimally apply these metamaterials to achieve high-level deformation goals. Since microstructures typically consist of thin features that concentrate stress, they are prone to plastic deformation and fracture even under mild deformations of the macro-scale object. A key goal of my work is to design microstructures that minimize such stress concentrations, improving the metamaterials' robustness in practice. The approach I propose is based on a novel, efficient, exact solution to the worst-case stress analysis problem for periodic microstructures which supports several failure criteria (e.g., maximum principal stress or von Mises stress). I introduce an algorithm for designing microstructures that minimize a worst-case stress measure while achieving a particular target elasticity tensor and satisfying fabrication constraints (minimum thickness, overhang). Structures designed with this algorithm achieve a typical worst-case stress reduction factor of 5x, which translates into practical robustness improvements demonstrated in lab tests of 3D printed samples.