3D Periodic Cellular Materials with Tailored Symmetry and Implicit Grading

Abstract

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.

Neural Metamaterial Networks for Nonlinear Material Design

“…Designing metamaterials with desired macromechanical properties is a problem that spans many areas explored in graphics, including geometry processing, physics-based modeling, and computational fabrication. Consequently, there has recently been a surge in works that explore various types of metamaterials [Efremov et al 2021;Musialski 2020, 2022;Martínez et al 2019Martínez et al , 2017Schumacher et al 2018;Tricard et al 2020]. For example, Schumacher et al [2018] characterize the in-and out-of-plane behavior of structured sheet materials.…”

“…proposed a methodology for creating 3D-printable, weave-like materials with desired mechanical properties. Based on star-shape metrics, Martínez et al [2019] and Efremov et al [2021] introduce spatially graded meta-materials that cover a wide range of elastic properties. Martínez et al [2017] leverage procedural Voronoi foams to efficiently create orthotropic microstructures.…”

Mechanical and corrosion performance of biodegradable iron porous structures

“…[18][19][20] There are several examples of structures that exhibit a gradient in the dimension of the unit cells with a spatial variation in solid volume fraction. 18,[21][22][23][24][25][26][27][28] Graded cellular structures allow for mimicking the bone structure, promoting a change in the fluid flow inside the structures, thus adjusting the biodegradation behaviour, 23 being also a way to reduce the stiffness in the metallic scaffolds. 19,[29][30][31][32] Different possibilities can be used to construct graded cellular structures based on several distributions of cell size, porosity, strut thickness and cell shape.…”

“…18–20 There are several examples of structures that exhibit a gradient in the dimension of the unit cells with a spatial variation in solid volume fraction. 18,21–28 Graded cellular structures allow for mimicking the bone structure, promoting a change in the fluid flow inside the structures, thus adjusting the biodegradation behaviour, 23 being also a way to reduce the stiffness in the metallic scaffolds. 19,29–32…”

Nature-inspired architected materials using unsupervised deep learning

“…Several other computational tools for automated and tileable microstructure design have been recently introduced, such as a framework for two-scale topology optimization 28 , tileable microstructures from families of related structures 29 , tileable microstructures derived from Voronoi diagrams induced by starshaped metrics 30 , 3D star-shaped tile sets emerging from a discrete growth process in a lattice 31 , computationally mapping auxetic, conventional, and transitional unit cells into cellular solids 32 , and using combinatorial search over topologies to obtain parametric cubic patterns with isotropic elastic materials 33 . These methods have generated fascinating metamaterials with applications in topology optimization 28 , controlled elasticity 29,33 , shape-matching 32 , and others.…”