ACM Transactions on Graphics (Proc. ACM SIGGRAPH 2023), 42(4)

Beyond Chainmail: Computational Modeling of Discrete Interlocking Materials

Université de Montréal
ETH Zürich
ETH Zürich
ETH Zürich

Fig. 1. Discrete Interlocking Materials are governed by strongly coupled, highly anisotropic, and asymmetric deformation limits. Our method is able to capture and reproduce these effects for many types of interlocking materials (a). Using native-scale simulations as a basis (b), we construct macromechanical deformation limits on bending and stretching (c) which we use to develop an efficient macro-scale simulation model (d).


We present a method for computational modeling, mechanical characterization, and macro-scale simulation of discrete interlocking materials (DIM)---3D-printed chainmail fabrics made of quasi-rigid interlocking elements. Unlike conventional elastic materials for which deformation and restoring force are directly coupled, the mechanics of DIM are governed by contacts between individual elements that give rise to anisotropic deformation constraints. To model the mechanical behavior of these materials, we propose a computational approach that builds on three key components. (a): we explore the space of feasible deformations using native-scale simulations at the per-element level. (b): based on this simulation data, we introduce the concept of strain-space boundaries to represent deformation limits for in- and out-of-plane deformations, and (c): we use the strain-space boundaries to drive an efficient macro-scale simulation model based on homogenized deformation constraints. We evaluate our method on a set of representative discrete interlocking materials and validate our findings against measurements on physical prototypes.



We would like to thank Charles Gingras for the valuable discussion, and Ronan Hinchet for helping with the measuring setup and fabricating some of the physical prototypes. We are also grateful to the anonymous reviewers for their valuable comments. This work was supported by the Discovery Grants Program and the Discovery Accelerator Awards program of the Natural Sciences and Engineering Research Council of Canada (NSERC). Computing equipment has been funded through an infrastructure grant from the Canada Foundation for Innovation (CFI). This work was also supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No. 866480), and the Swiss National Science Foundation through SNF project grant 200021_200644.