Data-driven finite elements for geometry and material design

Abstract

Figure 1: Examples produced by our data-driven finite element method. Left: A bar with heterogeneous material arrangement is simulated 15x faster than its high-resolution counterpart. Left-Center: Our fast coarsening algorithm dramatically accelerates designing this shoe sole (up to 43x). Right-Center: A comparison to 3D printed results. Right: We repair a flimsy bridge by adding a supporting arch (8.1x) speed-up. We show a High-Res Simulation for comparison. AbstractCrafting the behavior of a deformable object is difficult-whether it is a biomechanically accurate character model or a new multimaterial 3D printable design. Getting it right requires constant iteration, performed either manually or driven by an automated system. Unfortunately, previous algorithms for accelerating three-dimensional finite element analysis of elastic objects suffer from expensive precomputation stages that rely on a priori knowledge of the object's geometry and material composition. In this paper we introduce Data-Driven Finite Elements as a solution to this problem. Given a material palette, our method constructs a metamaterial library which is reusable for subsequent simulations, regardless of object geometry and/or material composition. At runtime, we perform fast coarsening of a simulation mesh using a simple table lookup to select the appropriate metamaterial model for the coarsened elements. When the object's material distribution or geometry changes, we do not need to update the metamaterial library-we simply need to update the metamaterial assignments to the coarsened elements. An important advantage of our approach is that it is applicable to non-linear material models. This is important for designing objects that undergo finite deformation (such as those produced by multimaterial 3D printing). Our method yields speed gains of up to two orders of magnitude while maintaining good accuracy. We demonstrate the effectiveness of the method on both virtual and 3D printed examples in order to show its utility as a tool for deformable object design.

Real2Sim

“…Recently, Torres et al [2016] presented a numerical coarsening scheme for co-rotational linear elasticity including treatment of highresolution boundary conditions. For non-linear materials, Chen et al [2015] introduced a data-driven coarse numerical simulation approach for object design and fabrication. They later included dynamic motions as well, introducing dynamics-aware numerical coarsening [Chen et al 2017].…”

SimuLearn

“…Data-driven simulation methods have recently been used to accelerate simulation in various ways, such as numerical coarsening [10], subspace dynamics modeling [13], and reaction-diffusion [21]. These approaches use accurate simulators to trade precomputation effort for better runtime performance.…”

Spectral coarsening of geometric operators

“…3 for comparison). Chen et al [2015] extend this idea via a data-driven lookup table. Chen et al [2018] consider numerical coarsening for regular-grid domains, where matrix-valued basis functions on the coarse domain are optimized to again agree with the six smallest deformation modes of a fine mesh through a global quadratic optimization.…”