Neural Metamaterial Networks for Nonlinear Material Design

TL;DR

This paper introduces Neural Metamaterial Networks (NMN), a differentiable neural representation for nonlinear metamaterials, enabling efficient inverse design of materials with tailored mechanical properties through gradient-based optimization.

Contribution

The work presents NMN, a novel neural network-based method that encodes nonlinear metamaterial behavior and facilitates inverse design, overcoming discontinuities in traditional modeling.

Findings

NMN provides smooth, differentiable mappings from structure parameters to mechanical performance.

The approach enables automatic design of materials with specific strain-stress and stiffness profiles.

Compared to native-scale optimization, NMN shows improved efficiency and robustness.

Abstract

Nonlinear metamaterials with tailored mechanical properties have applications in engineering, medicine, robotics, and beyond. While modeling their macromechanical behavior is challenging in itself, finding structure parameters that lead to ideal approximation of high-level performance goals is a challenging task. In this work, we propose Neural Metamaterial Networks (NMN) -- smooth neural representations that encode the nonlinear mechanics of entire metamaterial families. Given structure parameters as input, NMN return continuously differentiable strain energy density functions, thus guaranteeing conservative forces by construction. Though trained on simulation data, NMN do not inherit the discontinuities resulting from topological changes in finite element meshes. They instead provide a smooth map from parameter to performance space that is fully differentiable and thus well-suited for gradient-based optimization. On this basis, we formulate inverse material design as a nonlinear programming problem that leverages neural networks for both objective functions and constraints. We use this approach to automatically design materials with desired strain-stress curves, prescribed directional stiffness and Poisson ratio profiles. We furthermore conduct ablation studies on network nonlinearities and show the advantages of our approach compared to native-scale optimization.