Heterogeneous Metamaterials Design via Multiscale Neural Implicit Representation

TL;DR

This paper introduces a neural network framework for designing heterogeneous metamaterials by learning a continuous multiscale representation, enabling seamless, high-resolution structures without predefined datasets, suitable for various engineering applications.

Contribution

The work presents a novel neural implicit representation that jointly models macroscale and microscale features, ensuring compatibility and continuous design space exploration for metamaterials.

Findings

Successfully designed heterogeneous mechanical metamaterials.

Achieved seamless unit cell connectivity without post-processing.

Enabled arbitrary high-resolution structure generation.

Abstract

Metamaterials are engineered materials composed of specially designed unit cells that exhibit extraordinary properties beyond those of natural materials. Complex engineering tasks often require heterogeneous unit cells to accommodate spatially varying property requirements. However, designing heterogeneous metamaterials poses significant challenges due to the enormous design space and strict compatibility requirements between neighboring cells. Traditional concurrent multiscale design methods require solving an expensive optimization problem for each unit cell and often suffer from discontinuities at cell boundaries. On the other hand, data-driven approaches that assemble structures from a fixed library of microstructures are limited by the dataset and require additional post-processing to ensure seamless connections. In this work, we propose a neural network-based metamaterial design framework that learns a continuous two-scale representation of the structure, thereby jointly addressing these challenges. Central to our framework is a multiscale neural representation in which the neural network takes both global (macroscale) and local (microscale) coordinates as inputs, outputting an implicit field that represents multiscale structures with compatible unit cell geometries across the domain, without the need for a predefined dataset. We use a compatibility loss term during training to enforce connectivity between adjacent unit cells. Once trained, the network can produce metamaterial designs at arbitrarily high resolution, hence enabling infinite upsampling for fabrication or simulation. We demonstrate the effectiveness of the proposed approach on mechanical metamaterial design, negative Poisson's ratio, and mechanical cloaking problems with potential applications in robotics, bioengineering, and aerospace.