Learning the nonlinear dynamics of soft mechanical metamaterials with graph networks

TL;DR

This paper introduces a machine learning framework using graph networks and Gaussian process regression to model and simulate the nonlinear dynamics of soft mechanical metamaterials efficiently, capturing complex behaviors with reduced computational cost.

Contribution

The work develops a novel graph network-based approach combined with Gaussian process regression to accurately model nonlinear spring mechanics from continuum data, enabling efficient dynamic simulations.

Findings

Significantly reduces computational cost compared to direct numerical simulation.

Achieves comparable accuracy in modeling nonlinear dynamics.

Easily incorporates defects and inhomogeneities for design purposes.

Abstract

The dynamics of soft mechanical metamaterials provides opportunities for many exciting engineering applications. Previous studies often use discrete systems, composed of rigid elements and nonlinear springs, to model the nonlinear dynamic responses of the continuum metamaterials. Yet it remains a challenge to accurately construct such systems based on the geometry of the building blocks of the metamaterial. In this work, we propose a machine learning approach to address this challenge. A metamaterial graph network (MGN) is used to represent the discrete system, where the nodal features contain the positions and orientations the rigid elements, and the edge update functions describe the mechanics of the nonlinear springs. We use Gaussian process regression as the surrogate model to characterize the elastic energy of the nonlinear springs as a function of the relative positions and orientations of the connected rigid elements. The optimal model can be obtained by "learning" from the data generated via finite element calculation over the corresponding building block of the continuum metamaterial. Then, we deploy the optimal model to the network so that the dynamics of the metamaterial at the structural scale can be studied. We verify the accuracy of our machine learning approach against several representative numerical examples. In these examples, the proposed approach can significantly reduce the computational cost when compared to direct numerical simulation while reaching comparable accuracy. Moreover, defects and spatial inhomogeneities can be easily incorporated into our approach, which can be useful for the rational design of soft mechanical metamaterials.