Learning the nonlinear dynamics of soft mechanical metamaterials with graph networks

by   Tianju Xue, et al.

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.



page 6

page 15


Model Order Reduction for Temperature-Dependent Nonlinear Mechanical Systems: A Multiple Scales Approach

The thermal dynamics in thermo-mechanical systems exhibits a much slower...

How to Compute Invariant Manifolds and their Reduced Dynamics in High-Dimensional Finite-Element Models?

Invariant manifolds are important constructs for the quantitative and qu...

Modeling and simulation of nematic LCE rods

We introduce a nonlinear, one-dimensional bending-twisting model for an ...

On the nonlinear stochastic dynamics of a continuous system with discrete attached elements

This paper presents a theoretical study on the influence of a discrete e...

Using Nonlinear Normal Modes for Execution of Efficient Cyclic Motions in Soft Robots

With the aim of getting closer to the performance of the animal musclesk...

A Framework for Data-Driven Computational Dynamics Based on Nonlinear Optimization

In this article, we present an extension of the formulation recently dev...

Direct dissipation-based arc-length approach for the cracking elements method

Dissipated energy, representing a monotonically increasing state variabl...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.