  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.
