Machine learning-based generation of discrete-element models for nonlinear wave propagation in elasto-plastic metamaterials

Nonlinear elastic metamaterials (NLEMs) support a variety of dynamic phenomena that enable the manipulation of large-deformation elastic waves. Full-scale dynamic simulation of NLEMs is often prohibitively expensive due to the importance of complex, sub-wavelength geometry. Low-order effective medium models based on mass-spring lattices [Wallen et al., arXiv:2407.20434 (2024)] have recently been developed to capture history-dependent effects of plasticity for 1-D simulation of nonlinear wave propagation in NLEMs. However, the model developed therein requires significant preparatory effort to obtain empirical constitutive relations and their derivatives via a complex, ad-hoc curve-fitting procedure. Here, an alternative method is proposed whereby trained deep neural networks provide the constitutive relations, allowing for application of automatic differentiation methods to obtain derivatives for implicit solution of the differential-algebraicequations of motion. The networks are trained using cyclical force–displacement data from a finite-element model of a unit cell of interest, which exhibits buckling under elasto-plastic deformation. The trained neural networks are then incorporated into the discrete-element framework of Wallen et al. to simulate wave propagation in a chain of unit cells.