Plasticity in nonlinear elastic metamaterials: Low-order dynamic modeling

Nonlinear elastic metamaterials have been shown to admit a variety of rich, dynamical features that can be leveraged to tailor the propagation of mechanical waves. Since these materials derive their properties from intricate, subwavelength geometries, direct numerical simulations are often prohibitively expensive at scales of interest. To overcome this limitation, reduced-order models, typically in the form of effective continua or discrete lattices that capture the essential features of the material at sufficiently long wavelengths, have been developed. While many prior studies have implemented these models successfully, the vast majority have considered only recoverable elastic deformations with linear damping and neglected history-dependent effects, such as plasticity and friction. In this presentation, we introduce an effective lattice modeling framework for nonlinear elastic metamaterials undergoing plastic deformation. Due to the history-dependent nature of plasticity, this framework generally yields a system of differential-algebraic equations whose computational cost is significantly greater than a purely elastic system of similar size. We apply the method to several examples of interest and explore means to obtain phenomenological elastic-plastic models for general material architectures.