  Nonlinear elastic metamaterials are known to support a variety of dynamic
phenomena that enhance our capacity to manipulate elastic waves. Since these
properties stem from complex, subwavelength geometry, full-scale dynamic
simulations are often prohibitively expensive at scales of interest. Prior
studies have therefore utilized low-order effective medium models, such as
discrete mass-spring lattices, to capture essential properties in the
long-wavelength limit. While models of this type have been successfully
implemented for a wide variety of nonlinear elastic systems, they have
predominantly considered dynamics depending only on the instantaneous
kinematics of the lattice, neglecting history-dependent effects, such as wear
and plasticity. To address this limitation, the present study develops a
lattice-based modeling framework for nonlinear elastic metamaterials undergoing
plastic deformation. Due to the history- and rate-dependent nature of
plasticity, the framework generally yields a system of differential-algebraic
equations whose computational cost is significantly greater than an elastic
system of comparable size. We demonstrate the method using several models
inspired by classical lattice dynamics and continuum plasticity theory, and
explore means to obtain empirical plasticity models for general geometries.
