Strongly Nonlinear Wave Propagation in Elasto-plastic Metamaterials: Low-order Dynamic Modeling

TL;DR

This paper develops a low-order lattice-based model for nonlinear elastic metamaterials that incorporates plastic deformation, enabling efficient simulation of history-dependent effects like wear and plasticity in complex geometries.

Contribution

It introduces a novel modeling framework that captures plasticity in nonlinear elastic metamaterials, extending beyond traditional instantaneous kinematic models.

Findings

The framework produces differential-algebraic equations for plastic systems.

Demonstrates models inspired by lattice dynamics and continuum plasticity.

Explores empirical plasticity models for various geometries.

Abstract

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.