Strongly nonlinear wave propagation in elasto-plastic metamaterials: Low-order dynamic modeling

Wallen, Samuel P.; DeLima, Washington; Haberman, Michael R.

doi:10.1016/j.jmps.2025.106276

Strongly nonlinear wave propagation in elasto-plastic metamaterials: Low-order dynamic modeling

Journal Article · Fri Jul 18 00:00:00 EDT 2025 · Journal of the Mechanics and Physics of Solids

DOI:https://doi.org/10.1016/j.jmps.2025.106276· OSTI ID:3007092

^[1]; DeLima, Washington ^[2]; ^[1]

Univ. of Texas, Austin, TX (United States)
Kansas City Plant (KCP), Kansas City, MO (United States)

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. Here, 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, thereby gaining insight into the influence of microstructural plasticity on effective material performance, which can be used to improve the design of nonlinear mechanical metamaterials.

View Accepted Manuscript (DOE)

Research Organization:: Kansas City Plant (KCP), Kansas City, MO (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: NA0002839

OSTI ID:: 3007092

Report Number(s):: NSC--614-6840

Journal Information:: Journal of the Mechanics and Physics of Solids, Journal Name: Journal of the Mechanics and Physics of Solids Vol. 204; ISSN 0022-5096

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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