Nonlinear force response of modular lattice-based metamaterials

Abstract

Lattice-based metamaterials provide lightweight platforms where local instabilities can govern the global mechanical response, enabling applications in energy routing, vibration isolation, and impact mitigation. Although much progress has been made in controlling deformation and buckling sequences through geometric design, the behavior of coupled nonlinear units over a large range of strain rates and their history-dependent response is less explored. Here, we investigate lattice-based mechanical metamaterials whose nonlinear buckling behavior can be harnessed through modular architectures. By combining modular units in series, we show that their interaction gives rise to emergent force responses, including transient weakening and enhanced force attenuation, that are absent in the individual modules. Furthermore, selected designs exhibit training behavior under cyclic loading, transitioning between distinct buckling states and revealing a history-dependent mechanical response. Our results demonstrate that modular, instability-driven metamaterials can be programmed and tuned not only through geometry but also through loading history, opening new avenues for designing a nonlinear stress-response in mechanical systems.