Diffusive buckling fronts in lattice-based metamaterials

TL;DR

This paper studies how buckling instabilities propagate as fronts in overdamped, lattice-based metamaterials, demonstrating control via geometry and dissipation, with experimental validation and a reaction-diffusion modeling framework.

Contribution

It introduces a novel reaction-diffusion model for buckling fronts in overdamped metamaterials, linking geometry and material properties to front propagation control.

Findings

Buckling fronts can be directed by lattice geometry.

Viscoelastic dissipation influences front speed and direction.

Experimental results validate the reaction-diffusion model.

Abstract

Mechanical metamaterials can be designed to exhibit unique mechanical properties, including tunable auxetic behavior as well as multi-stability, which arise from the geometry and configuration of the constituent building blocks. Lattice-based metamaterials, in particular, provide lightweight platforms where local instabilities can dictate the global response, with applications in energy routing, vibration isolation, and impact mitigation. In underdamped structures, perturbations have been found to propagate as nonlinear waves, e.g., transition waves or solitons. Here we investigate the opposite limit of overdamped, highly dissipative lattice metamaterials. Focusing on three-dimensional structures, we uncover how buckling instabilities, triggered by compression, propagate as fronts that shape the macroscopic behavior. We demonstrate in experiments on 3D-printed simple cubic lattices how global and local buckling modes can be controlled via the lattice geometry. By incorporating viscoelastic dissipation into a 3D-continuum model, we show that strain-driven buckling fronts obey coupled reaction-diffusion equations. The diffusion and reaction coefficients, determined by local geometry, material properties, and strain, select the propagation direction and enable steering of the fronts. This establishes a predictive and experimentally validated framework for the control of cascading mechanical instabilities in lattice-based metamaterials.