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Abstract Mechanical metamaterials can be designed to exhibit unique mechanical properties, including tunable auxetic behavior as well as multistability, 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 and vibration isolation. 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 3D 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. 

Impacted with sufficiently large stress, a dense, initially liquidlike suspension can be forced into a solidlike state through a process known as shear jamming. While the onset of shear jamming has been investigated extensively, much less is known about the resulting solidlike state in the high-stress limit and, in particular, about its failure mode. We report on experiments that produce such high-stress failure by impacting dense suspensions with a cylindrical rod moving at controlled speed. Using suspensions of cornstarch particles we vary the impact speed over several orders of magnitude and change the fluid viscosity as well as the surface tension in order to identify the conditions for failure. The results are compared with similarly dense suspensions of potato starch or polydisperse silica particles. In all cases where the shear-jammed suspension fails by fracturing, similar to brittle solids, we observe two types of cracks: a primary circular crack around the impacting rod followed by secondary radial cracks. Mapping out the onset of radial fracturing for different particle volume fractions $\varphi$ and impact speeds, we identify the requirements for failure via crack formation to occur with at least 50% likelihood and record the corresponding normal stress ${\sigma }_{\text{N}}$ on the impactor. We find that this likelihood is not particularly sensitive to changes in particle diameter, but increases when the solvent's viscosity or its surface tension are reduced. In the state diagram for dense suspensions we use these data to delineate the upper limit of shear-jammed rigidity and the crossover into a fracture regime at large $\varphi$ and large ${\sigma }_{\text{N}}$ , several orders of magnitude above the stress required for the onset of shear jamming. We find that the onset of fracturing in many cases is correlated with signatures of internal ductile deformation of the shear-jammed material underneath the impactor, observable in ${\sigma }_{\text{N}}$ as a function of axial strain. However, for smaller suspension volumes and larger impact speeds, we find strain hardening up to the point of fracturing. This more brittle behavior results in a modulus that, just before crack formation, is roughly an order of magnitude larger than what we observe in shear-jammed suspensions undergoing internal ductile deformation. 

Addition of very large particles softens the shear-thickening response. The magnitude of this softening increases systematically with particle size. 

Acoustic levitation in air provides a containerless, gravity-free platform for investigating driven many-particle systems with nonconservative interactions and underdamped dynamics. In prior work the interactions among levitated particles were limited to attractive forces from scattered sound and repulsion from hydrodynamic microstreaming. We report on experiments in which contact cohesion provides a third type of interaction. When particle size and separation are both much smaller than the sound wavelength, this interplay of three interactions results in forces that are attractive over several particle diameters, become repulsive at close approach, and are again attractive at contact. In the presence of sound-induced athermal fluctuations that generate particle collisions, the interplay of these three forces enables the formation of particle chains with anisotropic interactions that depend on chain size and shape due to multibody effects. With the control of the kinetic pathways and the strength of the contact cohesion, different patterns can be assembled, from triangular lattices to labyrinthine patterns of chains to lacelike networks of interconnected rings. These results shed light on the multibody character of acoustic interactions and can be utilized to direct the self-assembly of particles. Published by the American Physical Society2025 

Magnetically responsive, mechanically flexible microstructures are desirable for applications ranging from smart sensors to remote-controlled actuation for surgery or robotics. Embedding magnetic nanoparticles into a thin matrix of elastic material enables high flexibility while exploiting the magnetic response of the individual particles. However, in the ultrathin limit of such nanocomposite materials, the particles become too small to sustain a permanent dipole moment. This implies that now large magnetic field gradients are required for actuation, which are difficult to achieve with externally applied fields. Here, we demonstrate through experiment and simulation that monolayer sheets of close-packed paramagnetic nanoparticles in a uniform applied field can generate large local field gradients through particle interactions. As a result, a strong collective magnetization is obtained that leads to large deflections of freestanding sheets already in moderate applied fields. Exploiting the vector nature of the applied field, we furthermore find that it is possible to induce more complex curvature and twist the sheets. Finally, we show that paramagnetic nanoparticle monolayers applied as coatings can generate sufficient force to deflect strips of nonmagnetic material that is several orders of magnitude thicker. 

Dynamic compression of elastic foam filled with non-Newtonian fluid can be rationalized by fluid rheology and foam pore size distribution.