Elastogranular mechanics: far-from-equilibrium behaviors of thin elastic structures deforming in granular matter
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Abstract
Confined thin elastic objects are abundant in nature. With spatial constraints typically arising from a combination of different loading profiles, confining media, or coupling effects, the unique deformation strategies of slender structures, with their propensity to buckle, bend, fold, & wrinkle, is observed across a range of different length scales, from the nano-scale folding of graphene and the microscopic wrinkling of cellular membranes, to the macroscopic development of plant root networks. Much previous work has focused on growing or deforming thin structures confined by rigid, fixed boundaries. Comparatively, much less is known about the behavior of thin structures interacting with compliant or transitional boundaries, such as those formed by granular materials.
By varying the geometries of slender elastic structures embedded within a granular medium and studying the resulting buckling behaviors under area or displacement control, we have established an experimental framework allowing us to apply the results of classical elastic stability theory to deformations occurring within complex & fragile media. These elastogranular systems couple the finite deformations of slender, flexible bodies with the qualitative phase changes observed in granular materials, which may transition between being gas, fluid, or solid-like states of matter. The elongation of a slender elastica in a 2D monodisperse medium leads to two length scales {∆c,λc} encoding system behavior before and after a critical jamming point φj, while introducing bidispersity into the same experiments changes the underlying structural composition/order in the grains, allowing bending energy in the elastica to relax as the medium transitions from crystalline solid to a more fluid-like amorphous state. The planar injection of a pinched elastic loop shows the intricate coupling between large elastic deformations and developing boundaries, while the buckling morphologies of a slender elastic ring compressed in a granular gas shows promise as a device-free probe of mechanical packing properties. These results will bring new insight into the behavior of deformable structures within granular media, colloidal systems, and soft gels, and will be relevant in the study of plant root morphogenesis, the modeling of animal movements, the design of soft robots, and in developing smart, steerable optical & surgical tools.