Shape-Shifting Structures by Jamming on a Deformable Manifold

The form and function of some organs, such as the lungs and intestines, and the development of the embryo are dictated in part by the mechanical interaction between cells and an elastic manifold. Differential growth or shape change produces an instability, resulting in a competition between the packing and rearrangement of the cells and the stress localization and deformation of the manifold. Oftentimes these dynamics are modeled by neglecting the granular nature of the cells and treating them as a continuum, which is helpful but can miss mesoscale features. Here we present a study of granular matter coupled to an elastic manifold. By tuning the stiffness and thickness of the manifold, the density and growth of the particles, and the parameters of the particle-particle and particle-manifold coupling, we investigate a rich phase diagram of emergent behaviors – ranging from a bilayer-growth-like regime, to a granular rearrangement and pop-off dictated regime, to a regime governed by manifold stress-localization that is reminiscent of the crumpling of paper. We delineate these regimes numerically, providing a map of potential behaviors, guidelines for when a continuum approach might be sufficient, and a tool for if the granular nature of the particle layer must be considered.