Poking on Pasta Strainers: The Rigidity of Elastic Gridshells

We study the linear mechanical response of a hemispherical elastic gridshell under point-load indentation. An elastic gridshell comprises an initially planar network of elastic rods that is actuated into a 3D shell-like structure by compressing its outer boundary. We have recently introduced a novel framework to design nearly hemispherical gridshells. Our designs harness the theory of Chebyshev nets, which describes the kinematics of a medium that is anisotropically inextensible. First, we lay a square grid of Nitinol rods over an etched acrylic mold, and, then, we pour an elastomeric polymer over the crossing points to produce joints that impose positional constraints. Compressing the boundary points of the originally flat grid yields a 3D shell-like geometry. We systematically vary the geometric parameters of the gridshells and measure their structural rigidity (force per unit indentation displacement). Combining experiments, simulations, and scaling analyses leads to a master curve that relates the structural rigidity of the gridshell to its geometric and material properties. Our results indicate that the mechanical response of the gridshell, and the underlying characteristic forces, are dictated by Euler's elastica instead of shell-related quantities.