Modelling a Feather as a Strongly Anisotropic Elastic Shell

Feathers exhibit a highly anisotropic behaviour, governed by their complex hierarchical microstructure composed of individual hairs (barbs) clamped onto a spine (rachis) and attached to each other through tiny hooks (barbules). Previous methods in computer graphics have approximated feathers as strips of cloth, thus failing to capture the particular macroscopic nonlinear behaviour of the feather surface (vane). To investigate the anisotropic properties of a feather vane, we design precise measurement protocols on real feather samples. Our experimental results suggest a linear strain-stress relationship of the feather membrane with orientation-dependent coefficients, as well as an extreme ratio of stiffnesses in the barb and barbule direction, of the order of 104. From these findings we build a simple continuum model for the feather vane, where the vane is represented as a three-parameter anisotropic elastic shell. However, implementing the model numerically reveals severe locking and ill-conditioning issues, due to the extreme stiffness ratio between the barb and the barbule directions. To resolve these issues, we align the mesh along the barb directions and replace the stiffest modes with an inextensibility constraint. We extensively validate our membrane model against real-world laboratory measurements, by using an intermediary microscale model that allows us to limit the number of required lab experiments. Finally, we enrich our membrane model with anisotropic bending, and show its practicality in graphics-like scenarios like a full feather and a larger-scale bird. Code and data for this paper are available at https://gitlab.inria.fr/elan-public-code/feather-shell/.