Mechanics and transient morphing of soft hygroscopic bilayers

Abstract

Motivated by pine cones and plant seeds that open or close in response to changes in humidity thanks to the shrinking or swelling of hygroscopic bilayers, and given the recent interest in artificial systems that mimic the hygroscopic motility of seeds, we consider bilayers consisting of two adhering elongated thin layers made of hygroscopic gels, modeled as active, transversally isotropic elastic materials. The direction of transverse isotropy is set as one of the fibers that are present in both biological and synthetic materials. As a special, biologically relevant case, we consider one of the two layers passive. This work develops a three-dimensional model for the coupled evolution of elastic deformations and moisture content (solvent concentration). Based on this model, a numerical scheme for solving the evolution equations coupling mechanical equilibrium and diffusion has been constructed based on the Finite Element Method. The equations are formulated in weak form and solved using Comsol Multiphysics. We have applied our model to compute transient configurations and their steady-state equilibrium limits in some relevant test cases. These configurations are then analyzed to understand the influence of the various geometric and physical parameters.