Thesis title: Shape morphing of soft active sheets
Biological systems often exploit their capability to respond to environmental stimuli to achieve complex shapes and perform some necessary living functions. Inspired by nature, scientists developed synthetic soft active materials whose deformation is induced by non-mechanical actions, and that mimic, for example, the shape transformation of plants, in which a variety of organs such as flowers, leaves, pods and tendrils respond to variations of light, humidity or temperature. As in plants the tissue composition and its microstructural cell anisotropy play an important role, so also for synthetic materials the design of the material structure is fundamental for programming its final shape. Up to date, some exciting achievements have been made and successfully applied in a variety of fields, including biomedical devices, drug delivery, soft robotics, sensors and actuators.
This thesis aims to investigate the morphing of soft active sheets, focusing on flat metric structures such as beams, plates and cylindrical shells, via theoretical analysis, numerical simulation and experimental validation. The work focuses on those soft materials in which the morphing can be driven by elastic or inelastic growth such as gels, nematic elastomers or biological tissues. The adopted strategy to achieve bending is based on a through-the-thickness mismatch realized by stacking two homogeneous layers with different properties on top of each other. Specifically, three processes that induce bending in bilayer structures are explored: the differential swelling between two layers with different elastic moduli, the shrinking of a layer containing solvent glued to a passive layer, the diffusion of the solvent from one layer to the other.
The first process is used in the study of the swelling-induced eversion and flattening of naturally curved gel beams, and in the shaping from sphere-like to nearly developable shapes of rectangular gel plates. In the latter, the final shape depends on several geometrical and mechanical factors. Reinforcing fibers can be crucial in controlling shaping under swelling and greatly influence the characteristics of the final shapes. Swelling is analyzed with a fully coupled nonlinear three-dimensional stress-diffusion model. A revised version of the Flory-Rehner free energy is adopted to model the presence of the fibers.
The second process is carried out experimentally through the fabrication of bilayer sheets with one passive layer of polydimethylsiloxane (PDMS) and one layer of PDMS mixed with silicone oil; the morphing is induced by extracting the oil from the elastomer. The experiment concerns the study of bending of shrinking beams. The problem is also set within the context of three-dimensional finite elasticity with distortions, considering the total extraction of oil as an isotropic bulk contraction. The latter is also used to investigate the eversion of cylindrical bilayer shells after oil extraction. It is shown how the geometry and the initial fraction of oil affect the shape at equilibrium, which can be in the form of cylindrical shells with axes orthogonal to the original one, saddle-like shapes and doubly curved shapes.
The third and last process is explored starting from the experiment described above, letting the oil initially contained in a single layer diffuse into the layer made of only PDMS, without extracting it. The resulting transient bending is numerically simulated through the stress-diffusion model and a simplified way to predict the steady-state curvature is proposed.
Furthermore, as regards swelling/shrinking of bilayer beams, the problem is also addressed from an energetic point of view, highlighting the importance of the choice of the deformation measures for the formulation of reduced analytical models. In particular, explicit formulas for the curvature and the stretch of the middle axis are provided for naturally curved growing beams.