UV light-driven deformations in photoactive fiber-reinforced planar annular membranes

Abstract

Engineered fibers such as azobenzene—a photoresponsive material—change their stress free or natural reference length in response to ultraviolet (UV) light. This work focuses on the mechanics of a plane annular membrane formed from a homogeneous incompressible nonlinear elastic material reinforced by an axisymmetric distribution of activated fibers lying in a plane parallel to the mid-surface. The lengths of these fibers can be triggered to change by non-mechanical influences such as temperature change or radiation from an UV light source. Each fiber has the shape of a plane spiral curve that extends from the inner to the outer radius. The membrane is attached to a rigid circular disc at the inner boundary. The outer boundary can have a prescribed radial stretch. A new constitutive model for the UV-activated fiber-reinforced medium is developed. Boundary value problems that combine twist with radial expansion are formulated and solved as a system of ordinary differential equations. Corresponding finite element (FE) models are also developed. Results show that the contraction of the spiral fibers will lead to a shape change, a shearing deformation in the radial-circumferential plane, and a distribution of shear stresses within the membrane. The resulting shear deformation may cause a principal stress to become negative indicating wrinkling. The shearing deformation disappears in the special cases of radial and circumferential fiber distributions while negative principal stresses might still present. We consider conditions where wrinkling may be avoided by imposing a radial stretch. We also investigate the regimes of instability due to the compressive stress in the membrane using FE methods. Such understanding is critical to multiple applications including designing soft robotic devices that can be actuated by active fibers, biomechanical modeling of biological phenomena (e.g., vasoconstriction and vasodilation in blood vessels, the peristalsis motion in urinary and gastrointestinal tract systems), and complex deformation in muscular hydrostats of animals.