Inverse Design of Tightly-Woven Smart Fabrics

Threads that undergo controlled deformations in response to environmental stimuli open the door to the manufacturing of fabrics that can change their shape on demand. This can be realized with a variety of smart materials such as liquid crystal elastomers or shape-memory polymers. In this talk we discuss the geometry and deformation of a simple woven fabric whose threads are pre-programmed with some response field. We focus on the tight weaving regime, where threads undergo a jamming transition and further in-plane deformations are strongly suppressed. The result is a direct relation between the actuation profile and the shape of the actuated fabric. We use this relation to study the inverse design problem -- given a target surface, we calculate the thread parameters at each point needed to induce morphing of the fabric into the desired shape upon actuation. The inverse problem is resolved by constructing a suitable coordinate system on the target surface. We show that such constructions exist locally on every smooth surface. We further show an algorithm for finding approximate global solutions using tools from discrete differential geometry. We thus provide explicit recipes for the manufacturing of tightly-woven fabrics that morph into arbitrary target shapes.