Novel insights into the design of stretchable electrical systems.

Soft electronics have recently gathered considerable interest because of their biomechanical compatibility. An important feature of deformable conductors is their electrical response to strain. While development of stretchable materials with high gauge factors has attracted considerable attention, there is a growing need for stretchable conductors whose response to deformation can be accurately engineered to provide arbitrary resistance-strain relationships. Rare studies addressing this issue have focused on deterministic geometries of single rigid materials, limiting the scope of these strategies. We introduce the novel concept of periodic stretchable patterns combining multiple conductive materials to produce tailored responses. Using shortest path algorithms, we establish a computationally efficient selection method to obtain the required resistance-strain relationship. Using this algorithm, we identify and experimentally demonstrate constant resistance-strain responses up to 50% elongation using a single microtextured material. Last, we demonstrate counterintuitive sinusoidal responses by integrating three materials, with interesting applications in sensing and soft robotics.