Tuning Crumpled Sheets for An Enhanced Flexoelectric Response

Flexoelectricity is a universal phenomenon present in all dielectrics that couples electrical polarization to strain gradients and vice-versa. Thus, structures and configurations that permit large strain gradients facilitate the design of an enhanced electromechanical coupling. In a recent work, we demonstrated the prospects for using crumpling of essentially arbitrary thin sheets for energy harvesting. Crumples, with their defect-like nature, admit singular and rapidly varying deformation fields and are thus ideal for engineering sharp non-uniformities in the strain field. In this work, we consider how to tune the design of crumpled sheets for a significant flexoelectric response. Specifically, we analytically derive the electromechanical coupling for a thin crumpled sheet with varying thickness and graded Young's modulus as key design variables. We show that the electromechanical coupling of such crumpled sheets can be tuned to be nearly five times those of the homogeneous film.