Materials with electroprogrammable stiffness and adhesion can enhance the performance of robotic systems, but achieving large changes in stiffness and adhesive forces in real time is an ongoing challenge. Electroadhesive clutches can rapidly adhere high stiffness elements, although their low force capacities and high activation voltages have limited their applications. A major challenge in realizing stronger electroadhesive clutches is that current parallel plate models poorly predict clutch force capacity and cannot be used to design better devices. Here, we use a fracture mechanics framework to understand the relationship between clutch design and force capacity. We demonstrate and verify a mechanics-based model that predicts clutch performance across multiple geometries and applied voltages. On the basis of this approach, we build a clutch with 63 times the force capacity per unit electrostatic force of state-of-the-art electroadhesive clutches. Last, we demonstrate the ability of our electroadhesives to increase the load capacity of a soft, pneumatic finger by a factor of 27 times compared with a finger without an electroadhesive.