Cellular structures with an internal contact-mechanism are investigated. These contact-aided compliant mechanisms are shown to reduce the local tensile stresses, thereby providing additional global strain before yielding or fracture failure compared to honeycomb or auxetic cellular structures. An analytical model for such structures is developed and it is validated using FEA simulations. Two different materials are considered for comparison. More than 100% improvement in global strain capability is possible using the contact. A high-strain morphing aircraft skin is examined as an application of these mechanisms. The contact-aided cellular compliant mechanisms are more advantageous in terms of both the structural mass as well as the global strain compared to a non-contact design. In the application considered the stress-relief mechanism increased the global strain capability by as high as 37%.