Compared to materials with a straight geometry, materials with a corrugated architecture have shown potential to improve ductility without sacrificing strength due to the unbending of the corrugation during loading. The purpose of this research was to study the effect of geometric and material parameters on the stress-strain response of materials with a corrugated geometry and understand what controls the unbending process and under what conditions improved ductility was achievable. This involved studying isolated corrugations and corrugation reinforced composites under tensile and transverse compressive loading by performing parametric studies using Finite Element Modeling (FEM) simulations. These simulations showed that improvements in ductility are directly related to the degree of corrugation present and can be attributed to an initial bending dominated process. The unbending of the corrugation leads to an evolving geometry which causes the material to strengthen and ultimately delays necking. For corrugated composites, it was found that there is significant interplay between the properties of the components and the geometry of the corrugation. To obtain a benefit in ductility through corrugation, the matrix must have sufficiently high work hardening to accommodate the unbending corrugation without itself necking, but also have sufficiently low flow stress relative to the reinforcement yield strength to prevent the corrugation from stretching instead of unbending. Also, if the boost in work hardening from unbending occurs too early, no gain in ductility is achieved. In addition to these findings, tools for predicting the strength and ductility of these materials were developed, including an analytical model for the isolated corrugations and a series of benefit maps and surfaces for the corrugated composites. These tools proved to be fairly effective. Finally, the FEM findings were compared to experimental stress-strain curves and strain maps for validation and showed relatively good qualitative agreement. / Thesis / Doctor of Philosophy (PhD) / It is uncommon to find a material that possesses both high strength as well as the ability to elongate a lot without failing. One way to achieve this combination of properties is to use a wavy or corrugated structure that provides increased elongation when loaded due to the straightening of the corrugation. The purpose of this thesis was to study how materials which possess a wavy or corrugated geometry behave when they are subjected to a stretching load. This research utilized computer simulations and simple experimental testing to evaluate both isolated corrugations and corrugations embedded in another material. It was found that the amount of improvement in elongation is dependent on the initial amount of waviness. Also, whether a material shows improved elongation depends on whether the corrugation is able to unbend, which in turn depends on the corrugation geometry and the relative mechanical properties of the two materials.