Foraging is constrained by the energy within resources and the mechanics of acquisition and assimilation. Thick molar enamel, a character trait differentiating hominins from African apes, is predicted to mitigate the mechanical costs of chewing obdurate foods. The classic expression of hyperthick enamel together with relatively massive molars, termed megadontia, is most evident in Paranthropus, a lineage of hominins that lived about 2.7–1.2 million years ago. Among contemporary primates, thicker molar enamel corresponds with the consumption of stiffer, deformation-resistant foods, possibly because thicker enamel can better resist cracking under high compressive loads. Accordingly, plant underground storage organs (USOs) are thought to be a central food resource for hominins such as Paranthropus due to their abundance, isotopic composition, and mechanical properties. Here, we present a process-based model to investigate foraging constraints as a function of energetic demands and enamel wear among human ancestors. Our framework allows us to determine the fitness benefits of megadontia, and to explore under what conditions stiff foods such as USOs are predicted to be chosen as fallback, rather than preferred, resources. Our model predictions bring consilience to the noted disparity between functional interpretations of megadontia and microwear evidence, particularly with respect to Paranthropus boisei.