| Abstract: | Instabilities and the localization of damage often signal the impending failure of most mechanical systems—for instance, in the formation of creases in crumpled sheets; the catastrophic collapse of soda cans and space rockets; and the fracture of brittle solids. I will explore three everyday systems: the evolution of damage networks in thin sheets subjected to crumpling and re-crumpling, the buckling behavior of soda cans, and the generation of rough surfaces in fractured gels. In each case, patterns emerge from a nuanced interplay of material heterogeneity, mechanical instabilities, spatial constraints, and spontaneous localization. By integrating experimental observations with primarily phenomenological models, I will loosely connect these disparate systems and suggest that localization not only dictates failure but also shapes the pathways of damage evolution, linking the physics of failure to broader themes of stability, dynamics, and catastrophic transformation.
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