Mathematics Colloquia and Seminars

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In this talk I will discuss a type of phase transitions in solids which lead to large deformations. These solid-to-solid transitions, known as martensitic transformations, give rise to interesting physical phenomena, important applications, and substantial challenges from the point of view of analysis. In my talk I will present analytical results and numerical methods, including rigorous upper and lower bounds of the overall homogenized elastic energy for materials in polycrystalline form as well as methods for the estimation of the response of martensitic single crystals to applied forces. Using these methods I will calculate the deformations that NiTi alloys can withstand coherently (i.e. without cracking or breaking). I will finally comment on the implications of our single-crystal results to the simulation of TiNi polycrystals. These constructions have revealed a number of remarkable characteristics in the behavior of martensitic materials - including the existence of vanishing elastic constants in polycrystals, as well as a large range of deformations for NiTi in single crystalline form.