Mathematical Sciences: Material Instabilities in Solids

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This research will analyze mathematical models for certain polymers and ductile materials in order to predict the failure of such materials under external forces. The models to be used are nonlinear elasticity and viscoelasticity. Mathematically, the problems involve the existence of singular solutions to quasilinear elliptic and hyperbolic systems, and the existence of minimizers with singularities for problems in the calculus of variations. This work has applications to material failures associated with the formation of cavities in the material and failures due to wrinkling of the material surface.