Variational Methods for Material Defect Evolution

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LarsenDMS-1009653 The investigator studies the evolution of defects inmaterials (e.g., fracture, damage, dislocation plasticity) usinga progression of models from global minimization-basedquasi-statics to full dynamics. Global minimization models arenow well understood, but very little is understood in the morephysically realistic settings of local minimization-based anddynamic problems. Specifically, existence is open for bothcohesive and sharp-interface (Griffith) dynamic fracture, andeffective macro-scale models for local minimization-baseddislocation plasticity are unknown. The investigator seeks tomake significant progress on these and related problems. The propagation of defects in materials is of obviousfundamental importance, yet in the most physically realisticsettings mathematical foundations and analysis are lacking,leaving engineering models largely ad hoc. The investigatorworks on developing mathematical support in these areas, leadingto improved models, better understanding of solutions, andimproved (and justified) algorithms for computing simulations.