Variational Methods for Material Defect Evolution

Worcester Polytechnic Institute, Worcester MA

Investigators

Abstract

Larsen DMS-1009653 The investigator studies the evolution of defects in materials (e.g., fracture, damage, dislocation plasticity) using a progression of models from global minimization-based quasi-statics to full dynamics. Global minimization models are now well understood, but very little is understood in the more physically realistic settings of local minimization-based and dynamic problems. Specifically, existence is open for both cohesive and sharp-interface (Griffith) dynamic fracture, and effective macro-scale models for local minimization-based dislocation plasticity are unknown. The investigator seeks to make significant progress on these and related problems. The propagation of defects in materials is of obvious fundamental importance, yet in the most physically realistic settings mathematical foundations and analysis are lacking, leaving engineering models largely ad hoc. The investigator works on developing mathematical support in these areas, leading to improved models, better understanding of solutions, and improved (and justified) algorithms for computing simulations.