Variational Methods for Material Defect Evolution

研究人员使用从基于全局最小化的准静力学到全动力学的一系列模型来研究材料中缺陷(例如，断裂、损伤、位错塑性)的演化。全局极小化模型目前已被很好地理解，但在基于局部极小化和动态问题的更现实的环境中理解的很少。具体地说，粘性和尖界面(Griffith)动态断裂的存在是开放的，基于局部最小化的位错塑性的有效宏观尺度模型尚不清楚。调查人员寻求在这些问题和相关问题上取得重大进展。缺陷在材料中的传播具有明显的基本重要性，但在大多数物理上现实的环境中，缺乏数学基础和分析，这使得工程模型在很大程度上是临时的。研究人员致力于在这些领域发展数学支持，导致改进的模型，更好地理解解，以及改进(和证明)计算模拟的算法。

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.