Variational Fracture with Loads

载荷变分断裂

• 批准号: 2206114
• 负责人: Christopher Larsen
• 金额: $ 27.19万
• 依托单位: Worcester Polytechnic Institute
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-07-01 至 2025-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2206114&HistoricalAwards=false
• 关键词: Variational; Fracture; Loads

For a large range of applications, from civil infrastructure to national defense, understanding the failure of materials is critical. The ability to predict failure depends on modeling and on the mathematics available to formulate and analyze models, and to justify numerical methods. Over the last twenty years, there have been significant mathematical advances in this area, particularly in fracture mechanics, but these results are largely limited to models without applied forces. However, the inclusion of applied forces is relevant for applications. This project aims to improve the current mathematical formulation for fracture in materials in equilibrium with applied forces, to extend this formulation to models for material evolution, and to study certain features of these evolutions related to the presence of applied forces. The project offers training research opportunities for doctoral students. The ability to accurately predict failure depends on the quality of the underlying mathematical modeling of defects, as well as on understanding fundamental properties of solutions. Until recently, variational models for static and quasi-static fracture have been limited to Dirichlet boundary conditions, since there do not exist solutions to the seemingly most natural formulation that includes Neumann boundary conditions, i.e., boundary loads. The aim of the project is to improve on a recently introduced static formulation for variational fracture with boundary loads which can have solutions, to extend this static model to the quasi-static case and show existence of solutions, and to study the possibility of existence of energy drops in quasi-static models.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

对于从民用基础设施到国防的各种应用，了解材料的失败至关重要。 预测故障的能力取决于建模和可用的数学来制定和分析模型，并证明数值方法是合理的。 在过去的二十年中，该领域有显着的数学进步，尤其是在断裂力学中，但是这些结果在很大程度上仅限于没有施加力的模型。但是，施加力的纳入与应用有关。该项目旨在改善与施加力平衡中材料中断裂的当前数学公式，以将该公式扩展到材料演化的模型，并研究这些演变的某些特征，这些发展与施加力的存在相关。 该项目为博士生提供了培训研究机会。 准确预测故障的能力取决于缺陷的基本数学建模的质量，以及理解解决方案的基本特性。 直到最近，静态和准静态断裂的变异模型还限于Dirichlet边界条件，因为没有对包括Neumann边界条件（即边界负载）的看似最自然的配方的解决方案。该项目的目的是改善最近引入的静态配方，用于具有边界负荷的变异性骨折，可以具有解决方案，将这种静态模型扩展到准静态案例并显示解决方案的存在，并研究了能量降低的可能性，并可能在准静态模型中进行了静态奖励，这反映了NSF的合法传统和范围的范围，以此来评估其智力范围，并具有良好的构建。 标准。