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大范围应用，了解材料的失效是至关重要的。预测失败的能力取决于建模和可用于建立和分析模型的数学，以及证明数值方法的合理性。在过去的二十年里，在这一领域有了重大的数学进步，特别是在断裂力学方面，但这些结果在很大程度上局限于没有外力的模型。然而，所施加的力的包含与应用程序相关。这个项目的目的是改进目前材料断裂在外力作用下的平衡数学公式，将该公式扩展到材料演化模型，并研究这些演化与外力存在相关的某些特征。该项目为博士生提供了培训和研究机会。准确预测故障的能力取决于缺陷的基本数学建模的质量，以及对解决方案的基本属性的理解。直到最近，静态和准静态断裂的变分模型一直局限于Dirichlet边界条件，因为似乎最自然的包含Neumann边界条件的公式，即边界载荷，不存在解。该项目的目的是改进最近引入的具有边界载荷的变分断裂的静态公式，该公式可以有解，将该静态模型扩展到准静态情况并证明解的存在，并研究准静态模型中存在能量降的可能性。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。