LEAPS-MPS: Time-Discrete Regularized Variational Model for Brittle Fracture in Novel Strain-Limiting Elastic Solids

LEAPS-MPS：新型应变限制弹性固体中脆性断裂的时间离散正则化变分模型

• 批准号: 2316905
• 负责人: Mallikarjunaiah Muddamallappa
• 金额: $ 22.48万
• 依托单位: Texas A&M University Corpus Christi
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-09-01 至 2025-08-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2316905&HistoricalAwards=false
• 关键词: LEAPS; MPS; Time; Discrete; Regularized

The study of evolving fractures in brittle elastic solids has been and still is a challenging topic for applied mathematicians, physicists, and engineers, and its interest to the archival literature continues to increase rapidly. The instantaneous impact and growth of brittle fractures are inherently dangerous to a variety of mechanical systems such as large structures, ships, pressurized airplane cabins, and orthopedic implants in the human body. Therefore, a fundamental understanding of the failure of materials due to fracture is essential for applications. A central theme of this project is the development of models using novel implicit constitutive relations applicable to brittle fracture in elastic solids. Developing convergent numerical schemes for the new fracture theory and simulation of evolving fractures is another crucial objective of this research. The project will provide research training opportunities in mathematics and scientific computing for postdoctoral associates and graduate students.In the last few decades, substantial progress has been made in formulating mathematically well-posed models for quasi-static and dynamic propagation of fractures in ideally elastic solids. However, many of these approaches use a linear constitutive relation which admits a well-documented logically inconsistent singularity. An alternative approach is to use constitutive relations which limit the strain values uniformly in the entire material body. The overarching objective of this project is to use the latter to study the behavior of elastic materials and to predict experimentally observed phenomena. The investigator will develop a fully discrete finite element method for quasi-static as well as elastodynamical fracture evolution. Both will be formulated as a constrained energy minimization of a regularized variational model consisting of two terms, one representing the nonlinear elastic bulk energy defined by virtue of strain-limiting constitutive relationship, the other the surface energy of a fracture. Another objective of this project is to develop parallel finite element solvers for the regularized phase-field fracture model and to analyze the numerical solutions. The computational framework will be tested on classical benchmark cases in solid mechanics and convergence analysis will be performed using a manufactured solution. The mathematical models and the finite element techniques emerging from this research will have broader applicability in computational mechanics, for example they will be of practical interest in the study of fractures in high-strength materials such as gum metals and titanium alloys.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.

对于应用数学家，物理学家和工程师而言，对脆性弹性固体中不断发展的裂缝的研究一直是一个具有挑战性的话题，其档案文献的兴趣继续迅速增加。脆性断裂的瞬时影响和生长对各种机械系统（例如大型结构，船只，加压飞机舱和人体中的骨科植入物）固有危险。 因此，对裂缝导致材料失败的基本了解对于应用至关重要。 该项目的一个核心主题是使用适用于弹性固体中脆性断裂的新型隐式构型关系开发模型。为新的断裂理论开发收敛的数值方案和不断发展的裂缝的模拟是这项研究的另一个关键目标。该项目将为博士后伙伴和研究生提供数学和科学计算的研究培训机会。在过去的几十年中，在制定了数学上良好的模型，用于用于准静态且动态繁殖的理想弹性固体中的裂缝。但是，其中许多方法都使用线性构型关系，该关系在逻辑上有据可查的奇异性不一致。另一种方法是使用构成关系，该关系在整个物质体中均匀地限制应变值。该项目的总体目的是利用后者研究弹性材料的行为并预测实验性观察到的现象。研究者将开发出完全分散的有限元方法，用于准静态和弹性动力裂缝的演变。两者都将作为由两个术语组成的正则变异模型的约束能量最小化，一个代表一个非线性弹性体积能量，该模型是由菌株限制的本构关系定义的，另一个是断裂的表面能。该项目的另一个目的是为正则化相位场断裂模型开发平行的有限元求解器，并分析数值溶液。计算框架将在固体力学中的经典基准案例上进行测试，并将使用制成的解决方案进行收敛分析。 The mathematical models and the finite element techniques emerging from this research will have broader applicability in computational mechanics, for example they will be of practical interest in the study of fractures in high-strength materials such as gum metals and titanium alloys.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.