Robust Polyhedral Finite Element Methods for Pervasive Fracture Simulations

本计画的研究目标是发展一个强大的计算断裂工具，以模拟材料与结构中普遍存在的三维断裂过程。在极端载荷条件下，材料和结构中的断裂程度是普遍的-大量裂纹可以成核、合并、分支并在任意方向上扩展。内聚四面体有限元（每个单元4个刻面）目前是这种复杂模拟的首选方法，但在这种断裂模拟中显示出网格依赖性。由于存在比四面体网格中更多的刻面，多面体网格为裂纹形成和生长提供了更多的路径。将审查与数值模拟中的弱收敛性（碎片质量分布、裂纹路径）有关的问题，并将进行验证研究，以评估断裂模拟的收敛性。这些新的计算断裂模拟工具可以克服确定性四面体有限元网格的现有局限性，从而为计算断裂研究这一关键领域的突破铺平道路。该项目的成功成果将改变最大和最复杂的破坏模拟的方式，并为多面体有限元方法的许多新应用开辟道路。该项目的潜在影响将在基于物理的断裂建模中具有重要意义：例如，金属材料的脆性和韧性断裂、生物材料、岩石物理学、岩石力学、CO2封存和流体驱动断裂（水力压裂）都是相关的应用。该教育计划的重点是研究生课程中先进的有限元方法和断裂的整合。与桑迪亚国家实验室的Bishop博士的外部合作将使开发的新方法能够在实验室纳入大规模软件代码，并为研究生提供丰富的夏季实习机会，使他们能够在计算失效力学的前沿领域工作。

The research objective of this project is to develop a robust computational fracture tool to simulate pervasive three-dimensional fracture processes in materials and structures. Under extreme loading conditions, the extent of fracture is pervasive in materials and structures - multitude of cracks can nucleate, coalesce, branch, and propagate in arbitrary directions. Cohesive tetrahedral finite elements (4 facets per element) are presently the method-of-choice for such complex simulations, but show mesh-dependencies in such fracture simulations. Due to the presence of many more facets than in a tetrahedral mesh, a polyhedral mesh provides more pathways for crack formation and growth. Issues pertaining to weak convergence (fragment mass distribution, crack path) in the numerical simulations will be examined, and verification studies will be conducted to assess convergence of the fracture simulations. These novelties in a computational fracture simulation tool can overcome the existing limitations of deterministic tetrahedral finite element meshes and thus pave the way for a breakthrough in this key area of computational fracture research.A successful outcome in this project will change the way the largest and most complex failure simulations are done, and open the way for many new applications of polyhedral finite element methods. The potential impact of this project will be significant in physics-based fracture modeling: for example, brittle and ductile fracture of metallic materials, biomaterials, geophysics, rock mechanics, CO2 sequestration, and fluid-driven fractures (hydraulic fracturing) are pertinent applications. The educational plan focuses on the integration of the research within graduate curricula on advanced finite element methods and fracture. The external collaboration with Dr. Bishop at Sandia National Laboratories will enable the new methods developed to be incorporated in large-scale software codes at the laboratory, and also provide an enriched summer internship opportunity for graduate students to work on topical areas at the forefront in computational failure mechanics.