Robust Polyhedral Finite Element Methods for Pervasive Fracture Simulations

本项目的研究目标是开发一种健壮的计算断裂工具来模拟材料和结构中普遍存在的三维断裂过程。在极端的载荷条件下，断裂的程度在材料和结构中是普遍存在的--大量的裂纹可以成核、聚合、分支，并向任意方向扩展。内聚四面体有限元(每个单元4个小平面)目前是这种复杂模拟的首选方法，但在这种断裂模拟中表现出网格依赖性。由于存在比四面体网格多得多的小平面，多面体网格为裂纹的形成和扩展提供了更多的路径。将审查与数值模拟中的弱收敛(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。计算断裂模拟工具的这些创新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进行最大规模和最复杂破坏模拟的方式，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裂缝建模方面产生重大影响：例如，金属材料、生物材料、地球物理、岩石力学、二氧化碳封存和流体驱动裂缝(水力压裂)的脆性和延展性裂缝都是相关的应用。教育计划的重点是在研究生课程中整合关于高级有限元方法和断裂的研究。与桑迪亚国家实验室的毕晓普博士的外部合作将使开发的新方法能够被纳入实验室的大型软件代码中，并为研究生提供丰富的暑期实习机会，让他们在计算失效力学的前沿领域开展工作。

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.