Probabilistic Simulation of Fracture by Meshless Methods

裂纹扩展是结构和力学系统中重要的破坏机制，需要精确的数值模型来实现必要的模拟，支持破坏预测。载荷、材料特性和裂纹尺寸等方面存在系统不确定性和风险，需要考虑基于可靠性的断裂力学分析。本提案的目的是开发一种新的随机无网格方法，用于预测二维和三维结构中含有裂纹缺陷的断裂响应特征和可靠性。这项工作将基于：(1)成熟的断裂力学理论，包括线弹性模型和弹塑性模型；(2)确定裂纹尖端应力和应变场的无网格和无网格/有限元综合方法以及连续体设计敏感性分析；(3)随机变量和随机场对载荷、材料性能和裂纹尺寸的不确定性的概率模型；(4)裂纹结构断裂响应和可靠度概率表征的随机无网格和仿真方法。对于无网格/有限元集成方法，无网格方法将用于接近裂纹区域的材料行为建模，而有限元方法将用于远离裂纹区域的材料行为建模。这种耦合具有极大地简化裂纹扩展分析的潜力，同时大大提高了精度水平。该研究为无网格方法和随机场理论的裂缝过程计算建模提供了一种创新和及时的方法。所提出的无网格方法在概率断裂力学领域具有很大的应用潜力。特别是，这些方法可以用于断裂控制和延长寿命，并且与设计和制造新飞机相关的巨额资本支出相比，老化结构仍然更低，延长寿命的理念将继续下去。然而，为了确定老化飞机的维护要求，以确保其持续的结构完整性和安全性，需要先进的寿命和剩余强度预测工具，例如本研究中提出的工具。这并不是航空航天业所独有的。同样的情况也存在于其他行业，比如化石燃料和核能行业，这些行业也在试图使用远远超过预期设计寿命的老旧电厂。因此，本研究提出的随机无网格方法可以帮助解决飞机、民用、核能、航空航天、汽车等行业共享的许多现实世界中与断裂相关的问题。迄今为止，涉及无网格方法的可靠性问题尚未得到解决。该项目下的随机无网格和无网格/有限元综合方法的发展将极大地推动断裂力学领域的最新技术，并解决概率结构力学中遇到的广泛的实际工程问题。

Crack propagation is an important failure mechanism in structural and mechanical systems requiring accurate numerical models to implement essential simulation supporting failure prediction. The existence of system uncertainty and risk in loads, material properties, and crack size requires a reliability-based fracture-mechanics analysis to be taken into account. The objective of this proposal is to develop a new stochastic meshless methodoloy for predicting fracture response characteristics and reliability if two-and three-dimensional structures containing crack-like defects. This effort will be based on: (1) well-established theories of fracture mechanics involving both linear-elastic and elastic-plastic models, (2) meshless and integrated meshless/finite element methods for determining crack-tip stress and strain fields and continuum design sensitivity analysis, (3) probabilistic models of uncertainties in loads, material properties, and crack size by random variables and random fields, and (4) stochastic meshless and simulation methods for probabilistic characterization of fracture response and reliability of cracked structures. For the integrated meshless/finite element method, the meshless method will be used to model material behavior in areas close to cracks and the finite element method in areas further away from cracks. Such a coupling has the potential to greatly simplify crack-growth analysis while simultaneously achieving a substantially improved level of accuracy. The proposed research represents an innovative and timely approach to computational modeling of fracture process by meshless methods and random field theory. The proposed meshless methods demonstrate significant potential for application in the field of probabilistic fracture mechanics. In particular, these methods can be used for fracture control and life extension of and aging structure remains lower than the huge capital expenditures associated with designing and building a new aircraft, the life extension philosophy will continue. However, in order to define maintenance requirements of an aging aircraft to ensure it's continued structural integrity and safety, advanced predictive tools for life and residual strength, such as the ones proposed in this study, are necessary. This is not unique to the aerospace industry. Identical conditions prevail in others, such as in fossil and nuclear power industries, which are also attempting to use aging power plants far beyond their intended design lives. As such, the stochastic meshless methods proposed in this study can help solve many real-world fracture-related problems shared by aircraft, civil, nuclear, aerospace, automotive, and other industries. To date, reliability problems involving meshless methods have yet to be solved. The development of stochastic meshless and integrated meshless/finite element methods under this prorgram will significantly advance the state-of-the-art in the field of fracture mechanics as well as address a wide range of practical engineering issues encountered in probabilistic structural mechanics.