金属动态断裂与破碎问题的扩展物质点法

Fracture and fragmentation of metals under extreme loading is an important problem focused in many fields, which involves extreme deformation and complex interactions of cracks, thus poses great challenges on numerical analysis. In this project, a novel extended material point method (XMPM) for fracture problem with extremely large deformation will be constructed based on the ideas of meshfree material point method (MPM) and extended finite element method (XFEM). The research of this project will include: 1. MPM formulation with enriched degrees of freedom (DOFs) will be constructed. Precise scheme for crack description under MPM framework will be developed based on the level set method. The XMPM framework will be set up. 2. The improved accurate computational scheme of the J-integral and the energy release rate will be investigated, and the computation of propagation criteria for dynamic fracture of metals will be studied. 3. The interaction treatment between crack surfaces after propagation and the self-contact algorithm will be investigated. The interaction of multiple cracks will be simulated with XMPM. 4. The implementation of XMPM and the application of XMPM in practical metal spalling and metal fragmentation will be investigated. The advantages of MPM in solving problems of extreme deformation will be fully inherited in XMPM, and the disadvantage of inaccurate description of cracks will be overcome. An advanced numerical method will be provided for the investigation of dynamic fracture of metals.

强冲击载荷下金属的断裂与破碎是多个领域关注的重要问题，涉及极端变形与复杂裂纹相互作用，对数值分析提出了很大的挑战。本项目拟结合近年来迅速发展的物质点无网格法和扩展有限元法的思想，建立适合于求解超大变形断裂问题的新型扩展物质点法。内容包括：1. 构建含有扩充自由度的物质点法求解格式，并结合水平集等方法发展物质点法框架下的裂纹精细描述方案，从而建立起扩展物质点法的理论框架；2. 研究物质点法框架下J积分、能量释放率的改进精准计算方案，探讨金属动态裂纹扩展准则的计算；3.研究扩展后裂纹面的处理与自接触算法，研究多裂纹相互作用下的扩展物质点法模拟； 4. 研究扩展物质点法的程序实现及其在实际金属层裂、破碎问题中的应用。扩展物质点法将充分发挥物质点法特别适于求解超大变形问题的优势，克服其裂纹描述较为粗糙的缺点，为金属动态断裂问题提供先进数值方法与计算手段。

强冲击载荷下金属的断裂与破碎是多个领域关注的重要问题,涉及极端变形与复杂裂纹相互作用,对数值分析提出了很大的挑战。本项目结合近年来迅速发展的物质点法和扩展有限元法的思想,建立了适合于求解超大变形断裂问题的新型扩展物质点法,大幅提升了物质点法的精度和稳定性。主要研究内容和重要成果包括: 1.构建了含有扩充自由度的物质点法新型求解格式,发展了物质点法框架下的裂纹精细描述方案,建立了针对复杂裂纹情况的J积分的准确计算方案,提出了能够显式精准描述裂纹及其动态扩展过程的扩展物质点法；2.提出了交错网格物质点法，从根本上解决了跨网格噪声基础问题，大幅提升了物质点法的精度和稳定性；3.对物质点法的临界时间步长计算、近不可压格式等核心理论做出了重要改进，拓展了物质点法的应用范围，提升了物质点法的精度、效率和稳定性；4.研究扩展物质点法等物质点法新型格式在自主研发的大型三维物质点法软件MPM3D中的实现，初步将新型方法应用于实际金属层裂、破碎问题。扩展物质点法充分发挥了物质点法特别适于求解超大变形问题的优势，克服其裂纹描述较为粗糙的缺点，为金属动态断裂与破碎问题提供了先进数值方法与计算手段。