杨鹏飞. 局部化破坏问题的物质点法研究. 清华大学博士学位论文，2013年4月

局部化破坏问题是结构安全设计以及武器毁伤效应评价中的重要研究内容, 数值仿真在这类问题的研究有着重要应用。局部化破坏的特点是伴随非连续破坏 面的产生材料发生局部大变形,这给传统数值方法带来了挑战。物质点法作为一 种质点类无网格方法,采用欧拉网格和拉格朗日质点双重描述,能有效处理大变 形问题,同时对于破坏面的描述不存在网格线的限制。本文基于物质点法,发展 了适用于模拟局部化破坏问题的有效数值计算方法。

针对局部化破坏问题中变形局部化的特点,本文提出了基于悬点的多级背景 网格物质法。在局部变形较大的区域使用高级别密网格及质点进行计算,而在远 离局部大变形的区域使用低级别疏网格及质点进行计算。为了避免当粗质点运动 到细网格中导致的数值断裂问题,本文还提出了与背景网格级别相适应的质点分 裂方法。本文采用多级背景网格物质点法研究了弹性波传播,Taylor 杆碰撞以及 弹体斜侵彻等问题。

冲击侵彻是引起材料局部化破坏的常见动载荷形式。为了捕捉弹体的运动过 程,传统物质点法要求创建足够大的背景网格区域,极大地增加了不必要的计算 消耗。针对此问题本文提出了多重移动背景网格物质点法,采用移动网格技术动 态调整背景网格区域,允许在同一求解体系下同时存在多套背景网格,并可以在 特定的情况下对物体的背景计算网格进行切换。本文应用多重移动背景网格物质 点法研究了弹丸冲击薄板以及弹体对多层靶板的侵彻问题。

金属延性断裂的数值模拟一直是计算力学领域的难点之一。本文发展了三维 脱聚模型描述材料失效界面的力学行为,将断裂行为的描述引入到本构方程中。 本文结合多级背景网格物质点法成功预测了含孔金属试件的裂纹扩展,同时还应 用脱聚模型研究了含初试缺陷试件的局部剪切带形成过程。

爆炸载荷下金属壳体首先在局部发生剪切拉伸混合失效,失效面扩展交汇后 形成金属破片。本文基于 Gurson 模型和 Weibull 随机失效分别从宏观和微观角度 研究了破片的产生过程。当使用 Gurson 模型时考虑材料的初始微观孔洞随机分 布,并使用 Tepla-F 失效模型。当不考虑微观孔洞时,Gurson 流动退化为 J2 流动, 使用基于宏观材料应变的 Weibull 随机失效方案。本文同时提出了基于背景网格 的碎片统计方法,结果显示金属壳体在高应变率效应下呈现脆性断裂的性质。

关键词:无网格法;物质点法;局部化;破坏;数值模拟

The localized material failure is very important in the study of structural safety and military weapon performance. Numerical simulation is widely used in these areas. Dis- continuity and large deformation are usually encountered in the localized failure prob- lems, which results in a great challenge for numerical simulation. As a meshfree particle method, material point method (MPM) discretizes the domain with a set of Lagrangian particles and solves the momentum equation by Eulerian background grid. As a result, MPM is capable to solve large deformation problems and discontinuity is not constrained by grid lines. In this study, the effective numerical method for localized failure problems is developed based on MPM.

As the deformation is usually localized in the localized failure problems, the multi- level background grid MPM is proposed. In this method, the fine grid cells and particles are used in the area of local large deformation while the course grid cells and particles are used in the other area. To avoid the numerical fracture problem which may be encoun- tered when course particles move into fine grid cells, a new particle splitting method is proposed. The multi-level background grid MPM is used to study the problems including the elastic wave propagation, Taylor bar impact and oblique penetration.

Impact and penetration are the common dynamic loads for localized failure prob- lems. To capture the orbit of the projectile, a sufficiently large background grid is usually established in traditional MPM, which significantly increases the computational cost. To solve this problem, the multi-moving background grid MPM is proposed. In this method, an improved moving grid method is used to dynamically adjust the solution area. Mean- while, multiple background grids are allowed in the framework of MPM. The multiple grids are solved independently and computational grid changing is allowed at certain con- dition. The multi-moving background grid MPM is used to study problems such as steel ball impacting a thin plate and multilayer penetration.

Ductile fracture is always one of the difficulties in computational mechanics. In this study a 3D decohesion model is developed to describe the mechanical behavior of the fail- ure interface. The fracture mechanism is considered to be a part of the constitutive model in this model. Based on the decohesion model, the crack growth of the metallic specimen

with asymmetric imperfection is successfully predicted by multi-level background grid MPM. The decohesion model is also applied to study localized shear band growth of the metallic plates with different imperfections.

The mixed tensile-shear failure usually first grow up in the local areas of the metallic shells driven by detonation. As the failure interfaces develop and mixed, the shell is frag- mented into pieces. In this study, the fragmentation is modeled based on Gurson model and Weibull random failure, from the microscopic and macroscopic aspects respectively. When considering microscopic damage of material, the plastic behavior is described by Gurson model with randomly-distributed initial void of material points. Gurson model degenerates to J2 plastic theory while the microscopic void is ignored, in which situation the Weibull random failure scheme will be used based on macroscopic strain. Meanwhile, a background-grid-based searching method is proposed to capture the statistical feature of the fragmentation. The result reveals that metallic shells tend to fracture in a brittle manner under high strain rate.

Key words: meshfree methods; material point method; localization; failure; numerical simulation