极端变形问题的物质点法研究进展

物质点法采用了拉格朗日和欧拉双重描述,将物体离散为一组在固定于空间的网格(欧拉描述)中运动的质点(拉格朗日描述),有效地综合了拉格朗日法和欧拉法的优点,是分析冲击爆炸等极端变形问题的一种有效方法. 本文系统总结了本课题组近年来针对冲击、爆炸和流固耦合等极端变形问题在物质点法算法方面的研究进展,并简要介绍了开发的三维显式并行物质点法数值仿真软件MPM3D及其在超高速碰撞、侵彻、爆炸、边坡失效、金属切削和流固耦合等问题中的应用.     

非均质材料热传导问题的扩展有限元法

针对非均质材料,提出了以导热系数为基本参数的热传导扩展有限元法。划分网格时不需要考虑材料界面的存在,因此网格的形成可以大大地简化,且可以获得高质量的网格。不含材料界面的单元,其温度场函数将退化为常规有限元的函数。含材料界面的单元,采用基于水平集的加强函数加强常规温度的近似,加强函数用于模拟界面。数值算例结果体现了该方法...     

A multiscale material point method for impact simulation

To better simulate multi-phase interactions involving failure evolution, the material point method (MPM) has evolved for almost twenty years. Recently, a particle-based multiscale simulation procedure is being developed, within the framework of the MPM, to describe the detonation process of energetic nano-composites from molecular to continuum level so that a multiscale equation of state could be formulated. In this letter, a multiscale MPM is proposed via both hierarchical and concurrent schemes to simulate the impact response between two microrods with different nanostructures. Preliminary results are presented to illustrate that a transition region is not required between different spatial scales with the proposed approach.     

无网格MPM法三维前处理系统设计

无网格法在解决爆炸冲击、裂纹扩展、高速碰撞以及大变形等问题时,由于与网格无关,能够避免有限元法因网格畸变计算精度降低或计算终止的矛盾,是目前求解固体力学问题的有效方法之一,也是近年来研究的热点。前处理对于无网格法数值计算是非常重要的环节,基于面向对象程序设计思想,应用C 和OpenGL开发了三维图形交互方式的MPM法前处理系统,提出了应用递归四叉树法、扫描表示法和CSG法划分任意形状非等间距的MPM法质点单元,为建立通用的无网格前处理平台提出了有效的解决方案。     

超高速碰撞问题的三维物质点法

简要介绍了物质点法（material point method）的离散原理,通过引入Johnson-Cook材料模型和Mie-Gruneisen状态方程,将其用于超高速碰撞问题的分析中,并编制了相应三维物质点法程序MPM3D。该方法避免了拉格朗日格式因网格畸变产生的数值困难,也克服了欧拉格式材料界面跟踪问题以及因非线性对流扩散项而引起的数值困难。利用该程序对Taylor杆高速碰撞问题和空间碎片防护超高速碰撞问题进行了数值模拟,所得数值结果与实验结果基本吻合,验证了程序的正确性,说明了物质点法在分析超高速碰撞问题时相对于有限元法的优势。     

Coupling the finite element method and molecular dynamics in the framework of the heterogeneous multiscale method for quasi-static isothermal problems

Multiscale models are designed to handle problems with different length scales and time scales in a suitable and efficient manner. Such problems include inelastic deformation or failure of materials. In particular, hierarchical multiscale methods are computationally powerful as no direct coupling between the scales is given. This paper proposes a hierarchical two-scale setting appropriate for isothermal quasi-static problems: a macroscale treated by continuum mechanics and the finite element method and a microscale modelled by a canonical ensemble of statistical mechanics solved with molecular dynamics. This model will be implemented into the framework of the heterogeneous multiscale method. The focus is laid on an efficient coupling of the macro- and micro-solvers. An iterative solution algorithm presents the macroscopic solver, which invokes for each iteration an atomistic computation. As the microscopic computation is considered to be very time consuming, two optimisation strategies are proposed. Firstly, the macroscopic solver is chosen to reduce the number of required iterations to a minimum. Secondly, the number of time steps used for the time average on the microscale will be increased with each iteration. As a result, the molecular dynamics cell will be allowed to reach its state of thermodynamic equilibrium only in the last macroscopic iteration step. In the preceding iteration steps, the molecular dynamics cell will reach a state close to equilibrium by using considerably fewer microscopic time steps. This adapted number of microsteps will result in an accelerated algorithm (aFE-MD-HMM) obtaining the same accuracy of results at significantly reduced computational cost. Numerical examples demonstrate the performance of the proposed scheme.     

物质点法的理论和应用

物质点法采用质点离散材料区域, 用背景网格计算空间导数和求解动量方程,避免了网格畸变和对流项处理, 兼具拉格朗日和欧拉算法的优势, 非常适合模拟涉及材料特大变形和断裂破碎的问题. 本文详细论述了物质点法在基本理论、算法和软件开发方面的进展, 包括广义插值物质点法、接触算法、自适应算法、并行算法、与其他算法的杂交和耦合等. 系统地总结了物质点法在超高速碰撞、冲击侵彻、爆炸、动态断裂、流固耦合、多尺度分析、颗粒材料流动和岩土失效等一系列涉及材料特大变形问题中的应用,展示了其相对于传统数值计算方法的优势.     

流固耦合不可压物质点法及其在晃动问题中的应用

作为一种混合拉格朗日欧拉法,物质点法在流固耦合问题中具有重要的应用前景。对于自由液面的流动问题,基于物质点法框架已建立了弱可压物质点法和完全不可压物质点法,但在处理流固耦合问题时遇到了困难。弱可压物质点法由于采用可压缩状态方程,导致求解时间步长过小,压力振荡严重,产生了非物理的飞溅现象;完全不可压物质点法基于投影算法和不可压条件,消除了弱可压物质点法的压力振荡,提高了时间步长,但难以处理移动边界问题。基于变分形式的投影算法提出了一种新型流固耦合不可压物质点法,得到了体积加权的压力泊松方程PPE(Pressure Poisson Equation),解决了完全不可压物质点法无法处理不规则边界和移动边界的问题。采用流固耦合不可压物质点法研究了运动刚体容器中的液体晃动问题,并与已有实验和数值结果进行对比,验证了算法的正确性和精度。     

Coupling finite difference method with finite particle method for modeling viscous incompressible flows

A hybrid approach to couple finite difference method (FDM) with finite particle method (FPM) (ie, FDM-FPM) is developed to simulate viscous incompressible flows. FDM is a grid-based method that is convenient for implementing multiple or adaptive resolutions and is computationally efficient. FPM is an improved smoothed particle hydrodynamics (SPH), which is widely used in modeling fluid flows with free surfaces and complex boundaries. The proposed FDM-FPM leverages their advantages and is appealing in modeling viscous incompressible flows to balance accuracy and efficiency. In order to exchange the interface information between FDM and FPM for achieving consistency, stability, and convergence, a transition region is created in the particle region to maintain the stability of the interface between two methods. The mass flux algorithm is defined to control the particle creation and deletion. The mass is updated by N-S equations instead of the interpolation. In order to allow information exchange, an overlapping zone is defined near the interface. The information of overlapping zone is obtained by an FPM-type interpolation. Taylor-Green vortices and lid-driven shear cavity flows are simulated to test the accuracy and the conservation of the FDM-FPM hybrid approach. The standing waves and flows around NACA airfoils are further simulated to test the ability to deal with free surfaces and complex boundaries. The results show that FDM-FPM retains not only the high efficiency of FDM with multiple resolutions but also the ability of FPM in modeling free surfaces and complex boundaries.     

颗粒材料柱体崩塌物质点法数值模拟

为了研究颗粒材料崩塌的运动规律和堆积特性,采用物质点法对颗粒材料柱体崩塌试验进行数值模拟,并将模拟结果与试验结果进行对比验证。对颗粒材料柱体崩塌过程中颗粒的流动特性(滑动距离、堆积高度、速度、能量和动能通量的演化)进行了分析。进一步探究了颗粒材料柱体高宽比对颗粒流动能通量的影响,从而反应颗粒材料柱体崩塌过程中颗粒流的破坏能力。颗粒材料柱体高宽比越大,颗粒材料柱体外侧边缘颗粒速度越大,其溃散的程度更加强烈,并且滑动距离和动能均在增大。对于动能通量的分布,水平方向越靠近初始颗粒材料柱体,动能通量越大。     

Solving material nonlinear structural problems by a finite analytic method in local coordinates

The purpose of this paper is to develop a finite analytic (FA) numerical solution for the elasto-plastic problem of the total theory. Schemes for the FA method in local coordinates for solving non-linear governing equations in the form of Navier equations are derived, which can be utilized to solve the problem in a domain of arbitrary geometry. Numerical illustration shows that the schemes are effective and practical.     

功能梯度材料板件三维分析的半解析梯度有限元法

将半解析有限元与梯度有限元相结合,形成一种半解析梯度有限元来求解功能梯度材料板件问题。该方法兼有有限元法的适应性强、程序统一,半解析有限元法的节省单元与计算工作量,梯度有限元法的适应构件内部材料性能任意梯度分布等特点,并实现用一维数值计算给出构件三维分析结果。算例分析表明了方法的精度、功能与上述特点,充分揭示了功能梯度材料板件力学响应的三维形态。半解析梯度有限元法可推广应用到其他功能梯度材料面结构的各类分析中。     

球对称形式物质点法及其在水下爆炸中的应用

利用物质点法求解三维远场水下爆炸冲击响应问题时,爆炸冲击波到达结构物之前传播过程的计算会消耗大量的计算资源,影响求解效率。针对这一问题,并考虑到水下爆炸冲击波在自由场中的传播特点,提出了一维球对称形式的物质点法,对球形炸药水下爆炸过程进行了数值模拟,并与Cole公式以及DYNA计算结果进行了比较,结果吻合较好,验证了一维球对称形式物质点法的正确性。在此基础上,提出了基于物质点法的重映射算法,将爆炸冲击波在自由场中的传播过程在一维球对称模型中进行计算,并将计算结果映射到三维模型中,以便继续完成计算过程,有效避免了计算资源在冲击波传播过程计算上的消耗。     

A hybrid immersed boundary and material point method for simulating 3D fluid–structure interaction problems

A numerical method is developed for solving the 3D, unsteady, incompressible Navier–Stokes equations in curvilinear coordinates containing immersed boundaries (IBs) of arbitrary geometrical complexity moving and deforming under forces acting on the body. Since simulations of flow in complex geometries with deformable surfaces require special treatment, the present approach combines a hybrid immersed boundary method (HIBM) for handling complex moving boundaries and a material point method (MPM) for resolving structural stresses and movement. This combined HIBM & MPM approach is presented as an effective approach for solving fluid–structure interaction (FSI) problems. In the HIBM, a curvilinear grid is defined and the variable values at grid points adjacent to a boundary are forced or interpolated to satisfy the boundary conditions. The MPM is used for solving the equations of solid structure and communicates with the fluid through appropriate interface‐boundary conditions. The governing flow equations are discretized on a non‐staggered grid layout using second‐order accurate finite‐difference formulas. The discrete equations are integrated in time via a second‐order accurate dual time stepping, artificial compressibility scheme. Unstructured, triangular meshes are employed to discretize the complex surface of the IBs. The nodes of the surface mesh constitute a set of Lagrangian control points used for tracking the motion of the flexible body. The equations of the solid body are integrated in time via the MPM. At every instant in time, the influence of the body on the flow is accounted for by applying boundary conditions at stationary curvilinear grid nodes located in the exterior but in the immediate vicinity of the body by reconstructing the solution along the local normal to the body surface. The influence of the fluid on the body is defined through pressure and shear stresses acting on the surface of the body. The HIBM & MPM approach is validated for FSI problems by solving for a falling rigid and flexible sphere in a fluid‐filled channel. The behavior of a capsule in a shear flow was also examined. Agreement with the published results is excellent. Copyright © 2007 John Wiley & Sons, Ltd.     

土体颗粒物流动物质点法模拟的弹塑性和非牛顿流体本构模型比较研究

土体颗粒物流动是一种典型的大变形破坏,具有非牛顿流体的流动特征。准确模拟土体颗粒物的流动及冲击过程,对滑坡和泥石流等地质灾害的防治具有重要意义。物质点法是一种无网格粒子类方法,已在各类大变形问题中得到了广泛应用。以往土体颗粒物流动的模拟,通常采用弹塑性本构模型,但缺乏对非牛顿本构模型的模拟分析。本文引入非牛顿本构模型的模拟分析,旨在为土体颗粒物流动模拟提供一种新的方法与思路。非牛顿本构模型的模拟分析是将非牛顿广义Cross模型引入三维物质点法,通过人工阻尼力模拟颗粒间的摩擦力,对土体颗粒物的坍塌、沿斜面滑动以及冲击障碍物等问题进行了动态模拟,研究了其运动全过程,并与弹塑性本构模型的模拟结果进行了对比验证。结果表明,基于非牛顿流体本构模型的物质点法可以较好地模拟土体颗粒物加速、减速到再次稳定的流动全过程及其对障碍物的冲击效应。     

非均质固体炸药冲击起爆的物质点法

将点火增长方程引入到物质点法中,编制了相应的计算程序MPM-SDT,并求解了冲击起爆问题.通过与传统算法和实验结果的比较,验证了物质点法应用于冲击起爆问题的可行性.物质点法避免了Lagrange法的网格畸变缠结和Euler法的对流误差.最后,对钨、铜、钢等材料破片撞击屏蔽炸药问题进行了多组数值模拟.3种材料对屏蔽炸药的...     

板壳畸变单元的无网格和有限元自动耦合方法

板壳大变形时单元的严重畸变会使计算精度降低。无网格局部Petrov-Galerkin法是一种真正的无网格方法,能够消除网格畸变,但比有限元法计算效率低。根据板壳网格畸变的局部性特点,利用过渡单元法,基于板壳网格质量,建立了板壳的网格严重畸变区域由有限元分析切换为无网格分析的自动耦合算法,实现了有限元法和无网格局部彼得罗夫．迦辽金法的耦合。应用实例表明：通过自适应耦合,既能发挥有限元法计算效率高的特点,又能发挥无网格法适合大变形分析、没有网格畸变造成计算困难的特点。     

多相介质爆炸冲击响应物质点法数值模拟

为了解决当炸弹在近场爆炸时爆轰波驱动破碎的弹片共同作用于混凝土墙壁的过程中所涉及的多物理场计算和多相介质耦合分析等问题,利用物质点法(material point method, MPM)不需要考虑物质间的分界面、耦合条件自动满足等特点,应用无网格MPM法对两种类型的炸弹（带金属外壳和不带金属壳）产生的爆炸场、弹片破碎和混凝土墙壁的破坏进行数值模拟。数值结果表明,无网格MPM法是计算多相介质爆炸效应的一种有效的算法。     

基于物质点法的轨道炮刨削机理三维数值研究

基于轨道炮结构特点以及冲击热力学理论,采用物质点法建立了轨道微颗粒诱发刨削的三维模型,模拟了轨道刨削的形成过程,并对其产生机理与影响因素进行了分析。结果表明:电枢与轨道的局域高速冲击产生瞬时的能量交换,形成的高热高压金属流对轨道表面的斜侵彻作用形成了刨坑;刨削的产生存在速度阈值,超过速度阈值,随着电枢速度增加,刨削越严重;低于速度阈值,可产生轨道擦伤;减小轨道表面微颗粒尺寸、增加电枢头部倾角均可降低刨削损伤。     

Finite cell method compared to h-version finite element method for elasto-plastic problems

The finite cell method （FCM） combines the high-order finite element method （FEM） with the fictitious domain approach for the purpose of simple meshing. In the present study, the FCM is used to the Prandtl-Reuss flow theory of plasticity, and the results are compared with the h-version finite element method （h-FEM）. The numerical results show that the FCM is more efficient compared to the h-FEM for elasto-plastic problems, although the mesh does not conform to the boundary. It is also demonstrated that the FCM performs well for elasto-plastic loading and unloading.