可控性的双层粒子刚体脆性破裂模拟动画

提出一种可控性的双层粒子模型的刚体脆性破裂动画的模拟框架。首先,使用接触力学分析撞击时固体内部产生的弹性位移并采用光滑粒子流体动力学进行离散求解,在此基础上建立一个可控性的内力分析模型。其次,提出一种双层粒子模型来对刚体进行建模,在保证内力计算精度的同时提高了刚体动力学中碰撞检测的效率。最后实现了多个刚体脆性模型场景的动画。该算法可适用于刚体脆性破裂模拟的动画应用。     

流-固交互及可变形体破裂的真实感模拟

为了模拟流体与动态环境的相互作用,提出一种流-固交互及可变形体破裂的真实感建模与绘制的算法.该算法使用光滑粒子流体动力学(SPH)与有限单元法(FEM)分别对流体与变形固体进行建模;再根据流-固交互作用的特点,给出一种快速分离液体表面粒子与固体表面网格的交互方法,并采用虚节点的流-固耦合模型模拟了液-固相互作用力.文中算法可用于多个流-固交互破裂的现象,如水管崩裂、水冲堤坝等.     

微可压缩SPH流体的稳定性固体边界处理算法

固流耦合,即流体的固体边界处理一直是基于物理的流体模拟技术的研究重点.为解决SPH流体模拟中固流耦合存在的交界面处流体粒子衰减和穿透问题,提出一种固体采样边界粒子与动量守恒保持的位置-速度修正方案相结合的固流耦合方法.首先在预处理阶段对快速格子形状匹配(fast lattice shape matching,FLSM)模型表示的固体边界进行表面和内部边界粒子采样;然后在运行过程中计算流体粒子密度和受力时考虑边界固体粒子的相对贡献;最后利用动量守恒保持的位置-速度修正方案对流体粒子进行位置和速度的修正.为了提高计算速度以满足交互式应用需求,把每个迭代步长内的计算完全并行化后加载到GPU上进行加速处理.实验结果表明,该算法实现了微可压缩SPH流体与刚体以及弹性体的双向耦合,并可以高效、稳定地模拟固流耦合中的非穿透、液滴飞溅、溶解等复杂现象.     

液固交互过程中固体破碎现象的实时模拟

提出一种适用于液固交互过程中的固体破碎模拟方法.针对传统液固交互边界处理算法复杂,难以实时模拟固体破碎的缺陷,本文基于SPH算法,提出对液体与固体使用统一的粒子表示,将预测校正方案应用于处理液固交互过程中固体之间的碰撞问题,从而将固体破碎过程简化为固体碎片边界粒子生成的过程,并使用形状匹配算法对固体碎片进行形状约束.实验结果证明,采用文中方法能够实时模拟出液固交互过程中,细节丰富的固体破碎现象,效果真实.     

基于GPU实现的大量刚体运动实时仿真

针对存在大量刚体运动的虚拟场景,提出一种基于在GPU上实现的实时仿真算法,利用GPU的并行计算能力,实时处理刚体交互,更新刚体状态.使用深度剥离技术,离散化刚体,并使其由一组具有相同大小的粒子表示.每一帧刚体间的运动交互则由粒子间的运动交互来实现.碰撞粒子对间的交互则用离散元法.通过统一网格方式,分割仿真域空间,以提高碰撞检测速率.实验证明,提出的新算法大幅度的提升了仿真大量刚体的速率.     

基于离散粒子群和禁忌搜索的网格资源调度算法

提出一种基于智能的网格资源分配和任务调度算法,由于网格资源调度是个离散问题,所以采用基于惯性权重的离散粒子群算法,针对离散粒子群算法在后期容易陷入局部最优的缺陷,将其与禁忌搜索算法相结合,在算法的前期采用离散粒子群算法进行搜索,在后期采用禁忌搜索算法进行局部搜索。并利用网格模拟工具Gridsim Toolkit开发一个网格模拟系统进行实验。实验结果表明,该算法具有较高的寻优能力。     

基于AHTPSO的连续属性离散化算法

针对粗糙集不能较好地处理连续型属性的问题,结合粗糙集理论和粒子群算法,提出基于自适应混合禁忌搜索粒子群的连续属性离散化算法。首先,该算法通过对参数的自适应更新操作,从而避免了粒子群出现早熟的现象;然后将粒子群当代得到的全局最优粒子送入禁忌算法中进行优化,有效地提升了算法的局部探索能力;在兼顾决策表系统一致性的同时,将划分的断点初始化为一群随机粒子,通过改进后粒子群的自我迭代得到最佳的离散化划分点。实验结果表明,与其他结合粗糙集的离散化算法相比,该算法具有更高的规则分类精度和较少的离散化断点个数,对连续属性的离散化效果较好。     

SPH固流交互中的实时固体破碎动画模拟

目的 针对固流交互中的固体破碎现象模拟研究较少、物理模型复杂、多求解器耦合性差、真实感与实时性难以兼顾等问题,提出一种适用于光滑粒子流体动力学（smoothed particle hydrodynamics,SPH）固流交互统一粒子框架的实时固体破碎模拟方法。方法 首先,结合断裂力学理论与统一粒子框架下固体边界粒子的空间和物理特性,构建基于物理的能量分析模型。然后,通过实时分析固体与流体之间的能量转化和自身能量平衡,将满足条件的粒子作为破碎发生的启发点。最后,采用基于几何的碎块生成方法,将启发点集作为种子点构建Voronoi图,完成碎块的生成。为确保模拟系统实时性,将模拟系统进行并行优化并加载至图形处理器（graphics processing unit,GPU）并行执行。结果 通过在不同复杂度和粒子规模的实验场景中进行模拟得到的结果表明,本文方法能够稳定地模拟固体受到流体冲击后发生的破碎现象,破碎细节真实感良好,在百万级粒子规模下能够满足实时性要求,可大规模并行执行且GPU加速效果显著,加速收益随场景规模增大而增大。结论 与现有研究相比,本文方法充分结合物理与几何方法的优点,与SPH统一粒子框架具有更高的耦合性,能够稳定地模拟固流交互中的固体破碎现象,细节符合现实世界物理规律,真实感渲染效果良好,可应用于洪涝、海啸、溃坝和泥石流等自然灾害的交互式预演、电子游戏特效等领域。     

基于粒子碰撞的粒子群算法求解带时间窗车辆调度问题*

带时间窗车辆调度问题属于离散NP-hard组合优化问题,传统的粒子群算法在离散域上表现了一定的劣性,对此提出了一种基于粒子碰撞的离散PSO算法来求解该问题。受物体相互碰撞之后物体的速度和位置会发生改变的现象启发,使当前粒子与个体最优和全局最优粒子发生碰撞来更新粒子的位置,以避免传统更新操作中的取整,保证种群的进化能力。采用Solomon’s VRP标准问题集的实例来对算法进行测试,实验结果数据表明了该算法的有效性。     

基于离散度与拉伸技术的粒子群优化算法

采用离散度作为衡量种群多样性的指标.在粒子群初始化阶段,种群的离散度必须满足一定的要求才能开始迭代;在算法迭代过程中,惯性权重、加速系数的调整都与当前粒子群的离散度相关;当种群的离散度小于一定数值时,进行保优重初始化,适应度函数拉伸操作,重新迭代.由于算法在初始化阶段依据离散度进行了限定,要求粒子尽量平均分布,算法运行...     

Meshless Animation of Fracturing Solids

We present a new meshless animation framework for elastic and plastic materials that fracture. Central to our method is a highly dynamic surface and volume sampling method that supports arbitrary crack initiation, propagation, and termination, while avoiding many of the stability problems of traditional mesh-based techniques. We explicitly model advancing crack fronts and associated fracture surfaces embedded in the simulation volume. When cutting through the material, crack fronts directly affect the coupling between simulation nodes, requiring a dynamic adaptation of the nodal shape functions. We show how local visibility tests and dynamic caching lead to an efficient implementation of these effects based on point collocation. Complex fracture patterns of interacting and branching cracks are handled using a small set of topological operations for splitting, merging, and terminating crack fronts. This allows continuous propagation of cracks with highly detailed fracture surfaces, independent of the spatial resolution of the simulation nodes, and provides effective mechanisms for controlling fracture paths. We demonstrate our method for a wide range of materials, from stiff elastic to highly plastic objects that exhibit brittle and/or ductile fracture.     

Reliability analysis of brittle structures under random loadings

A method for the reliability analysis of brittle structures subjected to random loads is proposed. The method is based on the weakest-link hypothesis and Weibull statistics for brittle materials. Initial flaws with a given expected size are assumed to be distributed at random with a certain density per unit volume. Basic concepts in random vibration theory and fracture mechanics are utilized in evaluating stress statistics, crack propagation and strength degradation. A structure fails when the stress intensity at any flaw reaches a critical value for rapid crack propagation. The failure of the structure is modeled as the first exceedance in random vibration theory. The effects of multi-vibration modes on the failure probability of the structure are included in the formulation. The evaluation of stress distribution and the computation of failure probability can be accomplished in a finite element analysis. Numerical examples on the evaluation of lifetime reliabilities of structures are given to demonstrate the feasibility of the proposed method.     

Fracture Patterns Design for Anisotropic Models with the Material Point Method

Physically plausible fracture animation is a challenging topic in computer graphics. Most of the existing approaches focus on the fracture of isotropic materials. We proposed a frame-field method for the design of anisotropic brittle fracture patterns. In this case, the material anisotropy is determined by two parts: anisotropic elastic deformation and anisotropic damage mechanics. For the elastic deformation, we reformulate the constitutive model of hyperelastic materials to achieve anisotropy by adding additional energy density functions in particular directions. For the damage evolution, we propose an improved phase-field fracture method to simulate the anisotropy by designing a deformation-aware second-order structural tensor. These two parts can present elastic anisotropy and fractured anisotropy independently, or they can be well coupled together to exhibit rich crack effects. To ensure the flexibility of simulation, we further introduce a frame-field concept to assist in setting local anisotropy, similar to the fiber orientation of textiles. For the discretization of the deformable object, we adopt a novel Material Point Method(MPM) according to its fracture-friendly nature. We also give some design criteria for anisotropic models through comparative analysis. Experiments show that our anisotropic method is able to be well integrated with the MPM scheme for simulating the dynamic fracture behavior of anisotropic materials.     

Application of an interface failure model to predict fatigue crack growth in an implanted metallic femoral stem

A novel computational modelling technique has been developed for the prediction of crack growth in load bearing orthopaedic alloys subjected to fatigue loading. Elastic-plastic fracture mechanics has been used to define a three-dimensional fracture model, which explicitly models the opening, sliding and tearing process. This model consists of 3D nonlinear spring elements implemented in conjunction with a brittle material failure function, which is defined by the fracture energy for each nonlinear spring element. Thus, the fracture energy criterion is implicit in the brittle material failure function to search for crack initiation and crack development automatically. A degradation function is employed to reduce interfacial fracture properties corresponding to the number of cycles; thus fatigue lifetime can be predicted. Unlike other failure modelling methods, this model predicts the failure load, crack path and residual stiffness directly without assuming any pre-flaw condition. As an example, fatigue of a cobalt based alloy (CoCrMo) femoral stem is simulated. Experimental fatigue data was obtained from four point bending tests. The finite element model simulated a fully embedded implant with a constant point load. Comparison between the model and mechanical test results showed good agreement in fatigue crack growth rate.     

Peridynamics‐Based Fracture Animation for Elastoplastic Solids

In this paper, we exploit the use of peridynamics theory for graphical animation of material deformation and fracture. We present a new meshless framework for elastoplastic constitutive modelling that contrasts with previous approaches in graphics. Our peridynamics‐based elastoplasticity model represents deformation behaviours of materials with high realism. We validate the model by varying the material properties and performing comparisons with finite element method (FEM) simulations. The integral‐based nature of peridynamics makes it trivial to model material discontinuities, which outweighs differential‐based methods in both accuracy and ease of implementation. We propose a simple strategy to model fracture in the setting of peridynamics discretization. We demonstrate that the fracture criterion combined with our elastoplasticity model could realistically produce ductile fracture as well as brittle fracture. Our work is the first application of peridynamics in graphics that could create a wide range of material phenomena including elasticity, plasticity, and fracture. The complete framework provides an attractive alternative to existing methods for producing modern visual effects.     

改进的流体模拟固体边界处理算法

流体模拟是计算机图形学的一个重要研究分支,流体的固体边界处理一直是流体 模拟的研究重点,光滑粒子流体动力学(SPH)方法中的镜像粒子法是处理固体边界的一个重要方 法。镜像粒子法通过靠近边界的流体粒子在边界外动态生成对应的镜像粒子来处理固体边界问 题,但随着边界复杂程度的提高,传统的镜像粒子法生成镜像粒子的复杂度也随之提高,模拟 效率随之降低。为此,文章对镜像粒子法进行改进,提出一种新的镜像粒子场量求值方法,有 效地降低了复杂边界情况下生成镜像粒子的复杂度,且使靠近边界的流体粒子场量更加均匀。 仿真实验结果表明,随着流体模拟粒子数的增加以及边界复杂程度的提高,该方法比传统镜像 粒子法效率高的优势也更加明显。     

固体入水的边界压力处理及表面粒子位置的修正

基于传统光滑粒子流体动力学(SPH)方法的边界力法、虚粒子法或耦合力法处理固体入水时,流 体与固体交互界面的粒子密度不连续、压力不稳定、固体边界处会发生部分流体粒子穿透或分离等现象,而流 体表面因为受到力的作用,表面破碎后,液面较粗糙。针对上述问题,结合边界力和虚粒子的优点,对耦合力 法进行改进,处理运动固体边界,阻止流体粒子穿透固体边界;改进交互界面的压力计算方法,提高计算精度, 稳定交互界面压力场;对流体表面的粒子位置进行校正,提升流体表面自由流动液面边界的模拟效果。通过经 典的二维固体入水实验,对该方法进行了验证,实验结果表明,本文方法在流体粒子与固体粒子交互后,交互 界面压力稳定,界面分离清晰无穿透,表面流体粒子分布均匀,流场的运动真实自然。     

Displacement-Correlated XFEM for Simulating Brittle Fracture

We present a remeshing-free brittle fracture simulation method under the assumption of quasi-static linear elastic fracture mechanics (LEFM). To achieve this, we devise two algorithms. First, we develop an approximate volumetric simulation, based on the extended Finite Element Method (XFEM), to initialize and propagate Lagrangian crack-fronts. We model the geometry of fracture explicitly as a surface mesh, which allows us to generate high-resolution crack surfaces that are decoupled from the resolution of the deformation mesh. Our second contribution is a mesh cutting algorithm, which produces fragments of the input mesh using the fracture surface. We do this by directly operating on the half-edge data structures of two surface meshes, which enables us to cut general surface meshes including those of concave polyhedra and meshes with abutting concave polygons. Since we avoid triangulation for cutting, the connectivity of the resulting fragments is identical to the (uncut) input mesh except at edges introduced by the cut. We evaluate our simulation and cutting algorithms and show that they outperform state-of-the-art approaches both qualitatively and quantitatively.     

T-stress,mixed-mode stress intensity factors,and crack initiation angles in functionally graded materials: a unified approach using the interaction integral method

For linear elastic functionally graded materials (FGMs), the fracture parameters describing the crack tip fields include not only stress intensity factors (SIFs) but also T-stress (nonsingular stress). These two fracture parameters are important for determining the crack initiation angle under mixed-mode loading conditions in brittle FGMs (e.g. ceramic/ceramic such as TiC/SiC). In this paper, the mixed-mode SIFs and T-stress are evaluated by means of the interaction integral, in the form of an equivalent domain integral, in combination with the finite element method. In order to predict the crack initiation angle in brittle FGMs, this paper makes use of a fracture criterion which incorporates the T-stress effect. This type of criterion involves the mixed-mode SIFs, the T-stress, and a physical length scale r_c (representative of the fracture process zone size). Various types of material gradations are considered such as continuum models (e.g. exponentially graded material) and micromechanics models (e.g. self-consistent model). Several examples are given to show the accuracy and efficiency of the interaction integral scheme for evaluating mixed-mode SIFs, T-stress, and crack initiation angle. The techniques developed provide a basic framework for quasi-static crack propagation in FGMs.