大规模颗粒系统的精确缩尺和粗粒化离散元方法

计算效率是制约工程尺度大规模颗粒系统离散元计算发展的重要因素,现有的粗粒化处理方法局限于特定应用并且缺少一般的理论依据。本文采用量纲分析方法,描述了在精确缩尺系统中各物理量应当满足的缩放定律;通过在粗粒化系统和原始系统的代表性体积单元之间建立质量、动量和能量的近似守恒关系,采用多尺度的描述方法得到了粗粒化系统与原始系统之间宏观和细观两种不同尺度的缩放关系,即双尺度粗粒化模型;精确缩尺系统中得到的缩放定律及离散元接触模型处理方法,完全适用于粗粒化系统中细观颗粒层面相关物理量的缩放,通过筒仓侧壁压力和休止角两个算例对精确缩尺模型在粗粒化系统中的有效性进行了验证。     

针对有砟道床动力特性分析的嵌入式离散元-有限元耦合方法

在离散元-有限元耦合方法中,离散元和有限元交界面处的耦合方式对整体有砟道床的力学行为影响显著.采用基于球形单元的镶嵌单元或粘结单元模拟有砟道床时,由于球形单元和有限单元表面的自锁能力较差,使道砟层在列车载荷作用下容易产生侧向滑移,导致数值模型不稳定.此外,在实际铁路道床中,底部道砟均不同程度地嵌入路堤.为此,发展了一种嵌入式离散元-有限元耦合方法,通过设置一层嵌入地基有限元模型中的球形颗粒传递离散元域和有限元域间的力学参数,实现离散元和有限元方法的耦合.数值结果表明,嵌入式离散元-有限元耦合模型能够有效降低有砟道床的侧向位移,数值结果更加稳定,在处理与有砟道床类似的连续介质与散体介质的耦合问题时推荐采用嵌入式耦合算法.     

离散颗粒集合体-Cosserat连续体模型的连接尺度方法

基于针对分子动力学-Cauchy连续体模型提出的连接尺度方法(BSM)[1,2],发展了耦合细尺度上基于离散颗粒集合体模型的离散单元法(DEM)和粗尺度上基于Cosserat连续体模型的有限元法(FEM)的BSM。仅在有限局部区域内采用DEM以从细观层次模拟非连续破坏现象,而在全域则采用花费计算时间和存储空间较少的FEM。通过连接尺度位移(包括平移和转动)分解,和基于作用于Cosserat连续体有限元节点和颗粒集合体颗粒形心的离散系统虚功原理,得到了具有解耦特征的粗细尺度耦合系统运动方程。讨论和提出了在准静态载荷条件下粗细尺度域的界面条件,以及动态载荷条件下可以有效消除粗细尺度域界面上虚假反射波的非反射界面条件(NRBC)。本文二维数值算例结果说明了所提出的颗粒材料BSM的可应用性和优越性,及所实施界面条件对模拟颗粒材料动力学响应的有效性。     

A Bridging Scale Method for Multi-scale Analysis of Granular Materials

本文提出了耦合细尺度上基于离散颗粒集合体模型的离散单元法（DEM）和粗尺度上基于Cosserat连续体模型的有限元法（FEM）的连接尺度方法（BSM）以研究颗粒材料的力学行为。采用Cosserat连续体模型和FEM模拟的粗尺度域覆盖全域,而采用离散颗粒集合体模型的DEM模拟的细尺度域仅限于需特别关注材料微结构演变和非连续变形行为的局部区域。对这两个区域间的界面提出了适当的界面条件及其实施方案。通过采用适当的连接尺度投影算子,空间离散的粗、细尺度耦合系统多尺度运动方程具有解耦和允许分别求解、因而也允许分别采用不同时间步长对粗、细尺度计算的特点,可极大地提高BSM的计算效率。文中二维地基数值算例结果说明了所陈述方法的可应用性,以及相对基于Cosserat连续体模型的FEM和基于离散颗粒集合体模型的DEM的优越性。     

颗粒材料多尺度分析的连接尺度方法

本文提出了耦合细尺度上基于离散颗粒集合体模型的离散单元法（DEM）和粗尺度上基于Cosserat连续体模型的有限元法（FEM）的连接尺度方法（BSM）以研究颗粒材料的力学行为。采用Cosserat连续体模型和FEM模拟的粗尺度域覆盖全域,而采用离散颗粒集合体模型的DEM模拟的细尺度域仅限于需特别关注材料微结构演变和非连续变形行为的局部区域。对这两个区域间的界面提出了适当的界面条件及其实施方案。通过采用适当的连接尺度投影算子,空间离散的粗、细尺度耦合系统多尺度运动方程具有解耦和允许分别求解、因而也允许分别采用不同时间步长对粗、细尺度计算的特点,可极大地提高BSM的计算效率。文中二维地基数值算例结果说明了所陈述方法的可应用性,以及相对基于Cosserat连续体模型的FEM和基于离散颗粒集合体模型的DEM的优越性。      

气固两相流介尺度LBM-DEM模型

LBM-DEM耦合方法通常是指一种颗粒流体系统直接数值模拟算法,即是一种不引入经验曳力模型的计算方法,颗粒尺寸通常比计算网格的长度大一个量级,颗粒的受力通过表面的粘性力与压力积分获得,其优点是能描述每个颗粒周围的详细流场,产生详细的颗粒-流体相互作用的动力学信息,可以探索颗粒流体界面的流动、传递和反应的详细信息及两相相互作用的本构关系,但其缺点是计算量巨大,无法应用于真实流化床过程模拟。本文针对气固流化床中的流体以及固体颗粒间的多相流体力学行为,建立了一种稠密气固两相流的介尺度LBMDEM模型,即LBM-DEM耦合的离散颗粒模型,实现在颗粒尺度上流化床的快速离散模拟。该耦合模型采用格子玻尔兹曼方法(LBM)描述气相的流动和传递行为,离散单元法(DEM)用于描述颗粒相的运动,并利用能量最小多尺度(EMMS)曳力解决气固耦合不成熟问题,以提高其模拟精度。通过经典快速流态化的模拟,验证了介尺度LBM-DEM耦合模型的有效性。模拟结果表明介尺度LBM-DEM模型是一种探索实验室规模气固系统的有力手段。     

SiCp/Al复合材料增强颗粒尺寸效应的细观分析

运用Voronoi方法建立了反映金属基颗粒增强复合材料(MMCp)微结构的多晶集合体代表性单元(RVE);采用Taylor关系推导了包含颗粒结构尺寸和体积分数参数的位错滑移硬化函数;建立了由300个平均粒度约为20μm的晶粒组成的多晶集合体代表性单元,并对MMCp3.5-5、MMCp3.5-10、MMCp10-5、MMCp10-10四种具有不同粒径和体积分数的铝基SiC颗粒增强复合材料在宏观均匀变形条件下的应力应变响应进行了数值模拟。计算结果表明:复合材料的应力应变模拟曲线与试验曲线吻合得较好,说明所推导的模型和硬化模式能够合理地描述颗粒增强尺度效应的变化趋势;多晶体模型也能够合理地表现复合材料内部应力应变在空间分布上的细观不均匀性。数值模拟结果反映了颗粒增强区承载着较大的载荷份额,而非颗粒存在区(基体)则承受着高达18%的应变,在两个区域的交界处出现了高达310MPa的应力集中,与已有文献试验观测的结果比较吻合。     

连续胶体材料化学-力学耦合有限元理论及其在ABAQUS中UEL程序实现

基于哈密顿原理,得到水凝胶的化学-力学耦合控制方程的等效积分形式和有限元形式。在整体坐标系下推导出用形函数表示的化学-力学耦合应变矩阵和单元刚度矩阵,并且得到在局部坐标系下的离散化形式。结合ABAQUS软件,编制了用户单元子程序UEL,通过数值算例验证了所开发单元的正确性,为在ABAQUS软件中实现各种耦合问题的有限元UEL编程提供了参考依据。     

基于混合方法的二维水力压裂数值模拟

水力压裂在页岩气开采中被广泛使用,采用数值方法研究压裂机理具有重要意义.基于连续-非连续单元法(CDEM) 和中心型有限体积法(FVM),提出解决水力压裂流固耦合问题的二维混合数值计算模型.该混合模型中,使用CDEM 求解应力场和裂缝扩展过程,使用FVM 求解裂隙渗流场.应力场裂缝扩展和渗流场均使用显式迭代求解, 并通过相互之间数据交换实现流固耦合.通过与KGD 理论模型进行对比, 验证数值模型的正确性.通过与颗粒离散元数值结果进行对比,验证数值模型的有效性.通过计算复杂缝网压裂模型,研究水力压裂机理,并说明该数值模型在水力压裂模拟中具有很好的前景.      

粘接-映射混合算法及其对颗粒材料中板的振动特性分析

结构与颗粒材料相互作用广泛存在于各工程领域,其研究过程中涉及的连续-离散耦合计算方法面对诸多挑战.本文提出了粘接-映射混合算法来研究连续体与离散介质耦合动力学问题.将连续体模型划分为内部区域及与颗粒接触的边界区域.边界区域采用粘接算法模拟连续体外部形状并使用高效的球形接触判断准则;提出一种包含Rayleigh阻尼映射的有限元映射质点弹簧算法来精确计算连续体内部区域内力和变形.二者相结合构成粘接-映射混合算法,并引入计算机集群和GPU(图形处理器)并行技术,对埋没于颗粒材料中受激振动固支方板的连续-离散耦合动力学问题进行了数值仿真研究.结果表明,粘接-映射混合算法有利于双层级并行算法的程序实现及优化,并在连续-离散耦合界面进行快速接触判断的同时实现对颗粒材料中方板位移、变形、振动形态等参数的研究.通过定幅扫频和定频变幅方式考察激振力频率和幅值对振动板非线性动力学行为的影响并观察到二倍周期现象,同时给出了该连续-离散耦合系统中颗粒体系的能量耗散特性.      

Evaluation of coarse-grained CFD-DEM models with the validation of PEPT measurements

Computational Fluid Dynamics coupled with Discrete Element Method (CFD-DEM) is a commonly used numerical method to model gas-solid flow in fluidised beds and other multiphase systems. A significant limitation of CFD-DEM is the feasibility of the realistic simulation of large numbers of particles. Coarse-graining (CG) approaches, through which groups of multiple individual particles are represented by single, larger particles, can substantially reduce the total number of particles while maintaining similar system dynamics. As these three CG models have not previously been compared, there remains some debate, however, about the best practice in the application of CG in CFD-DEM simulations. In this paper, we evaluate the performance of three typical CG methods based on simulations of a bubbling fluidised bed. This is achieved through the use of a numerical validation framework, which makes full use of the high-resolution 3D positron emission particle tracking (PEPT) measurements to rigorously validate the outputs of CFD-DEM simulations conducted using various different coarse-graining models, and various different degrees of coarse-graining. The particle flow behaviours in terms of the particle occupancy field, velocity field, circulation time, and bubble size and velocity, are comprehensively analysed. It is shown that the CG simulation starts to fail when the size ratio between the bed chamber and the particles decreases to approximately 20. It is also observed, somewhat surprisingly, that the specific CG approach applied to interparticle contact parameters does not have a substantial effect on the simulation results for the bubbling bed simulations across a wide range of CG factors.     

一种化学-力学耦合连续介质理论与数值格式

对化学驱动的连续介质化学-力学耦合系统进行研究,从热力学定律和化学势角度出发,推导了等温过程的化学-力学耦合本构关系和控制方程,利用变分方法建立了化学-力学耦合系统的能量泛函,得到化学-力学耦合控制方程的等效积分形式和相应的有限元列式. 结合算例,对连续介质的化学-力学耦合行为进行了数值计算,数值结果反映了化学与力学系统的相互耦合作用,即浓度变化能引起介质的变形,同样力学作用也能引起浓度重分布. 从全新的角度建立了描述连续介质的化学-力学耦合行为的基本理论和数值方法,能够较好地反映一类连续介质的化学-力学耦合行为.      

近场动力学与有限元方法耦合求解热传导问题

求解含裂纹等不连续问题一直是计算力学的重点研究课题之一,以偏微分方程为基础的连续介质力学方法处理不连续问题时面临很大的困难. 近场动力学方法是一种基于积分方程的非局部理论,在处理不连续问题时有很大的优越性. 本文提出了求解含裂纹热传导问题的一种新的近场动力学与有限元法的耦合方法. 结合近场动力学方法处理不连续问题的优势以及有限元方法计算效率高的优势,将求解区域划分为两个区域,近场动力学区域和有限元区域. 包含裂纹的区域采用近场动力学方法建模,其他区域采用有限元方法建模. 本文提出的耦合方案实施简单方便,近场动力学区域与有限元区域之间不需要设置重叠区域. 耦合方法通过近场动力学粒子与其域内所有粒子(包括近场动力学粒子和有限元节点)以非局部方式连接,有限元节点与其周围的所有粒子以有限元方式相互作用. 将有限元热传导矩阵和近场动力学粒子相互作用矩阵写入同一整体热传导矩阵中,并采用Guyan缩聚法进一步减小计算量. 分别采用连续介质力学方法和近场动力学方法对一维以及二维温度场算例进行模拟,结果表明,本文的耦合方法具有较高的计算精度和计算效率. 该耦合方案可以进一步拓展到热力耦合条件下含裂纹材料和结构的裂纹扩展问题.      

Integrated numerical model for vegetated surface and saturated subsurface flow interaction

The construction of an integrated numerical model is presented in this paper to deal with the interactions between vegetated surface and saturated subsurface flows. A numerical model is built by integrating the previously developed quasi-three-dimensional (Q3D) vegetated surface flow model with a two-dimensional (2D) saturated groundwater flow model. The vegetated surface flow model is constructed by coupling the explicit finite volume solution of 2D shallow water equations (SWEs) with the implicit finite difference solution of Navier-Stokes equations (NSEs) for vertical velocity distribution. The subsurface model is based on the explicit finite volume solution of 2D saturated groundwater flow equations (SGFEs). The ground and vegetated surface water interaction is achieved by introducing source-sink terms into the continuity equations. Two solutions are tightly coupled in a single code. The integrated model is applied to four test cases, and the results are satisfactory.     

A block particle coupled model and its application to landslides

To simulate the progressive failure of slope, a block particle coupled model is introduced. Particle oriented cell mapping(POCM) algorithm is used to enhance the search efficiency, and particlepoint, particle-edge, particle-face contact detecting method is adopted to establish contact pair between particles and blocks precisely. Strain softening Mohr Coulomb model with tensile cutoff is adopted for blocks, and brittle Mohr Coulomb model is used for particles. The particle-block replacement approach is used to describe the fracture and fragmentation process of continuum media. Once the cohesion or tensile strength of one block reaches zero, the block will be deleted,and particles are generated at the same place with all information inherited from the deleted block. Some numerical cases related to landslides demonstrate the precision and rationality of the coupled model.     

凹形多面体离散单元的水平集函数接触算法

多面体模型理论上可构造任意颗粒形态,然而受单元接触算法的限制,仅用于凸形颗粒材料的离散元模拟。对于具有凹形特征的多面体单元,单个接触点的搜索算法难以精确计算单元间的作用力。考虑多面体单元间存在单个或多个接触点的计算特性,本文发展了适用于凸形和凹形多面体颗粒材料的水平集函数接触算法。该方法通过点-三角形单元距离计算方法和奇-偶数判定方法建立多面体单元的零水平集函数和空间水平集函数,并对水平集函数进行三线性插值,可得到多面体单元间的单个或多个接触点。为检验水平集函数接触算法的可靠性,对球形和凹形多面体颗粒材料的堆积和倒塌过程进行离散元模拟,并分析颗粒形状对堆积密度和休止角的影响规律。     

Coupled rocking and sliding vibration response of a structure to harmonic horizontal ground motion

For a strip wall erected on a rigid strip foundation and supported by the surface of the ground, the dynamic soil-structure interaction under the action of the horizontal ground motion is investigated. The ground motion is idealized as vertically propagating, horizontal steady-state motion. Because the horizontal ground motion brings about the sliding vibration of the foundation as well as the rocking vibration, the coupled rocking and sliding vibration of the soil-structure system is considered in the present paper. For the contact between the ground and foundation, the following assumptions are made: 1) the contact is assumed to be welded, that is to say, the motion of the foundation is consistent with the ground; 2) the horizontal translation at each point on the bottom surface of the foundation is equal to a constant; 3) the distribution of the normal displacements under the foundation remains to be linear in the rocking vibration. For comparison, the case of uncoupled vibration is considered also. The use of Fourier transform method yields dual integral equations (for the case without coupling effect) or simultaneous dual integral equations (for the case with coupling effect). Both of them are solved by means of infinite series of orthogonal functions, the Jacobi polynomials. The numerical results show that there is a significant difference between the displacements of the foundation, the relative displacements of the top of the wall with respect to its base, and the distribution of contact stresses beneath the foundation, for the cases with and without coupling effect.     

A model of damage coupled to wear

The present paper presents a model of damage coupled to wear. The damage model is based on a continuum model including the gradient of the damage variable. Such a model is non-local in the sense that the evolution of damage is governed by a boundary-value problem instead of a local evolution law. Thereby, the well-known mesh-dependency observed for local damage models is removed. Another feature is that the boundary conditions can be used to introduce couplings between bulk damage and processes at the boundary. In this work such a coupling is suggested between bulk damage and wear at the contact interface. The model is regarded as a first attempt to formulate a continuum damage model for studying crack initiation in fretting fatigue.The model is given within a thermodynamic framework, where it is assured that the principles of thermodynamics are satisfied. Furthermore, two variational formulations of the full initial boundary value problem, serving as starting points for finite element discretization, are presented. Finally, preliminary numerical results for a simple one-dimensional example are presented and discussed. It is qualitatively shown how the evolution of damage may influence the wear behaviour and how damage may be initiated by the wear process.