模拟岩石材料脆性破裂过程的三维离散元模型

发展一种能够模拟岩石材料脆性破裂过程的三维不规则、可变形块体离散元模型.一方面,在裂纹扩展过程中动态地将潜在破坏的连续块体沿潜在破坏方向细化为若干子块体,并在子块体之间的界面上设置连接型弹簧;另一方面,连接型弹簧在满足张拉-剪切复合破坏准则时发生脆性破裂,转变为接触型弹簧,实现材料由连续到非连续的破裂.借助动态松弛技术完成求解,通过计算实例验证该方法的适用性.     

多体系统碰撞动力学中接触力模型的研究进展

接触碰撞行为作为大自然与多体系统中的常见现象, 其接触力模型对于多体系统的碰撞行为机理研究与性能预测至关重要. 静态弹塑性接触模型与考虑能量耗散的连续接触力模型是研究接触碰撞行为的两类不同方法, 在多体系统碰撞动力学中存在诸多共性与差异. 本文分别从上述两类接触模型的发展历程入手, 详细介绍了两类模型的区别与联系. 首先, 根据阻尼项分母中是否含有初始碰撞速度将连续接触力模型分为黏性接触力模型与迟滞接触力模型, 讨论了能量指数与Hertz接触刚度之间的关系, 阐述了现有连续接触力模型在计算弹塑性材料接触碰撞行为时存在的问题. 其次, 着重介绍了分段连续的准静态弹塑性接触力模型(可连续从完全弹性转换到完全塑性接触阶段), 分析了利用此类弹塑性接触力模型计算碰撞行为的技术特点. 同时, 以恢复系数为桥梁和借助线性化的弹塑性接触刚度, 避免了Hertz刚度对弹塑性接触刚度的计算误差, 根据碰撞前后多体系统的能量与动能守恒推导了弹塑性接触模型等效的迟滞阻尼因子. 探索了连续接触力模型与准静态弹塑性接触力模型之间的内在联系, 数值计算结果定量说明了人为阻尼项代表的能量耗散与弹塑性接触力模型中加卸载路径代表的能量耗散具有等效性. 另外, 为了避免阻尼项分母中初始碰撞速度在计算颗粒物质动态性能时导致的数值奇异问题, 通过求解等效的线性单自由度欠阻尼非受迫振动方程获得了阻尼项分母中不含初始碰撞速度的连续接触力模型, 并以一维球链为例, 证明了该模型相比EDEM软件使用的连续接触力模型具有更高的精度. 最后, 本文分析了当前多体系统碰撞动力学的研究现状, 并简要展望了多体系统碰撞动力学中接触力模型的发展趋势与面临的挑战.      

三维机织复合材料的弹性性能预报模型

建立了基于等效响应比拟技术的三维机织复合材料弹性性能预报模型．首先将三维机织物的结构单元分解为4个子元(经纱、纬纱、填充纱和接结纱),用几何模型去估算这些子元的体积分数．然后依据不同的外载形式,将复合材料的应力-应变关系等效地表达为3组诸子元所组成的三维弹簧网络．根据刚度系数的物理意义,采用不同的弹簧网络连接形式,并按体积平均化方法获得材料总体刚度矩阵中相应的刚度系数,进而计算得到三维机织复合材料的9个弹性系数．该模型考虑了层内交织经纱、层间交织接结纱的弯曲以及材料内部纯树脂区对三维机织复合材料弹性性能的影响．试验结果与模型的理论预测值进行比较,表明这个模型是有效的。     

三维连续与非连续变形分析

将石根华博士所提出的二维非连续变形分析——Discontinuous Deformation Analysis（DDA）方法扩展到三维情况,并对三维不连续块体进行有限元网格剖分,即块体之间的接触采用DDA描述,块体内部的位移场和应力场则采用有限单元法描述,从而将三维DDA与有限元方法结合起来,增强了DDA方法与有限元方法解决实际工程问题的能力,实现了三维连续与非连续变形分析.给出了基本公式的推导过程和各子矩阵的形式.典型接触、碰撞算例证明了所提出方法的有效性和正确性.     

三维数值流形方法的点-面接触模型

建立了三维流形元的点-面接触模型,给出了嵌入准则并应用罚方法强迫接触界面满足不嵌入和无拉伸条件约束求解,详细推导了法向弹簧、切向弹簧和摩擦力子矩阵并给出了接触状态(张开、滑动和固定)的模式变化准则,算例表明该模型的有效性。     

考虑接触应力非线性分布的接触力元模式及其验证分析

在作者提出的非连续变形计算力学模型中,采用接触力元模型描述多体接触界面上的接触特性．由于这种模型中假定接触应力沿接触界面为线性分布,从而得到的接触界面应力分布往往出现跳跃等非光滑性特征,该文对此进行了改进,采用具有高阶光滑性的非线性函数建立了能够考虑界面上接触应力非线性分布的接触力元模式,以期合理地揭示多体系统中界面的接触特性．对某一典型算例进行了数值计算,通过与大型通用非线性有限元结构分析软件ABASQUS的计算结果对比,验证了所建议计算模型的合理性与有效性．两种方法计算得到的界面接触对上的接触力基本相同;而由于采用的应力分布模式的假定不同,接触应力有所差别,由于在该文计算模型中接触对上的接触应力是按照未知量直接求得的,因此按照所建议的非线性接触力元模式所得到的接触应力更为合理．     

离散元法在求解三维冲击动力学问题中的应用

提出了三维连结型离散模型,建立了可实现连结型模型(用于连续介质)-接触型模型(用于非连续介质)转化的三维离散元计算程序,用来模拟连续介质转变为非连续介质的力学过程．利用该计算程序对冲击载荷下混凝土块体内(连续体情况下)的应力波传播过程进行了数值模拟．将计算结果的数值与LS-DYNA程序计算的结果进行比较,验证了该计算程序的计算精度．在此基础上,模拟了混凝土块体的动态破坏(连续介质向非连续介质转化)过程．其计算结果可用动画显示,得到的破坏形式与由实验得到的破坏形式相近．两个算例说明该离散元模型及其计算程序是模拟计算伴随有连续介质向非连续介质转变的动态破坏问题的有力工具．     

岩石圆盘径向压缩破坏的Voronoi子块体单元DDA方法模拟

非连续变形分析(DDA)方法是计算离散可变形块体系统力学行为的数值计算方法，可通过子块体单元DDA方法模拟岩石的开裂破坏。考虑到Voronoi多边形颗粒与细观尺度下岩石矿物晶粒形态的相似性，提出一种基于随机圆的Voronoi颗粒单元模型生成方法；并通过完整及带预制裂纹岩石圆盘径向压缩破坏的模拟，验证岩石破裂问题Voronoi子块体单元DDA模拟方法的适用性。结果表明，当子块体单元数较小时，圆盘表现出更高的整体强度；随着子块体单元数的增大，起裂处位置更接近真实，开裂破坏路径更清晰；子块体单元数较大时不同倾角预制裂纹圆盘破坏的模拟结果与实验结果高度吻合，并能有效反映圆盘中心加工小孔对开裂破坏路径的影响。使用Voronoi子块体单元DDA方法能够有效模拟岩石的开裂破坏过程，为进一步开展基于Voronoi颗粒单元模型的岩石开裂破坏模拟创造了条件。     

运动车辆横向振动半车模型分析

通过半车模型, 数值研究平滑路面上运动车辆车体的前两阶横向振动频率. 将车体模型化为两端自由的Euler-Bernoulli梁, 半车模型的车轮模型化为两个弹性不等的弹簧. 建立半车模型的数学模型描述车体的横向振动. 以两端自由的静态梁的模态为试函数和权函数, 通过高阶Galerkin截断计算车体横向振动的频率, 并研究车辆运行速度、车体刚度、弹簧刚度等参数对车体振动频率的影响.     

接触力优化设计的熵正则化方法

包含单侧接触的机械和结构系统中,接触面间的局部接触力很大时,容易导致结构局部磨损和破坏。利用结构优化的手段极小化接触面上的最大接触力是调整接触面上接触力分布的一个有效途径。然而在数学上,目标函数的不可微和约束中的接触条件导致该结构优化问题属于非光滑和非凸优化问题,因而常用优化算法的优化结果是不可靠的。为此,本文提出接触力优化的一个熵正则化模型,并利用基于正则化过程的序列二次结构优化算法求解。所提的方法在数值上避免了处理不可微问题,而且正则化参数的调整还有助于获得更小的局部最优解。以离散结构为例的数值算例验证了本文的模型和算法。     

均匀水流冲击下扭王字块断裂失稳过程的数值模拟研究

扭王字块是一种重要的港口防波堤护面块体,其断裂失稳过程与所受水流冲击力密切相关。文章以基于连续介质力学的离散元方法(CDEM)为基础,通过引入FVM算法及半弹簧-半棱联合接触模型,分别实现了大位移下单元变形的准确计算及单元接触的快速更新。基于改进后的CDEM方法,通过在扭王字块表面施加按流速方向逐渐增加的动态面力,对均匀水流冲击下单扭王字块的断裂过程及扭王字块群的失稳滑移过程进行了数值分析。通过分析,不同方向水流冲击下单扭王字块的主要断裂模式为沿着根部的折断,其断裂流速约为21~25m/s;不同吨位下扭王字块群的失稳模式为扭王字块单体从群体中跳出,其失稳流速约为4~11m/s。     

基于连续-非连续单元方法的露天矿三维台阶爆破全过程数值模拟

爆破开采是露天矿采选总成本控制的首要环节，数值模拟是进行露天矿爆破开采优化设计及爆破效果分析的有效手段。利用连续-非连续单元方法（continuum-discontinuum element method，CDEM）对露天矿的三维台阶爆破过程进行了模拟，通过朗道爆炸模型实现了爆炸作用力的精确计算，通过弹性-损伤-断裂本构实现了岩体损伤破裂过程的描述，通过半弹簧-目标面及半棱-目标棱的联合接触算法实现了破碎岩块碰撞、飞散及堆积过程的高效模拟。开展了小尺度单自由面爆破过程的数值模拟，计算给出的块度分布曲线、爆破漏斗体积等参数与文献中模型实验的结果基本一致，证明了CDEM及本文所述各类模型在模拟爆炸破岩方面的精确性。以鞍千矿南采区的露天铁矿爆破开采为研究对象，建立了3排21炮孔的三维台阶爆破概化模型，模拟了从炸药起爆、岩体损伤破裂到最后爆堆形成的全过程；计算结果表明，除后缘拉裂槽外，数值计算给出的爆堆形态、顶部鼓起高度等与现场的测试结果基本一致，证明了利用CDEM开展三维露天台阶爆破全过程模拟的可行性。     

三维非连续变形分析方法碰撞分析及其应用

将具有完备动力学理论的非连续变形分析(DDA)方法应用于块体碰撞研究。基于三维DDA(3D DDA)方法,按时步输出块体碰撞过程速度变化和接触嵌入量,进而得到块体碰撞恢复系数、冲量、冲击力。以此为参考指标,采用斜抛、面-面对心等碰撞模型,验证3D DDA方法模拟块体碰撞的有效性,并将3D DDA方法应用于多米诺骨牌倾倒、滚石边坡成灾及防护等算例分析,探讨了多米诺骨牌倾倒机制、滚石启动及运动行为、滚石灾害防护方案。结果表明:多米诺骨牌间距越大,同一块体被碰撞时间越迟,其最终稳定时间也越迟,与下一块体碰撞的动能越大;滚石运动呈侧向平动及转动三维运动特征,每一次碰撞,均引起动能、轨迹或状态的显著变化;滚石拦挡设施弹簧刚度越大,越先达到最大冲击力,最大冲击力随弹簧刚度的增加而减小;可结合树木阻挡效应,耗散滚石动能,降低滚石飞跃高度,使滚石灾害减轻或控制在防护范围以内。     

Stress response of a rubber block with frictional contact under axial loading

Rubber blocks (or springs) are structural components widely used in many applications. Design characteristics of a rubber block under axial loading are an apparent modulus (or compression modulus) and normal and shear stresses on contact surfaces. These are affected by a contact condition of the rubber block in contact with two rigid plates and the shape of the block. The problem of a rubber block bonded to two rigid plates has been solved using various approaches. In contrast, for a rubber block whose one surface is bonded to a rigid plate and the other surface in contact with a frictional surface, there is little work in spite of practical applications. For this contact condition, approximate solutions for rectangular blocks in plane strain and for axi-symmetric discs are derived under the assumption of Coulomb frictional contact. The problem is treated as an extension of the problem of an incompressible rubber block bonded to two rigid plates with one of the plates having a frictional interaction with the rubber block. In the linear range of deformation, finite element analysis and experimental results for rubber blocks with shape factors ranging from 1 to 6 are compared for the validation of analytic results. It is found that friction coefficients play important roles in the design characteristics of the rubber block.     

高速列车制动闸片摩擦块形状对制动界面摩擦学行为的影响

在自行研制的高速列车制动缩比试验台上,对六边形、五边形和圆形摩擦块进行拖曳制动试验,研究摩擦块形状对高速列车制动界面摩擦学行为的影响,并采用有限元方法分析了不同摩擦块形状下制动界面接触行为的差异,探讨了摩擦块形状对接触压力分布及表面热分布的影响. 结果表明:摩擦块形状显著影响了制动界面磨损特性及接触压力分布,使得制动盘产生不同的温度分布现象. 在本试验条件下,六边形摩擦块表面磨损轻微,接触平台大小较为均匀,而五边形和圆形摩擦块表面呈现明显的犁沟和剥落特征,且大接触平台占比较高;六边形摩擦块与制动盘拖曳制动过程,界面具有较大的接触面积,使得接触压力分布较为均匀,表现出较好的接触行为,而五边形和圆形摩擦块的接触行为相对较为复杂,与之对摩的制动盘产生明显的热聚集现象.      

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.     

考虑磨损的接触式端面密封模型及试验

针对油润滑窄端面接触式端面密封,建立了考虑端面稳定磨损的密封性能分析模型. 基于流体承载和固体接触承载共同平衡闭合力的传统思路,引入Archard磨损模型,创新性地提出沿窄端面径向方向磨损均匀假设,从而使用半解析方法得到近似固体接触力、流体承载力及介质膜厚分布. 在此基础上耦合密封环组件力和热变形,最终得到密封泄漏量、端面温度等性能参数. 相应台架试验结果也较好地验证了模型的正确性. 所建模型对于窄端面接触式端面密封的性能分析和密封优化设计具有指导意义.      

A semi-infinite chamfered contact solution and its application to almost complete contacts

The solution for a semi-infinite rigid block having a flat face but with a small, shallow edge chamfer, and pressed onto an incompressible half-plane, is considered. The surface traction distribution and internal state of stress under both normal and a monotonically increasing shearing force are found, and the characteristics of the solution explored. As an example it is employed to find the edge-solution for a finite square-ended but chamfered punch in contact with a half-plane.     

Measurement and Prediction of Machining Induced Redistribution of Residual Stress in the Aluminium Alloy 7449

The residual stress distributions in two 7449 aluminium alloy rectilinear blocks have been determined using neutron diffraction. Heat treatment included cold water immersion quenching and a period of precipitation hardening. Quenching induced very high magnitude residual stresses into the two blocks. One block was measured in this condition while the other was incrementally machined by milling to half thickness. Neutron diffraction measurements were made on the milled half thickness block at equivalent locations to the unmachined block. This permitted through thickness measurements from both blocks to be compared, revealing the redistribution of residual stresses induced by machining. A square cross section post in the centre of the machined face was left to act as a stress free reference sample. The distortions arising on the face opposite to that being milled were measured using a co-ordinate measuring machine. The residual stresses and distortion arising in the blocks have been compared to finite element analysis prediction and found to generally agree. Material removal only caused distortion and the residual stresses to redistribute; there was no stress relaxation evident.     

Galin’s problem for a spatial elastic wedge

We study a three-dimensional contact problem on the indentation of an elliptic punch into a face of a linearly elastic wedge. The wedge is characterized by two parameters of elasticity and its edge is subjected to the action of an additional concentrated force. The other face wedge is free from stresses. The problem is reduced to an integral equation for the contact pressure. An asymptotic solution of this equation is obtained which is effective for a given contact region fairly remote from the edge. Calculations are performed that allow one to evaluate the effect of a force applied outside the contact region on the contact pressure distribution. The problem under study is a generalization of L. A. Galin’s problem on a force applied outside a circular punch on an elastic half-space [1, 2]. In a special case of a wedge with an opening angle of 180° and zero contact ellipse eccentricity, the obtained asymptotic relation coincides with the expansion of Galin’s exact solution in a series. Problems of indentation of an elliptic punch into a spatial wedge with the face not loaded outside the contact region have been studied previously. For example, the paper [3] dealt with the case of a known contact region (asymptotic method) and the paper [4] considered the case of an unknown contact region (numerical method). The solution of Galin’s problem allowed the authors of [2] to reduce the contact problem on the interaction of several punches applied to a half-space to a system of Fredholm integral equations of the second kind (Andreikin-Panasyuk method). A topical direction in contact mechanics is the model of discrete contact as well as related problems on the interaction of several punches [2, 5–8]. The interaction of several punches applied to a face of a wedge can be treated in a similar manner and an asymptotic solution can be obtained for the case where a concentrated force is applied at an arbitrary point of this face beyond the contact region rather than on the edge.