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.     

柔性梁斜碰撞问题的非线性动力学建模和实验研究

本文研究柔性梁点面斜碰撞问题。用Hertz接触模型处理法向撞击力,分别用Hertz切向接触模型和Coulomb摩擦力模型处理粘滞状态和滑动状态的摩擦力。从精确的应变与位移的关系出发,用绝对节点坐标法建立了柔性梁的动力学方程。为了准确地处理斜碰撞切向运动的复杂状态,提出滑动-粘滞切换的准则,在此基础上,设计了斜碰撞实验,数值对比了法向撞击力和法向速度的时间历程的仿真计算结果与实验结果,验证了Hertz理论在斜碰撞情况下的正确性。另一方面切向速度的实验与理论的结果对照表明滑动-粘滞切换准则的有效性。     

人体--结构系统的水平振动实验

针对静止状态人对结构水平振动特性的影响,建立实验平台,分别测试并分析了质量块-结构系统、单人-结构系统、多人-结构系统水平自振频率与阻尼比变化规律.给出了两种人-结构系统静态水平耦合模型的比较分析以及人体的水平振动频率估计.结果表明:在分析静止状态下人对结构水平振动特性的影响时,人体不可简单作为质量块或质量-弹簧-阻尼系统,而应看作带人体刚性质量的质量-弹簧-阻尼系统.结合实验测试数据和人-结构系统水平耦合模型,得到人体水平前后向频率范围为0.236～3.748 Hz,人体水平左右向频率范围为0.194～5.32 Hz.     

构元组集模型对结构弹性损伤至断裂过程的描述及与内聚区模型的比较

结构的响应实质上是材料的响应,宏观结构损伤至断裂的发展过程也是材料性质不断演化的结果。构元组集模型从材料的微观物理变形机制出发,基于对泛函势理论和Cauchy-Born准则,抽象出两种构元——弹簧束构元和体积构元。在微观层次上,结构损伤和断裂的实质都是原子间键合力减弱和丧失的结果,而弹簧束构元是同一方向上的原子键的抽象,因此损伤可以通过弹簧束构元的响应曲线来反映。组集两种构元的响应,建立了材料的弹性损伤本构关系,从而能一致描述材料从弹性到损伤、破坏的发展过程。将构元组集模型的本构关系嵌入ABAQUS的用户材料单元子程序UMAT,实现对结构响应的数值模拟。本文模拟了包含中心预制裂纹三点弯曲梁的裂纹扩展过程,并与内聚区模型比较,给出了内聚区模型所假设的应力——位移关系曲线,并从材料损伤演化的角度对材料裂纹扩展过程做出了物理解释。     

构元组集损伤断裂模型及其与内聚区模型的比较

结构的响应实质上是材料的响应,宏观结构损伤至断裂的发展过程也是材料性质不断演化的结果.构元组集模型从材料的微观物理变形机制出发,基于对泛函势理论和Cauchy-Born准则,抽象出两种构元:弹簧束构元和体积构元.在微观层次上,结构损伤和断裂的实质都是原子间键合力减弱和丧失的结果,而弹簧束构元是同一方向上的原子键的抽象,因此损伤可以通过弹簧束构元的响应曲线来反映.组集两种构元的响应,建立了材料的弹性损伤本构关系,从而能一致描述材料从弹性到损伤、破坏的发展过程.将构元组集模型的本构关系嵌入ABAQUS的用户材料单元子程序UMAT,实现对结构响应的数值模拟.论文模拟了包含中心预制裂纹三点弯曲梁的裂纹扩展过程,并与内聚区模型比较,给出了内聚区模型所假设的应力-位移关系曲线,并从材料损伤演化的角度对材料裂纹扩展过程做出了物理解释.     

含摩擦与碰撞平面多刚体系统动力学线性互补算法

基于接触力学理论和线性互补问题的算法, 给出了一种含接触、碰撞以及库伦干摩擦, 同时具有理想定常约束(铰链约束) 和非定常约束(驱动约束) 的平面多刚体系统动力学的建模与数值计算方法. 将系统中的每个物体视为刚体, 但考虑物体接触点的局部变形, 将物体间的法向接触力表示成嵌入量与嵌入速度的非线性函数,其切向摩擦力采用库伦干摩擦模型. 利用摩擦余量和接触点的切向加速度等概念, 给出了摩擦定律的互补关系式; 并利用事件驱动法, 将接触点的黏滞-滑移状态切换的判断及黏滞状态下摩擦力的计算问题转化成线性互补问题的求解. 利用第一类拉格朗日方程和鲍姆加藤约束稳定化方法建立了系统的动力学方程, 由此可降低约束的漂移, 并可求解该系统的运动、法向接触力和切向摩擦力, 还可以求解理想铰链约束力和驱动约束力. 最后以一个类似夯机的平面多刚体系统为例, 分析了其动力学特性, 并说明了相关算法的有效性.      

固定接触界面切向静弹性刚度问题研究

根据两球体单峰同时受法向、切向载荷时微滑切向应力的分布以及MB模型,给出了界面的总切向接触静弹性条件刚度、总条件法向载荷的解析解。将切向接触静弹性条件刚度的解析解嵌入到有限元软件中,获得了整机的理论模态。以一款八四七厂华中工学院XHK5140型自动换刀计算机数控立式镗铣床上的结合部为研究对象,通过实验对解析解进行了定量验证。研究结果表明：在理论振型与实验振型一致的条件下,界面模型的相对误差在-19．2％～16．8％之间。     

结合部切向接触刚度分形模型研究

根据球体与平面接触的切向接触刚度和粗糙表面的接触分形理论，从理论上首次建立了结合部切向接触刚度分形模型，该模型具有尺度独立性。通过对所建模型的数字仿真，直观地给出了结合部切向接触刚度与其影响因素之间的非线性关系，并与实验研究结果具有较好的一致性，从而说明了该模型是合理的。     

低速冲击激励下嵌入黏弹性阻尼芯层的纤维金属混杂层合板动态响应预测模型

本文首次从解析角度建立了低速冲击激励下嵌入黏弹性阻尼芯层的纤维金属混杂层合板动态响应预测模型. 首先,结合经典层合板理论和冯$\cdot$卡门假设,建立了嵌入黏弹性芯层的纤维金属混杂层合板弹性损伤本构关系. 然后,将层合板受冲击时的变形分成接触和拉伸两个区域,在接触区域内,对金属层采用 Von Mises 失效准则,纤维层采用 Tsai-Hill 失效准则和对黏弹性层采用指数 Drucker-Prager 失效准则判断层合板损伤情况. 考虑不同材料层对冲击动态响应的贡献来修正两个变形区域的位移公式,进而计算结构因弹性变形产生的应变能,以及接触区域因塑性变形消耗的能量,实现每次失效事件发生后各层材料的能量、位移和冲击接触力的理论求解,并给出了结构动态响应分析的具体流程图. 最后,以嵌入 Zn33 黏弹性芯层的 TA2 钛合金混杂 T300 碳纤维/树脂层合板为研究对象,开展落锤冲击实验. 验证结果表明,理论预测与测试获得的冲击接触力、位移响应以及冲击载荷-位移曲线吻合较好,且关注的峰值点计算误差最大不超过 9%,进而验证了所提出的理论模型的有效性.      

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.      

Micromechanical analysis of fibrous piezoelectric composites with imperfectly bonded adherence

In this work, two-phase parallel fiber-reinforced periodic piezoelectric composites are considered wherein the constituents exhibit transverse isotropy and the cells have different configurations. Mechanical imperfect contact at the interface of the piezoelectric composites is studied via linear spring model. The statement of the problem for two-phase piezoelectric composites with mechanical imperfect contact is given. The local problems are formulated by means of the asymptotic homogenization method, and their solutions are found using complex variable theory. Analytical formulae are obtained for the effective properties of the composites with spring imperfect type of contact and different rhombic cells. Using the concept of a representative volume element (RVE), a finite element model is created, which combines the angular distribution of fibers and imperfect contact conditions (spring type) between the phases. Periodic boundary conditions are applied to the RVE, so that effective material properties can be derived. The fibers are distributed in such a way that the microstructure is characterized by a rhombic cell. The presented numerical homogenization technique is validated by comparing results with theoretical approach reported in the literature. Some studies of particular cases, numerical examples, and comparisons between the two aforementioned methods with other theoretical results illustrate that the model is efficient for the analysis of composites with presence of rhombic cells and the aforementioned imperfect contact.     

Modeling and dynamics analysis of helical spring under compression using a curved beam element with consideration on contact between its coils

Helical springs are indispensable elements in mechanical engineering. This paper investigates helical springs subjected to axial loads under different dynamic conditions. The mechanical system, composed of a helical spring and two blocks, is considered and analyzed. Multibody system dynamics theory is applied to model the system, where the spring is modeled by Euler–Bernoulli curved beam elements based on an absolute nodal coordinate formulation. Compared with previous studies, contact between the coils of spring is considered here. A three-dimensional beam-to-beam contact model is presented to describe the interaction between the spring coils. Numerical analysis provides details such as spring stiffness, static and dynamic stress for helical spring under compression. All these results are available in design of helical springs.     

Comparison of linear spring and nonlinear FEM methods in dynamic coupled analysis of floating structure and mooring system

This paper compares the dynamic coupled behavior of floating structure and mooring system in time domain using two numerical methods for the mooring lines such as the linear spring method and the nonlinear FEM (Finite Element Method). In the linear spring method, hydrodynamic coefficients and forces on the floating body are calculated using BEM (Boundary Element Method) and the time domain equation is derived using convolution. The coupled solution is obtained by simply adding the pre-determined spring constants of the mooring lines into the floating body equation. In FEM, the minimum energy principle is applied to formulate the nonlinear dynamic equation of the mooring system with a discrete numerical model. The ground contact model and Morison formula for drag forces are also included in the formulation. The coupled solution is obtained by iteratively solving the floating body equation and the FEM equation of the mooring system. Two example structures such as weathervane ship and semi-submersible structure are analyzed using linear spring and nonlinear FEM methods and the difference of those two methods are presented. By analyzing the cases with or without surge-pitch or sway-roll coupling stiffness of mooring lines in the linear spring method, the effect of coupling stiffness of the mooring system is also discussed.     

不同轮轨接触模型在车桥耦合振动中的比较

以工程实例为研究对象,建立了整车-整桥系统耦合振动数值分析模型。考虑车轮的跳轨和挤密情况,建立了单边弹簧-阻尼系统弹性轮轨接触模型。采用基于多体系统动力学和有限元法结合的联合仿真技术,计算了两种轮轨接触时动车组列车以不同车速通过大跨度连续桥梁的耦合振动响应。数值计算结果表明:两种轮轨接触模型的桥梁动力响应比较接近;列车的横向轮轨力、轮重减载率和脱轨系数相差较大,当速度为350km/h时,横向轮轨力增大了46.5%,轮重减载率增大了130.8%,脱轨系数增大了24.66%;用单边-弹簧阻尼系统弹性轮轨接触模型更符合实际。     

板材冲压成形有限元数值模拟界面摩擦约束处理方法

基于弹塑性大变形板材冲压成形增量有限元法,采用线性弹簧单元提出一种空间三维板材冲压成形等效界面摩擦力的处理方法.这种方法的优点是可以反映界面摩擦力的同步、被动产生效果,同时它还可以保证约束后刚度矩阵的对称性.将提出的摩擦约束处理算法引入自主开发的板材成形模拟软件FASTAMP,计算了汽车油底壳的成形过程,计算结果的厚度分布与实际冲压件吻合比较好,验证了等效界面摩擦力约束处理方法的有效性.     

Effective elastic shear stiffness of a periodic fibrous composite with non-uniform imperfect contact between the matrix and the fibers

In this contribution, effective elastic moduli are obtained by means of the asymptotic homogenization method, for oblique two-phase fibrous periodic composites with non-uniform imperfect contact conditions at the interface. This work is an extension of previous reported results, where only the perfect contact for elastic or piezoelectric composites under imperfect spring model was considered. The constituents of the composites exhibit transversely isotropic properties. A doubly periodic parallelogram array of cylindrical inclusions under longitudinal shear is considered. The behavior of the shear elastic coefficient for different geometry arrays related to the angle of the cell is studied. As validation of the present method, some numerical examples and comparisons with theoretical results verified that the present model is efficient for the analysis of composites with presence of imperfect interface and parallelogram cell. The effect of the non uniform imperfection on the shear effective property is observed. The present method can provide benchmark results for other numerical and approximate methods.     

Application of fractional-derivative standard linear solid model to impact response of human frontal bone

The impact of a rigid body on a thin plate with a buffer is investigated in this paper. A buffer is assumed as a linear spring fractional derivative dashpot which exhibits the viscoelastic features. The fractional-derivative standard linear solid model is suggested for describing the shock interaction of the impactor with a circular elastic plate. We assume that a transient wave of transverse shear is generated in the plate and the reflected wave does not have sufficient time to interact with the plate before the impact process is completed. The ray method is used outside the contact spot, but the Laplace transform method is applied within the contact region. The time-dependence of the contact force is determined. A numerical example is carried out by considering crash scenarios in frontal impacts of the human head which could estimate brain injury risks.     

Low-velocity impact response of sandwich beams with functionally graded core

The problem of low-speed impact of a one-dimensional sandwich panel by a rigid cylindrical projectile is considered. The core of the sandwich panel is functionally graded such that the density, and hence its stiffness, vary through the thickness. The problem is a combination of static contact problem and dynamic response of the sandwich panel obtained via a simple nonlinear spring-mass model (quasi-static approximation). The variation of core Young’s modulus is represented by a polynomial in the thickness coordinate, but the Poisson’s ratio is kept constant. The two-dimensional elasticity equations for the plane sandwich structure are solved using a combination of Fourier series and Galerkin method. The contact problem is solved using the assumed contact stress distribution method. For the impact problem we used a simple dynamic model based on quasi-static behavior of the panel—the sandwich beam was modeled as a combination of two springs, a linear spring to account for the global deflection and a nonlinear spring to represent the local indentation effects. Results indicate that the contact stiffness of the beam with graded core increases causing the contact stresses and other stress components in the vicinity of contact to increase. However, the values of maximum strains corresponding to the maximum impact load are reduced considerably due to grading of the core properties. For a better comparison, the thickness of the functionally graded cores was chosen such that the flexural stiffness was equal to that of a beam with homogeneous core. The results indicate that functionally graded cores can be used effectively to mitigate or completely prevent impact damage in sandwich composites.     

Soft-impact dynamics of deformable bodies

Systems constituted by impacting beams and rods of non-negligible mass are often encountered in many applications of engineering practice. The impact between two rigid bodies is an intrinsically indeterminate problem due to the arbitrariness of the velocities after the instantaneous impact and implicates an infinite value of the contact force. The arbitrariness of after-impact velocities is solved by releasing the impenetrability condition as an internal constraint of the bodies and by allowing for elastic deformations at contact during an impact of finite duration. In this paper, the latter goal is achieved by interposing a concentrate spring between a beam and a rod at their contact point, simulating the deformability of impacting bodies at the interaction zones. A reliable and convenient method for determining impact forces is also presented. An example of engineering interest is carried out: a flexible beam that impacts on an axially deformable strut. The solution of motion under a harmonic excitation of the beam built-in base is found in terms of transverse and axial displacements of the beam and rod, respectively, by superimposition of a finite number of modal contributions. Numerical investigations are performed in order to examine the influence of the rigidity of the contact spring and of the ratio between the first natural frequencies of the beam and the rod, respectively, on the system response, namely impact velocity, maximum displacement, spring stretching and contact force. Impact velocity diagrams, nonlinear resonance curves and phase portraits are presented to determine regions of periodic motion with impacts and the appearance of chaotic solutions, and parameter ranges where the functionality of the non-structural element is at risk.     

SI-Traceable Spring Constant Calibration of Microfabricated Cantilevers for Small Force Measurement

A variety of methods exist to measure the stiffness of microfabricated cantilever beams such as those used as mechanical sensors in atomic force microscopy (AFM). In order for AFM to be used as a quantitative small force measurement tool, these methods must be validated within the International System of Units (SI). To this end, two different contact techniques were used to calibrate the spring constant of a cantilever beam. First, a dynamic indentation-based method was used to measure the spring constant of a rectangular cantilever beam. These results were then compared against an SI-traceable spring constant measurement from an electrostatic force balance (EFB). The measurements agree within experimental uncertainty and within 2% for spring constants greater than 2 N/m. The use of this cantilever beam as a transfer artifact for in situ AFM cantilever calibration was then evaluated in comparison to the thermal calibration method. Excellent agreement is seen between these techniques, establishing the consistency of the thermal and dynamic indentation methods with SI-traceable contact cantilever calibration for the rectangular cantilever geometry tested. Disclaimer: This article is authored by employees of the U.S. federal government, and is not subject to copyright. Commercial equipment and materials are identified in order to adequately specify certain procedures. In no case does such identification imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the materials or equipment identified are necessarily the best available for the purpose.