切向荷载下弹塑性材料的微观位移特性

Fujimoto(2000)研究了受切向荷载作用的微凸体在完全弹性接触或完全塑性接触条件下的微观位移特性。而实际大多数微凸体在法向荷载作用下,因材料的弹塑性性质导致其接触是很难达到完全弹性接触或完全塑性状态的。因此,如何解决切向荷载作用下处于弹塑性接触状态的微凸体的微观位移特性就显得非常重要。作者以Fujimoto模型为基础,结合Cattaneo和Mindlin理论,研究了切向荷载作用下处于弹塑性接触状态微凸体的摩擦力-微观位移关系,并给出了一个计算实例,显示该文理论模型的合理性。     

An elastic mechanics model and computation method for geotechnical material

岩土材料内摩擦性质是岩土的基本力学性质之一,无论岩土处于何种受力状态,都应考虑岩土体的内摩擦力。然而,至今只有岩土极限分析与塑性力学中考虑岩土体的内摩擦力,而在弹性理论与能量理论等诸方面均未体现。认为岩土体无论是处于塑性状态还是弹性状态,都存在着内摩擦力,为此建立岩土材料弹性力学的摩擦体力学单元。基于土体试验提出黏聚力先发挥,摩擦力随变形逐渐发挥,并假设摩擦因数与应变成正比,由此确定摩擦力的计算,最后仿效线弹性力学计算方法,但此时摩擦体的剪切模量G已非常数,从而形成摩擦体的非线性弹性力学计算方法。算例表明,按该方法计算出的弹性地基上的位移和剪应力小于传统方法计算出的位移和应力值,这比较符合实际情况,表明采用摩擦体力学单元对岩土材料是合适的。     

岩土动力极限应变判据在边坡稳定分析中的应用

岩土材料受力从弹性进入塑性,最终发展到破坏,材料的屈服与破坏不同,屈服表示材料从弹性进入塑性状态,破坏表示从塑性发展到工程失稳。对于理想弹塑性材料,应力表述的判据难以区分屈服与破坏,为此提出采用极限应变作为岩土材料的破坏判据。给出了岩土材料动力极限应变的求解模型与方法,并以动力极限应变作为破坏准则,它既可以表述动力作用下材料的点破坏或开裂破坏,当点破坏贯通形成破坏面时,还可以表述材料整体破坏。通过地震作用下动力边坡工程算例,得到边坡滑体起裂的位置、演化过程和起裂极限荷载;当边坡中极限应变区贯通时得到边坡整体破坏极限荷载,并与数值极限分析中(超载法、强度折减法)采用位移不收敛破坏准则的计算结果比较,基本一致,验证了极限应变法在动力分析中的可行性。     

基于分形理论的两粗糙表面接触的黏滑摩擦模型EI北大核心CSCD

两粗糙表面的接触本质上是大量微凸体的接触,具有复杂的力学行为,连接界面的力学建模是重要的科学问题。从微观角度出发,对单个微凸体进行接触分析,并考虑了微凸体相互作用造成的基底面的下降,根据分形理论积分,建立了整个接触面的法向接触模型。利用该模型,可确定在给定法向预紧载荷下微接触截面积的概率密度函数;根据Mindlin模型、Masing准则和分形理论,建立了两粗糙表面接触的切向载荷与切向位移的关系,并研究了不同参数对系统能量耗散的影响。数值仿真结果表明,能量耗散随分形维数D增大而增大,随分形粗糙度参数G及法向预紧力增大而降低。     

切向加载、卸载和振荡强耦合下机床螺栓结合部之摩擦能量耗散机制

在保持微凸体受法向力恒定的状态下,侧重导出切向力和变形量的切向加载、切向卸载和切向振荡接触方程。当2个球形微凸体接触时,构建每循环中切向接触摩擦能量耗散力学模型。按照赫兹静力弹性法向接触理论,得到微凸体顶端曲率半径。根据微凸体分担法向力的光滑性与连续性法则,校正临界弹性变形微接触面积与临界变形量的数学表达式。面向有条件等式,在弹性和纯塑性变形基础上,建立整个结合部法向力与切向接触摩擦能量耗散的理论模型。以北京机电院高技术股份有限公司直线电机驱动Linear MC6000普莱诺五面体加工中心上的龙门横梁-导轨螺栓结合部为研究对象,分析法向预紧力、表面粗糙轮廓分形维数、切向力、分形粗糙度、相关因子、单轴向屈服应变及静摩擦因数等7个相对独立参数对切向接触摩擦能量耗散的影响规律。可视化的数值分析结果表明:切向接触摩擦能量耗散随着法向预紧力的增大先增大后减小;表面粗糙轮廓分形维数在较小范围内,切向接触摩擦能量耗散随着表面粗糙轮廓分形维数或分形粗糙度的增大而增大;表面粗糙轮廓分形维数在较大范围内,切向接触摩擦能量耗散随着表面粗糙轮廓分形维数或分形粗糙度的增加而减小;切向接触摩擦能量耗散随着切向力、相关因子、单轴向屈服应变的增加而加大;切向接触摩擦能量耗散随着静摩擦因数的增加而降低与经典结论完全相反,这是因为当静摩擦因数较大时,根据近代分形几何理论可知法向预紧力越大,微滑趋势将更小,导致较小切向接触摩擦能量耗散。     

颗粒弹塑性碰撞理论模型

以Hertz弹性接触力学为基础,假设材料为弹塑性强化材料,并考虑接触压力作用下颗粒球体接触面上材料进入塑性阶段后的应力调整与释放,提出了一种新的颗粒弹塑性接触理论。以此为基础,在准静态假设的基础上,研究了颗粒间的弹塑性碰撞问题,推导了相应的计算公式,并与其它弹塑性接触模型进行了比较。结果表明:按照该文模型预测的荷载变位曲线介于Hertz弹性解和Thornton解之间;强化系数越高,荷载变位曲线越接近Hertz弹性解,强化系数越低,越接近Thornton解,Thornton模型为该文模型的一个特例。在颗粒弹塑性碰撞过程中,本文理论预测的冲击力远远小于Hertz弹性解的预测结果,更与实际情况相符。     

巴西圆盘中心裂纹摩擦接触问题的逐点Lagrange乘子法

采用逐点Lagrange乘子法求解巴西圆盘中心裂纹在压剪荷载作用下裂纹面可能发生的摩擦接触问题。为了避免传统的Lagrange乘子法中总刚度阵求逆的困难,将Lagrange乘子逐点转到局部坐标系下,采用Gauss-Seidel迭代法求解法向和切向乘子,同时注意在求解的过程中对切向乘子约束修正,待所有点乘子求解完成后再变换到整体坐标系下迭代求解位移。与传统接触算法相比,该算法无需对总刚度阵求逆,降低了求解规模,提高了计算效率。通过该方法计算了巴西圆盘中心裂纹两种典型情况下的应力强度因子,计算结果与文献比较,吻合良好。考虑不同荷载角和裂纹长度对位移,应力强度因子和接触区的影响,并对不同摩擦系数下应力强度因子的影响进行了分析。结果表明:忽略裂纹接触摩擦作用,应力强度因子可能被高估。     

含硬涂层结构的表面微观接触新模型

为研究含有硬涂层的粗糙表面中微凸体和基体变形对表面微观接触特性的影响规律,利用Hertz接触理论分别求出微凸体和基体的接触刚度,利用不动点迭代法确定微凸体变形量,建立关于微凸体接触变形量的刚度模型,通过并联关系耦合接触刚度,建立新的接触表面微观接触模型。为验证新模型对含有硬涂层的粗糙表面接触特性描述的正确性,建立了不同大小和不同材料的单微凸体有限元模型,通过与Hertz模型、有限元分析结果比较,发现当基体材料和微凸体材料不同时,微凸体/基体系统的应力分布会不均匀,微凸体表面的接触力比材料相同时的接触力小,最大应力比材料相同时的最大应力大;在变形量很小的时候,Hertz模型解和新模型解都很好地与有限元分析结果相吻合,随着变形量的变大,有限元分析解和新模型解开始同时偏离Hertz模型解,但新模型解一直趋近于有限元分析解。     

一种考虑尺寸效应的颗粒材料流变模型及其验证

经典连续介质理论的粘塑性本构关系缺乏材料尺度的相关性,难以表征颗粒材料流变的尺寸效应,而Cosserat连续体中的内禀特征长度为刻画材料的尺寸效应提供了一种可能途径。该文旨在Cosserat连续体的理论框架下发展Perzyna粘塑性模型,以探讨颗粒材料流变的尺寸效应与影响机制。首先基于Drucker-Prager屈服准则导出了Cosserat连续体粘塑性模型的一致性算法,获得了过应力本构方程积分算法与一致切向模量的封闭形式,并在ABAQUS二次平台上采用用户自定义单元(UEL)予以程序实现。有限元数值算例模拟了软岩试样的三轴压缩蠕变和两种堆石料试样在常规三轴条件下的蠕变和应力松弛,数值预测结果与相应试验结果具有较好的一致性,表明该流变模型的适应性。同时,将颗粒的球型指数、圆度和平均粒径作为表征颗粒材料内禀特征长度的一种度量,以反映颗粒材料的试样尺寸及其颗粒粒径与形状对流变过程中的轴向应变、偏应变和偏应力的影响关系,表明所发展的流变模型可以捕捉颗粒材料流变行为的压力相关性和尺寸效应。     

考虑材料的拉压模量不同及应变软化特性的柱形孔扩张问题

建立了拉压模量不同及应变软化特性材料的柱形孔扩张理论。对于岩土类材料,提出用a及b分别作为拉压模量不同和软化特征的控制参数,运用不同模量弹性理论及应力跌落软化模型推导了Tresca和Mohr-Coulomb材料柱形圆孔扩张问题的应力及位移解。分析了不同模量及软化特性材料对柱形孔扩张的影响,结果表明:圆孔极限扩张压力,塑性区的发展规律,应力场,位移场等均随着模量参数a和软化系数b的变化而变化,因此若采用经典的弹性理论及传统的不考虑应变软化来对岩土类的工程材料进行设计计算,必会带来较大的误差。     

Analysis of the apparent friction of polymeric surfaces

The apparent friction coefficient is the ratio between the tangential force and the normal load applied to moving body in contact with the surface of a material. This coefficient includes a so-called “true local friction” at the interface and a “geometrical friction” which is the ploughing effect. The material underneath a moving tip may display various types of behaviour: elastic, elastic–plastic where elastic and plastic strain are present in the contact area, or fully plastic. As is usual in polymers, the material behaviour is time and temperature dependent and may exhibit strain hardening. A surface flow line model of a scratching tip which links the apparent friction to the local friction and contact geometry was recently proposed. An inverse analysis is used in the present work to estimate the local friction from the measured apparent friction and a knowledge of the contact area and tip shape. The polymer true friction coefficient displays temperature and sliding speed dependency, which may be attributed to the surface thermodynamics. It is shown that the local friction depends on the level of strain in the polymer at the contact interface.     

静动力弹塑性分析的杆系离散单元计算理论研究

杆系离散单元法的现有研究成果均假定接触本构模型的切向弹簧仅用于描述剪力引起的纯剪切变形,这与弯曲梁理论下剪力引起的变形情况不相符。该文针对该问题重新定义了切向弹簧,并根据能量等效原理系统推导了不考虑或考虑剪切变形工况接触本构模型的切向接触刚度系数计算公式。在此基础上,提出了杆系离散单元精细塑性铰法以描述结构的塑性开展问题,推导了颗粒间的弹塑性接触本构模型。采用自编程序对两个大型网壳结构分别进行了静、动力弹塑性行为分析,验证了接触本构模型正确性和精细塑性铰法的适用性。该文将杆系离散单元法的基本计算理论系统化,并补充了杆系离散单元法的弹塑性计算理论,为结构静、动力分析提供了新思路。     

Discrete element simulation of railway ballast: modelling cell pressure effects in triaxial tests

The paper investigates reproducing the effects of confining pressure on the behaviour of scaled railway ballast in triaxial tests in discrete element models (DEM). Previous DEM work, using a standard Hertzian elastic contact law with an elastic–perfectly plastic tangential slip model, has been unable to replicate the behaviour observed in laboratory tests across a range of confining pressures without altering both the material stiffness and the inter-particle friction. A new contact law modelling damage at the contacts between particles is introduced. Particle contact is via spherically-capped conical asperities, which reduce in height if over-stressed. This introduces plasticity to the behaviour normal to the contact surface. In addition, the inter-particle friction angle is varied as a function of normalized contact normal force. At relatively low normal forces the friction angle must be increased for peak mobilized friction angles to match the laboratory data, an effect that is attributed to interlocking at the scale of surface roughness. Simulation results show close agreement with laboratory data.     

土与结构接触面土体软/硬化本构模型及数值实现

基于土与结构接触面变形特性分析,将接触面土体的剪切滑动面与单元体三维应力状态下的八面体面相对应,通过土的三维弹塑性本构模型在八面体面上的剪切应力-应变关系,建立了接触面土体剪切应力-应变关系;将接触面土体法向压缩变形与侧限压缩条件相对应,通过侧限压缩条件下的荷载变形关系,建立了接触面土体法向应力-应变关系;进一步将接触面土体切向与法向耦合,建立了接触面土体本构模型,模型只有4个材料参数,参数物理意义明确,可由等向压缩试验和常规三轴压缩试验确定。与接触面土体试验结果的对比分析表明,所建立的本构模型可较好地描述接触面土体切向软/硬化特性与法向变形规律。结合有限元软件ABAQUS,编制了FRIC模型子程序,通过模拟土与结构界面剪切滑移过程表明,编制的FRIC子程序可较好地模拟土与结构界面接触的非线性力学行为。     

Modeling of hot isostatic pressing of metal powder with temperature–dependent cap plasticity model

In this paper, the coupled thermo–mechanical simulation of hot isostatic pressing (HIPing) is presented for metal powders during densification process. The densification of powder is assumed to occur due to plastic hardening of metal particles. The constitutive model developed is used to describe the nonlinear behavior of metal powder. The numerical modeling of hot powder compaction simulation is performed based on the large deformation formulation, powder plasticity behavior, and frictional contact algorithm. A Lagrangian finite element formulation is employed for the large powder deformations. A modified cap plasticity model considering temperature effects is used in numerical simulation of nonlinear powder behavior. The influence of powder-tool friction is simulated by the use of penalty approach in which a plasticity theory of friction is incorporated to model sliding resistance at the powder-tool interface. Finally, numerical examples are analyzed to demonstrate the feasibility of the proposed thermo–mechanical simulation using the modified cap plasticity model in the hot isostatic forming process of powder compaction.     

多体系统斜碰撞动力学中的结构柔性效应

本文针对重力场下作大范围回转运动的柔性梁与一固定斜面发生斜碰撞的情况,建立起系统含碰撞的一致线性化的动力学方程。根据Ｈｅｒｔｚ接触理论和线性切线接触刚度建立碰撞接触模型。针对结构不同刚度的情况进行了仿真计算,由仿真算例的计算结果可以看出,结构的柔性对碰撞过程中的微运动具有明显的作用,同时对降低由于碰撞而引起的能量损耗和减少碰撞作用力起到一定的效果。     

考虑驱动和负载状态的三自由度超声电机接触模型研究

建立了一种考虑不同运转情况的对于三定子多自由度超声电机的接触模型。介绍了三自由度超声电机的基本原理和结构并计算得出了其驱动转矩,引入Hertz接触理论和Mindlin理论对摩擦情况进行分析,考虑了摩擦因数的动态非线性和摩擦力分布的非线性变化,提出了一种新型的接触模型,改进了传统的线性摩擦模型;通过转矩关系和摩擦模型对电机不同运动情况下摩擦力分布进行分析,并用Matlab绘制相应的摩擦力分布图。分析结果验证了三自由度超声电机合理性,说明了三相压电定子接触状态根据驱动情况和负载而定,为进一步的优化设计和性能改进奠定了基础。     

Internal-variable constitutive model for rate-independent plasticity with hardening saturation surface

Summary An elastic-plastic material model with internal variables and thermodynamic potential, not admitting hardening states out of a saturation surface, is presented. The existence of such a saturation surface in the internal variables space — a consequence of the boundedness of the energy that can be stored in the material's internal micro-structure — encompasses, in case of general kinematic/isotropic hardening, a one-parameter family of envelope surfaces in the stress space, which in turn is enveloped by a limit surface. In contrast to a multi-surface model, noad hoc rules are required to avoid the intersection between the yield and bounding/envelope surface. The flow laws of the proposed model are studied in case of associative plasticity with the aid of the maximum intrinsic dissipation theorem. It is shown that the material behaves like a standard one as long as its hardening state either is not saturated, or undergoes a desaturation from a saturated hardening state, whereas, for saturated hardening states not followed by desaturation, it conforms to a combined yielding law in which the static internal variable rates obey a nonlinear hardening rule similar to that of analogous models of the literature. Additionally, the material is shown to behave as a perfectly plastic material for a class of (critical) saturated hardening states for which the stress state is on the limit surface. For nonassociative material models, it is shown that, under a special choice of the plastic and saturation potentials and through a suitable parameter identification, the well-known Chaboche model is reproduced. A few numerical examples are presented to illustrate the associative material response under monotonic and cyclic loadings.Dedicated to Prof. Dr. Dr. h. c. Franz Ziegler on the occasion of his 60th birthday