应力波对滑移弱化断层的动态触发作用

将断层简化为满足线性滑移弱化摩擦准则的理想裂纹界面。在考虑初始应力的条件下,研究了应力波通过两个相互接触的弹性半空间时的透射和反射关系。在此基础上,得出了应力波扰动断层时的初始滑移条件和不稳定滑移条件,并分析了断层动态触发与扰动应力波、断层特性和初始状态等因素的关系。当入射角一定时,入射波频率越高,所需振幅越大;断层的临界滑移越大,断层越稳定,扰动应力波所需振幅越大。     

纳米硬度实验中的多位错生成分析

本文利用边界单元法及基于Peierls-Nabarro模型的位错理论，分析了理想纳米触头下多位错的生成，得到了滑移面上多位错的构形以及表面位移与载荷的关系曲线。根据得到的计算结果分析了薄膜厚度的影响，得到了与已有实验结果相同的结论。通过把表面看成一个包含在无穷大弹性体中的无穷大弹性体中无穷大裂纹来考虑表面的影响，从而可以直接采用已有的边界积分方程。该方法在连续介质力学的计算中引入了包含原子信息的层间势能函数，为分析多尺度的力学问题提供了有效的方法。     

一般各向异性单侧接触界面上波的反射和折射

研究简谐弹性波在一般各向异性介质单侧接触界面上的反射和折射问题．利用Fouier分析方法将非线性Coulomb摩擦接触边界波动问题化为一组代数方程．给出了确定局部分离、滑移和粘着区的思路和方法及各区域的解；讨论了出现界面局部分离和滑移的条件．对特定材料组合情况进行了详细数值计算，给出了界面力、相对滑移速度、张开位移、高频谐波的反射折射系数等特征参量；考察了平面和反平面波动的耦合及整体滑移等．其中关于高频谐波的结果可对已有实验结果给出很好的定性解释．在大多数情况下，即使对摩擦系数无穷大的粘滞接触界面，分离区端部也总是存在一个很小的滑移区。     

型钢轻骨料混凝土粘结滑移本构关系研究

本文研究了型钢与轻骨料混凝土的局部粘结滑移本构关系. 在型钢表面刻槽贴应变片,并在与型钢应变片对应位置的混凝土表面贴应变片,由试验结果和分析：得到了型钢表面粘结应力沿锚固长度的负指数分布函数;绘制了局部滑移分布曲线;给出了加载端局部粘结滑移本构关系. 局部最大粘结应力主要与混凝土强度、配箍率、混凝土相对保护层厚度有关. 引入粘结滑移本构关系的型钢轻骨料混凝土梁有限元分析结果和试验结果吻合较好.     

干摩擦支承边界梁的非线性振动分析

研究梁具有纵向干摩擦边界条件时非线性振动。干摩擦力本构关系分别为粘住—滑动状态、瞬态滑动状态、粘住状态三种情形描述。首先由Ｈａｍｉｌｔｏｎ原理建立梁的动力学方程及其干摩擦力的边界条件，然后借助于Ｇａｌｅｒｋｉｎ法转化得到非线性常微分方程。采用谐波平衡原理进行系统的基波稳态响应求解，并讨论解的稳定性条件。数值计算利用ｔｕｒｂｏ－Ｃ语言在微机上完成，由此得到摩擦力参数改变时几种典型的频响特性曲线。     

应力波作用下颗粒介质的动力特性研究

运用微结构连续介质力学和多刚体系统动力学的理论方法，考虑了颗粒体的拓扑结构及颗粒体之间的局部非线性相互作用，通过引进恢复系数，导出了适合于大变形运动（包括平动和转动）情况下，颗粒体间的滑移和分离的宏观弹塑性本构关系。最后，还给出了几种规则排列条件下，颗粒介质的本构关系。     

数值仿真轴向运动黏弹性梁非线性参激振动

分别通过两种直接数值方法研究速度变化的经典边界条件下轴向运动黏弹性梁参数振动的稳定性。在控制方程的推导中,采用物质导数黏弹性本构关系和只对时间取偏导数的黏弹性本构关系;分别运用有限差分法和微分求积法对两种经典边界下轴向变速运动黏弹性梁的非线性控制方程求数值解,计算得到梁中点非线性参数振动的稳定稳态响应。数值结果表明,两种黏弹性本构关系对应的稳态响应存在明显差别,同时发现两种直接数值方法的仿真结果基本吻合,证明数值仿真具有较高精度。     

单侧摩擦接触约束夹杂物与平面波的动力相互作用--时域边界元分析

应用时域边界元法研究了瞬态平面波对单侧摩擦约束夹杂物的散射问题，假设界面摩擦遵守库仑定理，当入射波足够强时界面会出现局部分离和滑移，由于边界上的区域(分离区、滑移区和粘着区)是未知的，所以该问题实际上是个复杂的边界非线性问题，为了确定未知区域，该文发展了一种有效的迭代技术，作为算例，计算了一个无限域中圆柱埋置夹杂物对瞬态平面波的散射问题。     

钢－混凝土组合梁非线性有限元分析

提出了部分剪力连接钢-混凝土组合梁非线性有限元分析的简化模型，该模型同时考虑了钢、混凝土材料的非线性本构关系和剪力连接件的滑移非线性对组合梁刚度和强度的影响，推导了考虑滑移的剪力连接件单元刚度矩阵。利用该模型计算了连续组合梁的极限荷载、挠度、应力以及滑移，与已有的理论计算结果和实验结果吻合，证明本方法分析钢-混凝土组合梁非线性的可靠性和实用性。     

基于能量守恒理论的带肋钢筋-混凝土粘结滑移本构关系研究

针对钢筋-混凝土粘结滑移的劈裂破坏模式,将整个破坏过程分为未开裂的弹性阶段和带裂缝阶段。弹性阶段采用弹性厚壁圆筒模型,带裂缝阶段采用考虑混凝土软化特性的厚壁圆筒模型。基于这两种模型,研究了粘结滑移劈裂破坏过程的能量变化规律,推导出了两种模型的能量计算公式。利用能量守恒定律建立了钢筋-混凝土粘结滑移本构关系的微分方程,并通过数值积分方法得到了粘结滑移本构模型。该本构模型能够体现混凝土与钢筋材料参数和几何参数的影响,对不同形状的粘结滑移关系曲线具有较好的适应性。最后,将得到的本构关系与文献的试验结果进行对比,并分析了各参数的变化规律。     

Nucleation of partial dislocations at a crack and its implication on deformation mechanisms of nanostructured metals

Nucleation of partial dislocations at a crack is analyzed based a multiscale model that incorporates atomic information into continuum-mechanics approach. The crack and the slip plane as the extension of the crack are modeled as a surface of displacement discontinuities embedded in an elastic medium. The atomic potential between the adjacent atomic layers along the slip plane is assumed to be the generalized stacking fault energy, which is obtained based on atomic calculations. The relative displacements along the slip plane, corresponding to the configurations of partial dislocations and stacking faults, are solved through the variational boundary integral method. The energetics of partial dislocation nucleation at the crack in FCC metals Al and Cu are comparatively studied for their distinctive difference in the intrinsic stacking fault energy. Compared with nucleation of perfect dislocations in previous studies, several new features have emerged. Among them, the critical stress and activation energy for nucleation of partial dislocations are markedly lowered. Depending on the value of stacking fault energy and crack configuration, the saddle-point configurations of partial dislocations can be vastly different in terms of the nucleation sequence and the size of the stacking fault. These findings have significant implication for identifying the fundamental dislocation and grain-boundary-mediated deformation mechanisms, which may account for the limiting strength and the high strain rate sensitivity of nanostructured metals.     

Direct simulation of multiphase flows with modeling of dynamic interface contact angle

We describe a modeling technique for dynamic contact angle between a phase interface and a solid wall using a generalized Navier boundary condition in the context of a front-tracking-based multiphase method. The contact line motion is determined by the generalized Navier slip boundary condition in order to eliminate the infinite shear stress at the contact line. Applying this slip boundary condition only to the interface movement with various slip ratios shows good agreement with experimental results compared to allowing full fluid slip along the solid surface. The interface slip model performs well on grid convergence tests using both the slip ratio and slip length models. A detailed energy analysis was performed to identify changes in kinetic, surface, and potential energies as well as viscous and contact line dissipation with time. A friction coefficient for contact line dissipation was obtained based on the other computed energy terms. Each energy term and the friction coefficient were compared for different grid resolutions. The effect of varying the slip ratio as well as the contact angle distribution versus contact line speed was analyzed. The behavior of drop impact on a solid wall with different advancing and receding angles was investigated. Finally, the proposed dynamic contact model was extended to three dimensions for large-scale parallel calculations. The impact of a droplet on a solid cylinder was simulated to demonstrate the capabilities of the proposing formulation on general solid structures. Widely different contact angles were tested and showed distinctive characteristic behavior clearly.     

Boundary conditions of gas dynamic slip on a rough surface

The phenomenon of gas dynamic slip associated with the flow of a monatomic, slightly rarefied gas over a rough surface is investigated. It is assumed that the characteristic dimensions of the roughness are comparable with the molecular mean free path. It is shown that if there is anisotropy of the surface shape the relation between the slip velocity and the friction stress vector becomes tensorial. In this case for almost any orientation of the gas dynamic flow the so-called cross slip effect is observed. The symmetry of the slip coefficient matrix is proved for fairly general assumptions concerning the type of roughness, the law of reflection of molecules from the surface, and the law of intermolecular interaction. The components of the slip coefficient matrix are calculated by a variational method for a corrugated model of the roughness.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 180–184, January–February, 1987.     

The boundary element method applied to elastic contact problems with friction

In the current paper the boundary integral equations (BIE) for elastic contact problems with friction are derived from the incremental virtual work principle. After introducing contact conditions of adhesion and slip into BIE all variants on boundary are made to discretize by quadratic isoparametric boundary element. In the current paper not only an auto-increment loading law is presented but also the iterative calculation laws for open, slip and adhesion condition are given. The results of numerical examples are satisfactory.     

Simulations of magnetorheological suspensions in Poiseuille flow

Particle-level simulations are conducted to study magnetorheological fluids in plane Poiseuille flow. The importance of the boundary conditions for the particles at the channel walls is examined by considering two extreme cases: no friction and infinite coefficient of friction. The inclusion of friction produces Bingham fluid behavior, as commonly observed experimentally for MR suspensions. Lamellar structures, similar to those reported for electrorheological fluids in shear flow, are observed in the post-yield region for both particle boundary conditions. The formation of these lamellae is accompanied by an increase in the bulk fluid velocity. The slip boundary condition produces higher fluid velocities and thicker lamellar structures.     

DTM-BF method and dual solutions for unsteady MHD flow over permeable shrinking sheet with velocity slip

An unsteady magnetohydrodynamic (MHD) boundary layer flow over a shrinking permeable sheet embedded in a moving viscous electrically conducting fluid is investigated both analytically and numerically. The velocity slip at the solid surface is taken into account in the boundary conditions. A novel analytical method named DTMBF is proposed and used to get the approximate analytical solutions to the nonlinear governing equation along with the boundary conditions at infinity. All analytical results are compared with those obtained by a numerical method. The comparison shows good agreement, which validates the accuracy of the DTM-BF method. Moreover, the existence ranges of the dual solutions and the unique solution for various parameters are obtained. The effects of the velocity slip parameter, the unsteadiness parameter, the magnetic parameter, the suction/injection parameter, and the velocity ratio parameter on the skin friction, the unique velocity, and the dual velocity profiles are explored, respectively.     

Use of a modified torsional Kolsky bar to study frictional slip resistance in rock-analog materials at coseismic slip rates

The knowledge of shear resistance in earth faults is of fundamental importance to our understanding of the magnitude of stress drop and the associated energy release during typical seismic rupture events. In the present study a modified torsional Kolsky bar is employed to investigate frictional slip resistance in rock-analog materials (i.e., quartz and soda lime glass) at normal stresses of relevance to earthquake physics (30–80 MPa) and co-seismic slip rates. The results indicate the coefficient of kinetic friction to be in the range of 0.2 to 0.3. These values of the coefficient of friction are much lower when compared to those obtained in rocks at quasi-static slip rates. In all experiments slip weakening is observed and is preceded by slip strengthening. The slip weakening is understood to be due to thermal weakening induced by flash-heating at asperity contacts and requires a few mm of slip to be effective; the slip strengthening is understood to be due to an increase in the real area of contact at the asperity junctions due to localized plastic flow and subsequent coalescence and solidification of local softened/melt patches at the slip interface.     

Nonlinear sloshing of liquid in rigid cylindrical container with a rigid annular baffle: free vibration

In this paper, the free nonlinear sloshing of liquid in a rigid partially liquid-filled cylindrical container with a rigid annular baffle is investigated. The liquid domain is firstly divided into four simple sub-domains so that the liquid velocity potential in each sub-domain has continuous boundary conditions of class \(\hbox {C}^{1}\) . Then, based on the Bateman–Luke variational principle, the equivalent variational formulation of the free boundary problem for the liquid in a baffled container is derived. By introducing the generalized time-dependent coordinates, the surface wave height and the velocity potential are expanded in the form of generalized Fourier series. Substituting the series expression of surface wave height and velocity potential into the variational formulation enables us to obtain the infinite dimensional modal system. Finally, based on the Moiseev asymptotic relations, the infinite dimensional modal system is reduced to a finite dimensional modal system. Good agreements have been achieved by comparing the present results with those obtained from the Gavrilyuk’s solutions. The effects of baffle parameters and initial conditions on the nonlinear sloshing of liquid are discussed in detail.     

Invariant Boundary‐Value Problems of an Optimally Controlled Boundary Layer

The group properties of equations of the variational problem on finding a continuous law for velocity distribution of liquid injection into an incompressible laminar boundary layer in a planar case, which ensures the minimum friction force acting on the airfoil, are considered. It is shown that the optimal injection velocity on a wedge with x=0 is finite.