走滑式断层地震的折迭突变模型

利用过势函数微分形式的途径,计入远场外力功的影响,对走滑式断层地震机制进行分析．研究表明:突变理论中折迭突变模型展示的性状,与走滑式断层地震的主要特征之间一一对应．折迭突变可对包括震前、震后围岩-断层系统稳定性描述在内的断层失稳起、终点位置、断层失稳错距等作出描述．给出3种性状可相互印证的断层失稳围岩弹性能释放量图解．走滑式断层地震强度与围岩压力及围岩断层的刚度比等有关,围岩压力大、刚度比小、主切应力轴与发震断层面夹角大,则地震强度大．     

弹性应力波的双脉冲结构与平板冲击试验验证

对传统弹性应力波理论以及平板冲击下的应力波传播提出了重要修正.现有的弹性应力波理论在旋转运动以及与内力的对应关系、波动方程等方面存在理论缺失和不完备性.提出弹性体存在体积波和偏斜波,体积波可独立传播但偏斜波受体积波的影响,两种波构成一个弱耦合波系.平板冲击应为三维应变状态,体应变和偏应变两个波动变量依然保持二阶张量状态,但独立的波动变量可简化为一个体应变和一个偏斜主应变,波动方程简化为关于两个波动变量的弱耦合波动方程组.应力波的界面效应涉及了冲击加载面上应力波的激发和应力波在自由面上的反射,建立了加载面和自由面上边界条件与波动变量的依赖关系.冲击加载面上同时激发出体积波和偏斜波,但体积波与部分偏斜波组成一个以较快速度传播的复合脉冲,剩余偏斜波形成另一个以较慢速度传播的偏斜脉冲.两个入射脉冲在自由面上分别反射回来结构相同的复合脉冲和偏斜脉冲,即形成4个反射脉冲的传播.应力波的双脉冲结构与平板撞击下试件自由面速度的二次压缩现象是一致的,10发不同厚度的氧化铝平板冲击试验测得的二次压缩信号验证了偏斜脉冲的理论预测.     

形状记忆合金相变过程三维大变形有限元模拟

形状记忆合金（SMA）一直被作为智能材料开发,并被用于阻尼器、促动器和智能传感器元件．形状记忆合金（SMA）的一项重要特性,是它具有恢复在机械加卸载周期下产生的大变形而不表现出永久变形的能力．该文旨在介绍一种由应力产生的相变且可以描述马氏体和奥氏体之间的超弹性滞回环现象本构方程．形状记忆合金的马氏体系数假设为应力偏张量的函数,因此形状记忆合金在相变过程中锁定体积．本构模型是在大变形有限元的基础上执行的,采用了现时构型Lagrange大变形算法．为了方便地使用Cauchy应力和线性应变本构关系,使用了与旋转无关的Jaumann应力增率计算应力．数值分析结果表明,相变引起的超弹性滞回环可以有效地通过该文提出的本构方程和大变形有限元模拟．     

粘-弹性介质中渗流的有限元法分析

R.S.Sandhu和E.L.Wilson提出了弹性介质中渗流分析的有限元法[1],可以用来分析较复杂的工程问题,本文将此方法推广到粘-弹性介质情况.当土骨架是粘-弹性介质时,应力与应变的关系随时间变化,增加了问题的复杂性.本文提出了折算弹性张量的概念,即当有限元法计算中的时间间隔Δt预先给定时,在此间隔内应力增量和应变增量可以近似表示为线性关系.这些线性比例常数将称为折算弹性张量.Sandhu和Wilson方法仅能用于弹性介质情况,根据折算张量概念,本文方法适用范围推广到粘-弹性介质情况.     

冲击压缩下陶瓷材料中的破坏波模型

从多晶陶瓷材料细观结构非均匀性及其导致的应力奇异性分析出发,建立了陶瓷材料在冲击压缩下的本构关系,以及以表征材料损伤和破坏的非弹性体积应变为传播特征的破坏波控制方程,破坏层的非弹性体积应变包括由微裂纹成核、扩展引起的膨胀体积应变和由气孔塌陷引起的压缩体积应变两部分．结合92.93%氧化铝陶瓷板碰撞试验,数值模拟了冲击压缩下陶瓷材料中破坏波的传播过程,并对跨越破坏波阵面应力历程和剪切强度的变化规律进行了分析．     

饱和土体自重固结问题的相似解

采用了比以往更为普遍的土体物理力学性质假设,利用Hopf-Cole变换方法求得了厚层土体在自重应力作用下的非线性固结问题的完整解析解答．通过试验数据,将该解答与传统的大应变线性固结理论解答和基于实验数据的有限元数值解答相比较,结果表明,该解答能够更好地描述土体的实际固结过程,而由线性化固结理论所得的解答对固结过程中的沉降量和固结度的估计偏小．     

立方准晶材料的剪切裂纹问题

通过引入位移函数,使得立方准晶的轴对称弹性问题归结为求解一个高阶偏微分方程.在此基础上,研究了立方准晶含有圆盘状裂纹的剪切问题,得到了此问题弹性场的精确解析解,以及应力强度因子与应变能释放率.     

圆形硐室岩爆机制及其突变理论分析

硐室岩爆机制是围岩中处于极限状态的塑性变形集中区承载能力下降时,其中完好岩体部分以弹性方式卸载,当后者释放的弹性能超过前者形变耗散的能量时便发生岩爆．以岩体等效应变为状态变量,建立了硐室岩爆的突变模型,给出岩爆释放地震能计算式．分析表明: 岩爆发生条件与岩体的升降模量比及岩体裂隙发育程度有关;对于特定冲击倾向的岩体,存在相应的临界软化区深度,当满足岩爆发生条件,且软化区深度达到临界深度时会发生岩爆．     

单轴拉伸条件下细观非均匀性岩石损伤局部化和应力应变关系分析

岩石在拉应力状态下的力学特性不同于压应力状态下的力学特性．利用细观力学理论研究了细观非均匀性岩石拉伸应力应变关系包括:线弹性阶段、非线性强化阶段、应力降阶段、应变软化阶段.模型考虑了微裂纹方位角为Weibull分布和微裂纹长度的分布密度函数为Rayleigh函数时对损伤局部化和应力应变关系的影响,分析了产生应力降和应变软化的主要原因是损伤和变形局部化.通过和实验成果对比分析验证了模型的正确性和有效性．     

Ⅰ阶梯度损伤理论

从热力学基本定律出发,将应变张量、标量损伤变量、损伤梯度作为Helmholtz自由能函数的状态变量,利用本构泛函展开法在自然状态附近作自由能函数的Taylor展开,未引入附加假设,推导出Ⅰ阶梯度损伤本构方程的一般形式．该形式在损伤为0时可退化为线弹性应力-应变本构方程,在损伤梯度为0时可退化为基于应变等效假设给出的线弹性局部损伤本构方程．一维解析解表明,随着应力增大,损伤场逐步由空间非周期解变为关于空间的类周期解,类周期解的峰值区域形成局部化带．局部化带内的损伤变量将不同于局部化带外的损伤变量,由此可以反映出介质的局部化特征．损伤局部化并不是与损伤同时发生,而是在损伤发生后逐渐显现出来,模型的局部化机制开始启动;损伤局部化的宽度同内部特征长度成正比．     

基于声发射岩体压裂损伤演化特征研究

非常规油气储层体积压裂是油气开采的主要技术手段,准确地描述缝网压裂裂缝的演化规律是研究体积压裂的核心问题,运用声发射信号参数特征定义了岩体损伤变量,基于能量守恒原理,建立压裂岩体破裂与裂缝演化的折迭突变模型.通过选取吉林德惠菜园子页岩岩心开展了相关研究,理论计算与室内试验结果表明,岩体压裂具有突变破裂行为特征,理论计算结果与室内试验结果吻合较好.为后续裂缝演化研究奠定了科学基础.     

反平面剪切动态扩展裂纹尖端的弹-粘塑性场

采用Bingham弹性-粘塑性模型对反平面剪切动态扩展裂纹尖端的应力应变场进行了渐近分析．给出了适当的位移模式、推导了渐近方程并且给出了数值解．分析和计算表明对于低粘性情况,裂纹尖端场具有对数奇异性．对于高粘性情况,裂纹尖场具有幂奇异性A·D2对于临界情况,两种奇异性可以相互转换．揭示了粘性在裂纹尖端场研究中的重要作用．     

Analytic solutions of a reducible strain gradient elasticity model for solid cylinder with a cavity and its application in zonal failure

In this work, the reducibility condition of the fourth-order equilibrium equation in the strain gradient elasticity (SGE) model for solid cylinder with a cavity is obtained. When the reducibility condition is satisfied, the analytic displacement, generalized radial stress, and generalized angular stress can be solved out, and according to the higher-order coefficients, internal length scale, and Lamé constants, the displacement, generalized radial stress, and generalized angular stress are classified into four types: (1) conventional elasticity solution, (2) quasiperiodic SGE solution, (3) monotonous SGE solution, and (4) non-real-number solution. Quasiperiodic generalized radial stress and generalized angular stress are used to explain the occurrence of zonal failure of surrounding rock of a circular roadway. Numerical analysis with MATLAB is applied to study the influence of loading on zonal failure of surrounding rock of a circular raodway.     

Construction of the Equivalent Plastic Strain Increment

Strain hardening plastic deformation of a material possessing a yield locus (f(σ_ij)) which may be written as a homogeneous function of the stress components (σ_ij), and which obeys the classical associated flow rule for metals (e.g. Bishop and Hill, 1951) is considered. The material may be anisotropic and may display plastic dilatation. A method is given for constructing the equivalent plastic strain increment in such a way that the increment of plastic work is always equal to the product of the equivalent plastic strain increment and the equivalent yield stress. Construction of the equivalent plastic strain at a corner in the yield locus is given. The method given here is implied in classical treatments of hardening (e.g. Hill, 1950) but seems not to have been given explicitly heretofore.     

Repeating earthquakes,episodic tremor and slip: Emerging patterns in complex earthquake cycles?

The lack of regularity in earthquake cycles continues to be a confounding issue in earthquake science. Lately, observations of episodic nonvolcanic tremor and slip (ETS) along a few well‐instrumented tectonic plate boundaries are intriguing: these features recur together with predictable time intervals. Data now trace recurring ETS back to 1990 and no significant earthquake ever followed an ETS episode. This observation and the fact that stress drops associated with episodic slips are low, only on the order of 0.01 MPa, suggests that repeated ETS has little cumulative effects in priming the fault for the next large earthquake. Another known regularity in seismic activity is the so‐called repeating earthquakes that rupture the same patch of fault repetitively. Current hypotheses for repeating earthquakes point to the interaction of continual, aseismic fault slip with locked, seismogenic patches of the fault. Interestingly, ETS also recur near where the transition between brittle faulting and plastic flow is expected, although it is not clear how and why regularities in space and time are interconnected. New data show that ETS recurs throughout the entire length of the Cascadia subduction zone, thus ruling out any special, local factors as necessary conditions for ETS. Recurrence intervals of ETS vary along the Cascadia. Such variations are not governed by the rate of plate motion that ultimately drives the earthquake process, but they do coincide with variations in the geology of the overriding plate that can influence the rheology along the plate interface. To this end, we call attention to the Portevin‐Le Chatelier effect (PLC, or jerky flow) as a potential analog to the earthquake process. The dynamics of the PLC has been extensively studied and shows many intriguing features as the system goes from chaotic to self‐organized critical regimes as strain rate increases. In particular, the PLC exhibits not only stick‐slip behavior (stress serration) over time but also spatial interactions over extended regions—features that are necessary to account for complex spatio‐temporal variations associated with earthquake activities. © 2007 Wiley Periodicals, Inc. Complexity 12: 33–43, 2007     

隧洞围岩应力复变函数分析法中的解析函数求解

利用复变函数理论进行地下任意开挖断面隧洞围岩应力分析的前提,是根据围岩应力边界条件方程推导出两个解析函数．从Harnack定理出发,将隧洞围岩应力边界条件方程转化成积分方程;把Laurent级数有限项表示的映射函数引入积分方程中,将以任意开挖断面为边界条件的解析函数求解转化成以单位圆周线为边界条件的求解问题．对积分方程中各被积函数在讨论域内的解析性进行了分析,在此基础上利用留数理论求解了方程中各项积分值,并获得了用来表示任意开挖断面隧道围岩应力的两个解析函数通式．给出了圆形和椭圆形隧道的两个解析函数求解算例,所获得的结果与文献中的结果一致．利用留数理论推导出的两个解析函数通式,适用于任意开挖断面隧洞的围岩应力解析解的计算,且计算过程更为简单,计算结果更为精确．     

利用内聚力模型(CZM)模拟弹粘塑性多晶体的裂纹扩展

采用内聚力模型（CZM）,模拟多晶体中起裂于晶界的二维平面应变裂纹扩展．结果表明,弹粘塑性体中,初始裂纹尖端不会最先开裂．晶体本构的率敏感指数表征了塑性变形和内聚力区耗散两种机制的相互竞争．率敏感指数越大,塑性耗散能越大,内聚力区粘着能越小,使材料的塑性变形越容易,内聚力区诱发的破坏越不易;率敏感指数越小,材料响应越接近弹塑性性质,塑性耗散能减小,粘着能增大,外力功易转化为内聚力区的粘着能,使内聚力单元更易分离．增大内聚力区结合强度或临界张开位移使晶内和晶界的三轴应力度减小,即提高内聚力区韧性也使基体材料抗孔洞损伤能力提高．     

Numerical calculation of the tangent stiffness matrix in materials modeling

The Finite Element Method in the field of materials modeling is closely connected to the tangent stiffness matrix of the constitutive law. This so called Jacobian matrix is required at each time increment and describes the local material behavior. It assigns a stress increment to a strain increment and is of fundamental importance for the numerical determination of the equilibrium state. For increasingly sophisticated material models the tangent stiffness matrix can be derived analytically only with great effort, if at all. Numerical methods are therefore widely used for its calculation. We present our method to calculate the tangent stiffness matrix for the logarithmic strain measure. The approach is compared with other commonly used procedures. A significant increase in accuracy can be achieved with the proposed method. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)