Effect of surface stress and surface-induced stress on behavior of piezoelectric nanobeam

A new continuum model is developed to study the influence of surface stress on the behaviors of piezoelectric nanobeams. Different from existing piezoelectric surface models which only consider the surface properties, the proposed model takes surfaceinduced initial fields into consideration. Due to the fact that the surface-induced initial fields are totally different under various boundary conditions, two kinds of beams, the doubly-clamped beam and the cantilever beam, are analyzed. Furthermore, boundary conditions can affect not only the initial state of the piezoelectric nanobeam but also the forms of the governing equations. Based on the Euler-Bernoulli beam theory, the nonlinear Green-Lagrangian strain-displacement relationship is applied. In addition, the surface area change is also considered in the proposed model. The governing equations of the doubly-clamped and cantilever beams are derived by the energy variation principle. Compared with existing Young-Laplace models, the proposed model for the doubly-clamped beam is similar to the Young-Laplace models. However, the governing equation of the cantilever beam derived by the proposed model is very different from that derived by the Young-Laplace models. The behaviors of piezoelectric nanobeams predicted by these two models also have significant discrepancies, which is owing to the surface-induced initial fields in the bulk beam.     

损伤围岩中爆炸应力波动的数值模拟

应用有限元方法分析了硐室损伤围岩中爆炸应力波的传播和应力分布特征，通过引入JHC本构模型和岩石损伤变量D探讨了应力波作用下岩体的损伤演化模式。研究表明:围岩初始损伤对后续爆炸应力波的波动性质、作用范围和围岩应力分布具有不同程度的影响。当初始损伤超过某临界值后会显著地影响应力波的波动范围和围岩应力分布；在一定爆炸当量下，爆炸应力存在一个有效作用范围Lp，该范围塑性区以内，爆炸应力对岩体的损伤随围岩初始损伤增大而增大；有效作用范围Lp以外，围岩初始残余非弹性变形积累和单元残余拉应力可以平衡爆炸应力波动产生的损伤叠加效应，耗散了爆炸应力作用和波动能量。分析了产生在这种现象的原因。给出了有效作用范围Lp与围岩初始等效应力p之间的经验关系。     

A direct approach to fiber and membrane reinforced bodies. Part I. Stress concentrated on curves for modelling fiber reinforced materials

An approach is outlined to the equilibrium in fiber-reinforced materials in which the fibers are modeled as curves or lines with concentrated material properties. The system of forces representing the interaction of the fibers with the bulk matter is analyzed, and equilibrium of forces is derived from global laws. The displacements of the bulk matter are assumed to have continuous extension to the fibers. This forces the set of admissible deformations superquadratically integrable. This in turn forces the energy of the bulk of superquadratic growth. The material of the bulk matrix therefore cannot be linearly elastic. The energy of fibers can have a slower growth and can be quadratic. A formal set of assumptions is given under which an equilibrium state of minimum energy exists in the given external conditions. A weak form of equilibrium equations is derived for this equilibrium state. An explicitly calculable axisymmetric example is presented with an isotropic and quadratic energy of the matrix (linear elasticity) and linearly stretchable fiber. Since the superquadratic growth assumption is not satisfied, some peculiar features of the solution arise, such as the infinite limit of the radial displacement near the fiber. Nevertheless, from the obtained solution, we can compute the normal force in the fiber and the shear stress at the interface.     

深部岩体变形破坏的特征能量因子与应用

深部岩体在高地应力作用下储存了大量的弹性应变能。在开挖或爆破扰动作用下，原有的平衡状态被打破，围岩中形成了有势场和不平衡应力场。在不平衡力场和扰动场的共同作用下，岩体的变形与破坏表现出了诸如分区破裂化、大变形、岩爆以及人工地震等非线性行为。传统的连续介质理论并不能考虑岩体的构造特性与含能特性，因此无法很好地解释深部岩体的特殊非线性力学现象。特征能量因子从能量的角度出发，结合统计物理学观点，为分析深部岩体在动静荷载组合作用下的变形和破坏过程提供了有效的理论支撑。本文主要对特征能量因子进行了简要介绍，并回顾了其在深部岩体分区破裂以及动力诱发围岩不可逆变形等非线性工程灾害现象中的应用。     

不同采深煤(岩)体岩爆过程模拟分析

为了研究不同采深条件下诱发的岩体变形、岩爆、凸出和塌落特征,对采深120m~820m,间隔100m的8种工况开采后岩体破坏进行模拟。结合能量守恒理论和ΔU=Ue-U0来确定岩爆后由弹性势能转化为动能的ΔU。使用三维岩体爆破颗粒流模型将ΔU按照一定规则转化为岩爆飞石动能。模拟了各工况下开采后岩体变化情况,结果表明,采深为120m,220m和320m三种工况下不发生岩爆;420m开始发生岩爆;520m和620m在发生岩爆的同时也伴随开采面岩体凸出;720m和820m时具有岩爆、凸出和塌落现象。同时总结了岩爆特点,特别是提出岩爆是岩体系统为了保持自身能量平衡而向系统之外释放能量的过程。     

地应力水平对深埋隧洞爆破振动频谱结构的影响

爆破振动的频谱特性对隧洞安全施工具有重要意义。采用动力有限元方法，分析了不同地应力水平条件下围岩爆破振动频率特征，通过对实测爆破振动信号的时域和频域联合分析，研究了不同频带上的振动能量分布。结果表明，爆破振动的主频及各个振动能量优势频带都有随地应力水平升高而降低的趋势，伴随爆破破岩过程而发生的地应力瞬态卸载动力效应是产生这一现象的主要原因。地应力水平越高，爆破振动信号中20～100 Hz的低频振动能量比重越大。当爆区的地应力为20 MPa时，20～100 Hz频带内的振动能量可达到总振动能量的35%左右；当爆区的地应力为30～50 MPa时，20～100 Hz频带内的振动能量可达到总振动能量的50%以上。除地应力水平外，应力卸载速率及岩体的力学特性也对爆破振动主频具有显著影响，卸载速率越高，低频振动能量比重越大。卸载速率取决于掏槽爆破方式，直孔掏槽导致岩体应变能释放速率最高。岩体弹性模量越大，爆破振动的主频越高。     

Limiting stress of metals and the limiting state under creep conditions

We show that, as long as one deals with a plane stress state, the Coulomb-Mohr fracture criterion traditionally used in soil and rock mechanics is in a rather good agreement with the results of fracture experiments for metal materials under the conditions of creep caused by a long-term action of a constant load. We perform statistical analysis to compare the proposed theoretical limiting-stress-fracture-time dependencies with the experimental results given in [1–3] and the results of computations by other authors [1, 4, 5]. Just as in [6], the limiting state arising under the conditions of creep caused by long-term loading is considered in the case of plane strain. We use the solutions of the rigid-plastic problems on the pressure exerted by a flat die on a half-plane and the extension of a strip with angular notches to find the fracture time for the corresponding problems in the setting of a perfectly rigid-creeping body.     

煤体中爆炸应力波传播与衰减规律模拟实验研究

在岩石爆破理论的基础上分析了煤体中爆炸应力波的作用机理,借助损伤力学理论探讨了煤体在 爆炸应力波作用下的损伤断裂准则。煤体中爆炸应力波传播与衰减规律模拟实验结果表明:煤体中爆炸应力 波一般包含2段波形,第1段由压缩相和拉伸相组成简单波形,第2段是由多种作用形成的复杂波形;爆炸应 力波作用下,煤体首先承受压应力,而后承受拉应力,且压缩相的作用时间较拉伸相作用时间短;煤体中爆炸 应力波的衰减速度较一般岩体中的快,实验条件下应力波衰减因数符合=3-/(1-),爆炸应力波的主要 作用是在煤体中形成少量新裂隙、激活煤体中原生裂隙并打破煤体中瓦斯气体的平衡状态。     

节理岩体的爆破松动机理

利用应力波理论对节理岩体的爆破松动机理进行了探讨,同时利用动力有限元数值模拟方法验证了理论分析结果。研究表明,爆破荷载的加载阶段对岩体的挤压蓄能和快速卸载阶段的弹性回复是岩体产生后续松动位移的根本原因;节理岩体的爆破松动在开挖面的法向表现为岩体的剪切错动,在平行于开挖面方向表现为结构面的张开;拉格朗日坐标下的动力有限元数值方法,如ANSYS/LS-DYNA程序,能够较好地用来模拟节理岩体的爆破松动过程。     

Predicting the Dynamic Compressive Strength of Carbonate Rocks from Quasi-Static Properties

In this study, the split Hopkinson pressure bar testing method was used to quantify the dynamic strength characteristics of rocks with short cylindrical specimens. Seventy dynamic compression tests were conducted on 10 different carbonate rocks with the split Hopkinson pressure bar apparatus. Experimental procedure for testing dynamic compressive strength and elastic behaviour of rock material at high strain rate loading is presented in the paper. Pulse-shaper technique was adopted to obtain dynamic stress equilibrium at the ends of the sample and to provide nearly a constant strain rate during the dynamic loading. In addition to dynamic tests, the physical properties covering bulk density, effective porosity, P-wave velocity and Schmidt hardness of rocks, and mechanical properties such as quasi-static compressive strength and tensile strength were determined through standard testing methods. Multiple linear regression analyses were carried out to investigate the variation of dynamic compressive strength depending on physical and mechanical properties of rocks and loading rate. A three parameter model was found to be simple and provided the best surface fit to data. It was found that dynamic compressive strength of rocks increases with increase in loading rate and/or increase in rock property values except porosity. Statistical tests of regression results showed that quasi-static compressive strength and Schmidt hardness are most significant rock properties to adequately predict the dynamic compressive strength value among the other properties. However, P-wave velocity, quasi-static tensile strength of rocks could also be used to estimate the dynamic compressive strength value of rocks, as well, except the bulk density and effective porosity.     

偏压条件下大型地下厂房围岩变形稳定性分析

根据下坂地水库协力波斯电站工程建设实际,在现场调查和电站区勘探、测试资料基础上深入分析地下厂房地质条件,建立了能够反映厂区地形地貌、岩体结构和地应力状态的三维数值模型。根据地应力实测资料反演拟合初始地应力场背景值,采用三维弹塑性有限差分法模拟了在偏压条件下地下厂房、主变室开挖过程中围岩变形和稳定性状况,揭示了各开挖阶段应力的集中部位和围岩潜在破坏部位,这对于工程具有重要的指导意义。     

孔隙流体耦合效应对射流冲击应力分布的影响分析

运用全解耦流固耦合理论,建立了水射流冲击岩石介质流固耦合数值分析模型,给出了数值算法,计算分析了考虑和不考虑孔隙流体耦合效应对射流冲击岩石时应力分布的影响规律。结果表明,在射流冲击作用下,如不考虑孔隙流体耦合作用,最大拉应力位于冲击面,离冲击中心径向距离与喷距成正比,最大剪切应力位于岩石冲击中心下部约0.5倍喷嘴直径位置;如考虑孔隙流体耦合作用,最大拉应力位于岩石冲击中心下部约0.4倍喷嘴直径位置。数值分析结果可为水射流破岩机理研究中岩石破坏准则的选择提供依据。     

冲击速度和轴向静载对红砂岩破碎及能耗的影响

地下岩体工程爆破开挖中，距爆源不同距离处岩体承受的地应力和动载荷大小不同，从动载荷的角度表征岩石动态破坏结果与工程实际更吻合。为研究动载荷和地应力大小对岩体破碎和能量耗散特性的影响，利用动静组合加载试验装置，分别设置7个冲击速度和轴向静应力等级，对红砂岩试件进行冲击试验。根据试件的破碎状况，分析不同静应力工况下冲击速度对岩石破坏模式和机理的影响。计算不同工况下的应力波能量值，研究冲击速度和轴向静应力对岩石能耗特性的影响。对破坏试件进行筛分试验，研究岩石破碎分形维数随冲击速度和轴向静应力的变化关系。结果表明，随着冲击速度的增大，试件的破坏程度逐渐加大。无轴压时岩石试件破坏后整体仍是一个圆柱体，属于张拉破坏；有轴压时岩石试件宏观破坏后呈沙漏状，属于拉剪破坏。岩石耗散能随冲击速度的升高呈二次函数关系递增；轴向静应力越高，递增幅度越小。随着冲击速度的升高，岩石分形维数由零逐渐增加；随着轴向静应力的升高，分形维数由零转为大于零的临界冲击速度先升高后降低。     

考虑损伤的内变量黏弹-黏塑性本构方程

基于Rice 不可逆内变量热力学框架,在约束构型空间中讨论材料的蠕变损伤问题. 通过给定具体的余能密度函数和内变量演化方程推导出考虑损伤的内变量黏弹-黏塑性本构方程. 通过模型相似材料单轴蠕变加卸载试验对一维情况下的本构方程进行参数辨识和模型验证,本构方程能很好地描述黏弹性变形和各蠕变阶段.不同的蠕变阶段具有不同的能量耗散特点. 受应力扰动后,不考虑损伤的材料系统能自发趋于热力学平衡态或稳定态. 在考虑损伤的整个蠕变过程中,材料系统先趋于平衡态再背离平衡态发展. 能量耗散率可作为材料系统热力学状态偏离平衡态的测度;能量耗散率的时间导数可用于表征系统的演化趋势;两者的域内积分值可作为结构长期稳定性的评价指标.      

不同地质环境下的玄武岩岩体结构评价指标的选取

处于不同的地质环境下,玄武岩岩体结构具有不同的状态,在围压原位状态下,岩体结构面镶嵌紧密结合,岩体完整性好,岩体完整性系数与结构面最小间距具有不对应性,应选取完整性系数作为评价指标;而在岩体处于应力松弛状态下岩体完整性差,完整性系数评价指标和结构面间距评价指标具有很好对应性,应选取最小间距作为评价指标。本文通过对西南某水电站坝基岩体在处于不同的地质环境下岩体结构的评价,从而选取岩体完整性系数作为深部岩体结构评价的主要指标。     

金属材料在复杂应力状态下的塑性流动特性及本构模型

工程应用中,金属材料和结构往往处于复杂应力状态。材料的塑性行为会受到应力状态的影响,要精确描述材料在复杂应力状态下的塑性流动行为,必须在本构模型中考虑应力状态效应的影响。然而,由于在动态加载下材料的应变率效应和应力状态效应相互耦合、难以分离,给应力状态效应的研究和模型的建立造成很大困难。通过对Ti-6Al-4V钛合金材料开展不同加载条件下的力学性能测试,提出了一个包含应力三轴度和罗德角参数影响的新型本构模型,并通过VUMAT用户子程序嵌入ABAQUS/Explicit软件。分别采用新提出的塑性模型和Johnson-Cook模型对压剪复合试样的动态实验进行了数值模拟。结果表明,新模型不仅在对材料本构曲线的拟合方面具有较强的优势,而且由该模型所得到的透射脉冲和载荷-位移曲线均更加准确。因此,该模型能够更精确地描述和预测金属材料在复杂应力状态下的塑性流变行为。     

Fracture of sedimentary rocks under a complex triaxial stress state

Most sedimentary rocks have layered structure, and their strength properties are therefore anisotropic; as a consequence, the rock strength depends on the direction of the applied stresses. In this case, various fracture mechanisms are possible. The following two possible fracture mechanisms are considered: actions along the bedding planes, which are weakening surfaces, and along the planes where stresses exceeding the total rock strength are attained. A triaxial independent loading test bench was used to study the fracture conditions for layered rocks composed of productive oil-and-gas strata in complex true triaxial loading tests. The study shows a good qualitative agreement between experimental results and theoretical estimates.     

Equilibrium shapes of inflated inextensible membranes

This paper proposes an effective method for directly determining the final equilibrium shapes of closed inextensible membranes subjected to internal pressures. With reference to new high-performance textile materials, we assume that the mechanical response of a fabric membrane can be accurately represented by regarding it as a two-state material. In the active state, the membrane is subject to tensile stresses and is virtually inextensible; vice versa, in the passive state it is unable to sustain any compressive stress, so it contracts freely. Equilibrium of the membrane in the final configuration is enforced by recourse to the minimum total potential energy principle. The Lagrange multipliers method is used to solve the minimum problem by accounting for the aforesaid nonlinear constitutive law. The set of governing equations is solved for the unknown coordinates of the equilibrium surface points. Closed form solutions are obtained for fully wrinkled cylindrical and axisymmetric membranes under homogeneous boundary conditions, while a simple iterative procedure is used to numerically solve cases of axisymmetric membranes under various inhomogeneous boundary conditions. The soundness of the proposed method is verified by comparing the results with solutions available in the literature.     

Solid-phase combustion in a plane stress state. 2. Stability to small perturbations

Stability of a plane reaction front in the solid phase to small perturbations under conditions of a generalized plane stress state is studied with allowance of the coupled character of heat transfer and deformation processes and possible changes in the reaction rate under the action of internal stresses without external mechanical loading. The problem is solved analytically by the method of perturbations. Conditions of the loss of stability of various conversion regimes in some limiting cases are studied for different technological and physical parameters.     

深埋地下洞室断裂型岩爆机理的数值模拟

针对深部岩体中由断层、节理等不连续性结构面引发的岩爆地质灾害, 根据深埋地下隧洞中潜在发震断裂的分布特征和几何形态建立数值分析模型, 采用离散元单元法模拟存在刚性平直断裂的深部围岩的开挖响应, 并分别考察开挖接近并通过断裂附近时围岩应力状态的变化特征。通过探讨断裂的存在对围岩应力状态改变的作用机理, 揭示出断裂型岩爆是开挖面附近一定范围内存在的断裂构造在高应力作用下发生错动, 导致能量突然释放, 对围岩造成强烈冲击作用的结果, 基本与地震的断层“粘滑”机制相类似。