玻璃态高聚物PMMA的非线性粘弹-塑性本构方程

对航空有机玻璃(聚甲基丙烯酸甲酯,PMMA)实验测定了不同应变率下单轴压缩加卸载循环的应力-应变曲线,讨论了应力促进热激活塑性变形的活化粘壶理论,提出由标准线性体或Maxwell体与考虑应变硬化效应的活化粘壶作串联耦合的粘弹-塑性本构模型,给出了完备的微分和积分形式的本构方程组,用于拟合实测加卸载循环的应力-应变曲线,获得良好吻合的结果。对应变软化效应提出一种新的起因于粘弹变形滞后效应的理论说明,并对屈服后加载应力-应变曲线的走向特征作了理论解释。     

有关高填充聚合物损伤粘弹介质的非线性本构方程与脱湿损伤模型

本文从连续损伤力学的角度,提出了复合固体推进剂损伤粘弹介质的非线性本构方程,并对单轴定应变速率拉伸情况提出了脱湿损伤的演变模型.理论计算与实验结果吻合较好.     

有限厚压电层表面金属电极脱层的屈曲研究

基于弹性有限变形理论和压电弹性体偏场理论,对上、下表面有金属电极的压电材料板内存在穿透脱层的屈曲问题进行了分析.采用平面应变模型,远处作用有均匀压应变载荷.用Fourier积分变换,界面连续条件和上、下电极表面的边界条件将问题归为第二类Cauchy型奇异积分方程组.利用Gauss-Chebyshev积分公式将该方程组变为一齐次线性代数方程组,以确定脱层屈曲载荷.算例给出了中间层为PZT-4,上、下电极为Pt的结构在不同脱层长厚比时的临界应变及相应屈曲形状.同时分析了压电层的机电耦合效应对临界应变的影响.     

古水水电站工程区域堆积体边坡工程地质分析

基于弹性有限变形理论和电弹性体偏场理论,对半无限压电体及其表面电极层间存在 穿透脱层的屈曲问题进行了分析. 采用平面应变模型,在脱层远处作用有平行于脱层的应变 载荷. 使用Fourier积分变换,应用脱层界面的连续条件和电极表面的边界条件将问题归为 第2类Cauchy型奇异积分方程组. 利用Gauss-Chebyshev积分公式将奇异积分方程组变为 齐次线性代数方程组,以确定临界应变载荷. 通过数值算例,给出了底层为PZT-4材料、 电极为金属Pt在不同的脱层长厚比时的临界应变载荷和屈曲形状,分析了压电体的压 电、介电效应对屈曲载荷的影响. 另外给出了脱层屈曲时,脱层尖端奇异性振荡因子随不同 脱层长厚比的关系曲线.     

压电体表面金属电极脱层的屈曲分析

基于弹性有限变形理论和电弹性体偏场理论,对半无限压电体及其表面电极层间存在穿透脱层的屈曲问题进行了分析. 采用平面应变模型,在脱层远处作用有平行于脱层的应变载荷. 使用Fourier积分变换,应用脱层界面的连续条件和电极表面的边界条件将问题归为第2类Cauchy型奇异积分方程组. 利用Gauss-Chebyshev积分公式将奇异积分方程组变为齐次线性代数方程组,以确定临界应变载荷. 通过数值算例,给出了底层为PZT-4材料、电极为金属Pt在不同的脱层长厚比时的临界应变载荷和屈曲形状,分析了压电体的压电、介电效应对屈曲载荷的影响. 另外给出了脱层屈曲时,脱层尖端奇异性振荡因子随不同脱层长厚比的关系曲线.      

短纤维增强三元乙丙橡胶横观各向同性黏-超弹性本构模型

短纤维增强三元乙丙橡胶包覆薄膜,是一种应用于固体火箭发动机缠绕包覆装药的新型复合材料.为了描述其在工作过程中受振动、冲击等载荷作用时的力学行为,基于黏弹性理论和纤维增强连续介质力学理论,提出了一种考虑应变率强化效应的横观各向同性黏-超弹本构模型.模型中应变能函数被分解为超弹性应变能和黏性应变能,其中超弹性应变能包括表征各向同性的橡胶基体应变能和表征各向异性的纤维拉伸应变能,黏性应变能采用表征橡胶和纤维黏性响应的宏观唯象模型.选取表征各应变能的函数形式,经过数学变换、替代、叠加,求解确定最终的应力应变形式,明确模型参数获取的具体步骤,将预测结果与实验结果对比分析,准确性较高.研究表明:该模型能有效预测材料在低应变率下纤维方向为0?～45?的非线性率相关力学特性;模型形式易于实现有限元开发,对固体火箭发动机装药结构完整性分析具有参考价值.     

钢圆管在内爆加载下的层裂特性研究

利用完整回收技术,获得了20钢圆管在不同固体装药厚度、装药类型以及外壳条件的滑移内爆加载下形变和层裂的特征和规律,得到了钢圆管层裂的相对临界装药厚度等初步结果,分析了装药类型、装药厚度、外壳对钢圆管层裂的影响。     

分段装药爆炸应变场与裂隙场分布规律

为探究分段装药爆炸应变场与裂隙场分布规律,采用数字图像相关分析方法与电子计算机断层扫描实验方法,分析了孔内分段装药爆炸全场应变传播规律,建立了爆后“岩石—爆炸裂隙”的三维重构模型,描述了爆炸裂纹位置与形态的空间分布情况,得到岩石材料爆炸裂隙的分形维数与损伤度。研究结果表明：分段装药改变了连续装药对介质的全场应变形态,由一次应变改变为两次应变,在满足第一段炸药对介质的破坏作用下,同时加大了第二段炸药对介质的作用效应;上分段装药占比0.4时,下分段介质受爆炸作用应变峰值更大,更好满足工程实践中下半段岩体对爆炸能量的需求;相同装药系数下,连续装药结构爆炸裂纹没有贯穿试件整体,炮孔封堵段的爆炸裂纹较少,分段装药结构下,由于提高了炸药的位置,使得上部分岩体能够更好地利用炸药爆炸的能量破碎岩石;分段装药岩石整体损伤度较连续装药提高了23.5%,其中上分段岩石损伤差异较大,分段装药上分段损伤度比连续装药提高46.4%。     

含脱粘界面颗粒性复合材料的有效热膨胀系数

基于细观力学方法建立了包含脱粘界面在内的复合材料四相模型,将颗粒、脱粘界面和基体壳简化为椭球三相胞元,并通过Eshelby-Mori-Tanaka方法的推导得到颗粒和脱粘界面的热膨胀本征应变,进而对三相胞元热膨胀系数进行了预报.考虑到三相胞元在复合材料中随机分布,应用坐标变换公式得到复合材料平均热膨胀应变,进而求得复合材料的热膨胀系数.     

复合材料补片加固钢板的粘接应力与失效模拟

在ANSYS有限元软件中建立三维有限元模型,对复合材料补片单面加固钢板进行数值模拟,使用内聚力单元模拟胶层脱粘和扩展过程,有限元模型计算结果与试验结果吻合较好,弹性极限载荷和失效载荷的相对误差分别为9.6%和4.2%。计算得到了模型在拉伸载荷作用下的载荷-位移曲线、胶层剪应力和剥离应力分布情况以及补片x轴向应力分布情况。结果表明,胶层端部最先达到极限强度后出现开裂,脱粘从补片两端开始逐渐向中心扩展,且扩展过程是非对称的;当补片发生部分脱粘后,补片应力集中在未脱粘处,承载长度逐渐减小、承载能力逐渐降低。     

A conventional theory of mechanism-based strain gradient plasticity

There exist two frameworks of strain gradient plasticity theories to model size effects observed at the micron and sub-micron scales in experiments. The first framework involves the higher-order stress and therefore requires extra boundary conditions, such as the theory of mechanism-based strain gradient (MSG) plasticity [J Mech Phys Solids 47 (1999) 1239; J Mech Phys Solids 48 (2000) 99; J Mater Res 15 (2000) 1786] established from the Taylor dislocation model. The other framework does not involve the higher-order stress, and the strain gradient effect come into play via the incremental plastic moduli. A conventional theory of mechanism-based strain gradient plasticity is established in this paper. It is also based on the Taylor dislocation model, but it does not involve the higher-order stress and therefore falls into the second strain gradient plasticity framework that preserves the structure of conventional plasticity theories. The plastic strain gradient appears only in the constitutive model, and the equilibrium equations and boundary conditions are the same as the conventional continuum theories. It is shown that the difference between this theory and the higher-order MSG plasticity theory based on the same dislocation model is only significant within a thin boundary layer of the solid.     

Viscosity of Strain Gradient Effects on the Kinetics of Propagating Phase Boundaries in Solids

The theory of thermoelastic materials undergoing solid-solid phase transformations requires constitutive information that governs the evolution of a phase boundary. This is known as a kinetic relation which relates a driving traction to the speed of propagation of a phase boundary. The kinetic relation is prescribed in the theory from the onset. Here, though, a special kinetic relation is derived from an augmented theory that includes viscous, strain gradient and heat conduction effects. Based on a special class of solutions, namely travelling waves, the kinetic relation is inherited from the augmented theory as the viscosity, strain gradient and heat conductivity are removed by a suitable limit process.     

基于模态参数考虑边界条件变异的桥梁结构损伤识别

根据桥梁结构的实际工程特性,分析其边界条件变异、结构损伤及其参数变化,采用约束优化理论,建立以实测和理论模态参数误差平方和最小为目标函数的优化反演问题。基于矩阵摄动理论引入与结构动力方程对应的特征值和特征向量的一阶、二阶摄动量,将优化反演问题简化为非线性最小二乘法优化反演问题。针对桥梁结构边界条件对模态参数影响显著的实际情况,实施桥梁结构边界条件预识别,采用单元模态应变能方法预定位损伤,提出考虑边界条件变异的桥梁结构损伤识别具体流程。以一磁浮轨道梁方案为例,采用数值模拟进行边界条件变异及损伤的识别验证,结果表明:该方法能够有效识别边界条件的变异及构件损伤,识别参数的相对误差最大为12.48%,具有较高的识别精度。     

Crack tip field andJ-integral with strain gradient effect

The mode I plane strain crack tip field with strain gradient effects is presented in this paper based on a simplified strain gradient theory within the framework proposed by Acharya and Bassani. The theory retains the essential structure of the incremental version of the conventionalJ ₂ deformation theory. No higher-order stress is introduced and no extra boundary value conditions beyond the conventional ones are required. The strain gradient effects are considered in the constitutive relation only through the instantaneous tangent modulus. The strain gradient measures are included into the tangent modulus as internal parameters. Therefore the boundary value problem is the same as that in the conventional theory. Two typical crack problems are studied: (a) the crack tip field under the small scale yielding condition induced by a linear elastic mode-IK-field and (b) the complete field for a compact tension specimen. The calculated results clearly show that the stress level near the crack tip with strain gradient effects is considerable higher than that in the classical theory. The singularity of the strain field near the crack tip is nearly equal to the square-root singularity and the singularity of the stress field is slightly greater than it. Consequently, theJ-integral is no longer path independent and increases monotonically as the radius of the calculated circular contour decreases. The project supported by the National Natural Science Foundation of China (19704100 and 10202023) and the Natural Science Foundation of Chinese Academy of Sciences (KJ951-1-20)     

On bending of strain gradient elastic micro-plates

Bending of strain gradient elastic thin plates is studied, adopting Kirchhoff’s theory of plates. Simple linear strain gradient elastic theory with surface energy is employed. The governing plate equation with its boundary conditions are derived through a variational method. It turns out that new terms are introduced, indicating the importance of the cross-section area in bending of thin plates. Those terms are missing from the existing strain gradient plate theories; however, they strongly increase the stiffness of the thin plate.     

Analytical solutions for buckling of size-dependent Timoshenko beams

The inconsistences of the higher-order shear resultant expressed in terms of displacement(s) and the complete boundary value problems of structures modeled by the nonlocal strain gradient theory have not been well addressed. This paper develops a size-dependent Timoshenko beam model that considers both the nonlocal effect and strain gradient effect. The variationally consistent boundary conditions corresponding to the equations of motion of Timoshenko beams are reformulated with the aid of the weighted residual method. The complete boundary value problems of nonlocal strain gradient Timoshenko beams undergoing buckling are solved in closed forms. All the possible higher-order boundary conditions induced by the strain gradient are selectively suggested based on the fact that the buckling loads increase with the increasing aspect ratios of beams from the conventional mechanics point of view. Then, motivated by the expression for beams with simply-supported(SS) boundary conditions, some semiempirical formulae are obtained by curve fitting procedures.     

Nonlocal gradient-dependent modeling of plasticity with anisotropic hardening

This work addresses the formulation of the thermodynamics of nonlocal plasticity using the gradient theory. The formulation is based on the nonlocality energy residual introduced by Eringen and Edelen (1972). Gradients are introduced for those variables associated with isotropic and kinematic hardening. The formulation applies to small strain gradient plasticity and makes use of the evanescent memory model for kinematic hardening. This is accomplished using the kinematic flux evolution as developed by Zbib and Aifantis (1988). Therefore, the present theory is a four nonlocal parameter-based theory that accounts for the influence of large variations in the plastic strain, accumulated plastic strain, accumulated plastic strain gradients, and the micromechanical evolution of the kinematic flux. Using the principle of virtual power and the laws of thermodynamics, thermodynamically-consistent equations are derived for the nonlocal plasticity yield criterion and associated flow rule. The presence of higher-order gradients in the plastic strain is shown to enhance a corresponding history variable which arises from the accumulation of the plastic strain gradients. Furthermore, anisotropy is introduced by plastic strain gradients in the form of kinematic hardening. Plastic strain gradients can be attributed to the net Burgers vector, while gradients in the accumulation of plastic strain are responsible for the introduction of isotropic hardening. The equilibrium between internal Cauchy stress and the microstresses conjugate to the higher-order gradients frames the yield criterion, which is obtained from the principle of virtual power. Microscopic boundary conditions, associated with plastic flow, are introduced to supplement the macroscopic boundary conditions of classical plasticity. The nonlocal formulation developed here preserves the classical assumption of local plasticity, wherein plastic flow direction is governed by the deviatoric Cauchy stress. The theory is applied to the problems of thin films on both soft and hard substrates. Numerical solutions are presented for bi-axial tension and simple shear loading of thin films on substrates.     

Shear banding analysis of geomaterials by strain gradient enhanced damage model

Shear band localization is investigated by a strain-gradient-enhanced damage model for quasi-brittle geomaterials. This model introduces the strain gradients and their higher-order conjugate stresses into the framework of continuum damage mechanics. The influence of the strain gradients on the constitutive behaviour is taken into account through a generalized damage evolutionary law. A weak-form variational principle is employed to address the additional boundary conditions introduced by the incorporation of the strain gradients and the conjugate higher-order stresses. Damage localization under simple shear condition is analytically investigated by using the theory of discontinuous bifurcation and the concept of the second-order characteristic surface. Analytical solutions for the distributions of strain rates and strain gradient rates, as well as the band width of localised damage are found. Numerical analysis demonstrates the shear band width is proportionally related to the internal length scale through a coefficient function of Poisson’s ratio and a parameter representing the shape of uniaxial stress–strain curve. It is also shown that the obtained distributions of strains and strain gradients are well in accordance with the underlying assumptions for the second-order discontinuous shear band boundary and the weak discontinuous bifurcation theory.     

Gradient elasticity and nonstandard boundary conditions

Gradient elasticity for a second gradient model is addressed within a suitable thermodynamic framework apt to account for nonlocality. The pertinent thermodynamic restrictions upon the gradient constitutive equations are derived, which are shown to include, besides the field (differential) stress–strain laws, a set of nonstandard boundary conditions. Consistently with the latter thermodynamic requirements, a surface layer with membrane stresses is envisioned in the strained body, which together with the above nonstandard boundary conditions make the body constitutively insulated (i.e. no long distance energy flows out of the boundary surface due to nonlocality). The total strain energy is shown to include a bulk and surface strain energy. A minimum total potential energy principle is provided for the related structural boundary-value problem. The Toupin–Mindlin polar-type strain gradient material model is also addressed and compared with the above one, their substantial differences are pointed out, particularly for what regards the constitutive equations and the boundary conditions accompanying the solving displacement equilibrium equations. A gradient one-dimensional bar sample in tension is considered for a few applications of the proposed theory.     

基于广义应变梯度理论的纳米梁挠曲电效应研究

挠曲电效应是应变梯度与电极化的耦合，它存在于所有的电介质材料中。在纳米电介质结构的挠曲电效应研究中，应变梯度弹性对挠曲电响应的影响一直以来被低估甚至被忽略了。根据广义应变梯度理论，应变梯度弹性中独立的尺度参数只有三个，而文献中所采用的一个或两个尺度参数的应变梯度理论只是它的简化形式。基于该理论，论文建立了考虑广义应变梯度弹性的三维电介质结构的理论模型，并以一维纳米梁为例研究了其弯曲问题的挠曲电响应及其能量俘获特性。结果表明，纳米梁的挠曲电响应存在尺寸效应，并且弹性应变梯度会影响结构挠曲电的尺寸效应，特别是当结构的特征尺寸低于尺度参数时。论文的工作为更进一步理解纳米尺度下的挠曲电机理和能量俘获特性提供理论基础和设计依据。