马氏体相变微结构演化过程的模拟与分析

实验中观察到形状记忆合金在应力诱发马氏体相变过程中,出现多界面的微结构,马氏体相会逐渐长大变粗,同时会出现由马氏体形核造成的应力突然降低.用多阱的弹性能函数来刻画此相变与微结构演化过程,发现相变时会出现多界面的微结构且伴随着马氏体相的形核至奥氏体相的消失过程,出现了界面数先增后减的变化,同时应力会出现跳跃而不连续.相对应的动力学模型的有限差分的计算结果同样显示形核时出现了多界面的微结构并伴随着应力的大幅振荡,随着载荷的增加界面位置随之移动,使得马氏体相区域逐渐长大.理论分析与数值模拟的结果较好地刻画了实验中观察到的马氏体相变过程中的形核,产生多界面,再到马氏体逐渐长大这一微结构的演化过程.     

材料微结构演化的相场模拟

材料的各种宏观性能与其内部的微观结构密切相关,如何通过控制材料微结构的分布来提高其性能指标一直是工程界与学术界广泛关注的课题。由于场变量在界面的突变,传统的基于局部理论的突变界面模型在描述材料微结构演化方面存在一定的困难。基于非局部理论的相场法采用扩散界面的概念来描述界面,避开了理论上描述突变界面的困难,在模拟材料内部任意的组织形态和复杂的微结构演化方面具有独特的优点。本文首先介绍相场法的热力学理论基础,包括自由移动边界问题、扩散界面模型、非局部能量泛函、相场动力学方程及其常用求解方法。然后重点介绍铁电、铁磁和多铁性材料微结构演化的相场模拟,同时简要介绍相场法在软物质和锂离子电池材料微结构演化模拟中的应用,最后给出总结和展望。     

热弹性马氏体相变连续介质热力学研究

介绍形状记忆合金热弹性马氏体相变连续介质热力学研究方法和最新进展, 着重分析了在推广的非线性弹性力学的框架下, 应用变分方法研究热弹性马氏体相变的理论和方法、存在的问题及发展趋势. 首先介绍如何计算马氏体相变24种变体的变形梯度, 然后拓展非线性弹性力学, 引入描述相变的多阱非凸弹性势能, 进而讨论了界面能和非局部能对相变微结构和相变过程的影响的相关研究理论方法和进展.      

应力作用下NiTi形状记忆合金微结构演化的相场模拟及其本征应变率敏感性

基于Ginzburg-Landau动力学控制方程建立了NiTi形状记忆合金非等温相场模型,实现了对NiTi合金内应力诱导马氏体相变的数值模拟。同时将晶界能密度引入系统局部自由能密度,从而考虑多晶系统中晶界的重要作用。数值计算了单晶和多晶NiTi形状记忆合金在单轴机械载荷作用下微结构的动态演化过程和宏观力学行为,并重点研究了晶粒尺寸为60 nm的NiTi纳米多晶在低应变率下（0.0005～15 s?1）力学行为的本征应变率敏感性。研究结果表明,单晶NiTi合金系统高温拉伸-卸载过程中马氏体相变均匀发生,未形成奥氏体-马氏体界面。而纳米多晶系统在加载阶段出现了马氏体带的形成-扩展现象,在卸载阶段出现了马氏体带的收缩-消失现象。相同外载作用过程中,NiTi单晶系统的宏观应力-应变曲线具有更大的滞回环面积,拥有更优的超弹性变形能力。计算结果显示,在中低应变率下纳米晶NiTi形状记忆合金应力-应变关系表现出较明显的应变率相关性,应变率升高导致材料相变应力提升。这一应变率相关性主要源于相场模型中外加载荷速率与马氏体空间演化速度的相互竞争关系。     

大型转子-基础-地基系统的非线性动力分析

针对实际工程中的大型机组，在线性理论分析基础上，引入转子系统的非线性油膜力项，采用子结构模态综合法，形成一个比较接近实际大型汽轮发电机组的包括陀螺转子-非稳态非线性油膜转承-弹性基础-地基系统的非线性系统计算模型。通过对系统方程进行分块直接积分求解，得到了不同位置的轴承在不同转速和不同转子偏心量下引起的系统非线性动力学现象，为大机组的非线性分析和改进提供较完善的理论分析和计算的基础。     

带孔隙损伤的弹性固体的广义变分原理

应用弹性微结构理论,建立了具广义力场带孔隙损伤线弹性固体的基本模型．应用变积方法,同时分别建立了带孔隙损伤弹性固体四类和两类变量的广义变分原理,这些变分原理对应着带孔隙损伤弹性固体微分方程和初值边值条件．应用弹性微结构理论,建立了带孔隙损伤的弹性Timoshenko 梁的基本方程,得到带孔隙损伤的弹性Timoshenko 梁两类变量的广义变分原理．这些广义变分原理为近似求解带孔隙损伤的弹性问题提供了有效途径．     

弱界面复合材料中的基体裂纹

利用二维弹性力学模型研究了纤维增强复合材料中基体裂纹与弱界面的相互作用机理．文中首先导出各向异性弹性多层介质中刃型位错的基本解，然后运用这些基本解建立了弱界面复合材料中典型的Ｈ型缺陷的奇异积分方程组，通过求解这些方程得到外载荷的大小、弱界面的结合强度、界面的残余压力和摩擦系数、纤维与基体的弹性模量比等微结构参量与基体裂纹附近的应力场的关系     

复合材料周期性线弹性微结构的拓扑优化设计

提出复合材料周期性线弹性微结构拓扑优化设计的模型，模型1设计具有极值弹性特性的复合材料，模型2设计工况最刚微结构单胞。通过该模型和均匀化技术可以获得优化的微结构单胞，进而改善或者得到最优宏观特性的复合材料。为了便于制造和应用，用胞体材料而不是多相材料来得到复合材料的极值弹性特性和最大刚度。优化结果表明，该模型与数值方法相结合可以有效地实现微结构的拓扑优化设计。     

考虑相变的近场动力学热?力耦合模型及多孔介质冻结破坏模拟

多孔介质的传热传质现象广泛存在于自然界和工业领域中. 低温条件可能导致多孔介质中的组分发生相变, 并由此诱发材料损伤, 甚至导致结构失效破坏. 对这类破坏现象的预测需要精细化建模, 以能够反映物质的相变过程和材料的破坏特征. 本文采用热焓法改写经典的热传导方程, 在近场动力学框架下, 建立了一种考虑物质相变的热?力耦合模型, 发展了交错显式求解的数值计算方法, 进行了方板角冻结、热致变形和多孔介质冻结破坏等问题的模拟, 得到了方板的冻结特征、温度场和变形场的分布规律以及多孔介质的冻结破坏过程, 与试验和其他数值方法的结果具有较好的一致性. 研究表明, 本文所建立的考虑物质相变的近场动力学热?力耦合模型能够反映材料的非局部效应和物质相变潜热的影响, 准确捕捉相变过程中液固界面的演化特征, 再现多孔介质中材料相变、基质热致变形和冻结破坏过程, 突破了传统连续性模型求解这类破坏问题时面临的瓶颈, 为深入研究多孔介质冻融破坏过程和破坏机理提供了有效途径.      

A GENERALIZED PIEZOELECTRIC-THERMOELASTIC THEORY WITH STRAIN RATE AND ITS APPLICATION 1)

工程中大量材料的形变介于弹性与黏性之间, 既具有弹性固体特性, 又具有黏性流体特点, 即为黏弹性. 黏弹性使得材料出现很多力学松弛现象, 如应变松弛、滞后损耗等行为. 在研究受热载荷作用的多场耦合问题的瞬态响应时, 考虑此类问题中的热松弛和应变松弛现象, 对准确描述其瞬态响应尤为重要. 针对广义压电热弹问题的瞬态响应, 尽管已有学者建立了考虑热松弛的广义压电热弹模型, 但迄今, 尚未计入应变松弛. 本文中, 考虑到材料变形时的应变松弛, 通过引入应变率, 在Chandrasekharaiah广义压电热弹理论的基础之上, 经拓展, 建立了考虑应变率的广义压电热弹理论. 借助热力学定律, 给出了理论的建立过程并得到了相应的状态方程及控制方程. 在本构方程中, 引入了应变松弛时间与应变率的乘积项, 同时, 分别在本构方程和能量方程中引入了热松弛时间因子. 其后, 该理论被用于研究受移动热源作用的压电热弹一维问题的动态响应问题. 采用拉普拉斯变换及其数值反变换, 对问题进行了求解, 得到了不同应变松弛时间和热源移动速度下的瞬态响应, 即无量纲温度、位移、应力和电势的分布规律, 并重点考察了应变率对各物理量的影响效应, 将结果以图形形式进行了表示. 结果表明: 应变率对温度、位移、应力和电势的分布规律有显著影响.     

Rate-Independent Dynamics and Kramers-Type Phase Transitions in Nonlocal Fokker–Planck Equations with Dynamical Control

The hysteretic behavior of many-particle systems with non-convex free energy can be modeled by nonlocal Fokker–Planck equations that involve two small parameters and are driven by a time-dependent constraint. In this paper we consider the fast reaction regime related to Kramers-type phase transitions and show that the dynamics in the small-parameter limit can be described by a rate-independent evolution equation with hysteresis. For the proof we first derive mass-dissipation estimates by means of Muckenhoupt constants, formulate conditional stability estimates, and characterize the mass flux between the different phases in terms of moment estimates that encode large deviation results. Afterwards we combine all these partial results and establish the dynamical stability of localized peaks as well as sufficiently strong compactness results for the basic macroscopic quantities.     

Nonequilibrium thermodynamics of pseudoelasticity

Solid-solid phase transitions often exhibit hystereses, and a hysteresis indicates energy dissipation. Pseudoelasticity refers to a hysteretic loadingunloading characteristic observed in the stress-induced martensitic transformation of shape memory alloys.This paper describes the thermodynamic model ofideal pseudoelasticity, a largely schematized adaptation of the experimental observations, and it reviews the works of other authors on thermodynamics of pseudoelasticity. Different approaches vary widely and we have chosen to put them into perspective by contrasting their assumptions and predictions against those of ideal pseudoelasticity.Ideal pseudoelasticity receives support from the experimental results of Fu [1] and its thermodynamic properties have been exploited by Huo [2]. The model makes use of an analytical ansatz proposed by Müller [3] in which the hysteresis is assumed to be due to the presence of a coherency energy in solid phase mixtures. This model permits the study of stability of the equilibrium states and the calculation of the energy dissipation or entropy production during the phase transition: The equilibrium states of a phase mixture are found to be unstable in load-controlled processes and the dissipated energy is related to the coherency coefficient.We also discuss some open problems concerning the states inside the hysteresis loop and the formation of interfaces.     

Three dimensional large deformation analysis of phase transformation in shape memory alloys

Shape memory alloys（SMAs）have been explored as smart materials and used as dampers,actuator elements,and smart sensors.An important character of SMAs is its ability to recover all of its large deformations in mechanical loading-unloading cycles without showing permanent deformation.This paper presents a stress-induced phenomenological constitutive equation for SMAs,which can be used to describe the superelastic hysteresis loops and phase transformation between Martensite and Austenite.The Martensite fraction of SMAs is assumed to be dependent on deviatoric stress tensor.Therefore,phase transformation of SMAs is volume preserving during the phase transformation.The model is implemented in large deformation finite element code and cast in the updated Lagrangian scheme.In order to use the Cauchy stress and the linear strain in constitutive laws,a frame indifferent stress objective rate has to be used.In this paper,the Jaumann stress rate is used.Results of the numerical experiments conducted in this study show that the superelastic hysteresis loops arising with the phase transformation can be effectively captured.     

On the asymptotic behavior of a phase-field model for elastic phase transitions

We study the asymptotic behavior of a one-dimensional, dynamical model of solid-solid elastic transitions in which the phase is determined by an order parameter. The system is composed of two coupled evolution equations, the mechanical equation of elasticity which is hyperbolic and a parabolic equation in the order parameter. Due to the strong coupling and the lack of smoothing in the hyperbolic equation, the asymptotic behavior of solutions is difficult to determine using standard methods of gradient-like systems. However, we show that under suitable assumptions all solutions approach the equilibrium set weakly, while the phase field stabilizes strongly.     

Phase transitions induced by extension in a slender SMA cylinder: Analytical solutions for the hysteresis loop based on a quasi-3D continuum model

In this paper, we propose a quasi-3D continuum model to study the rate-independent hysteresis phenomenon in phase transitions of a slender shape memory alloy (SMA) cylinder subject to the uniaxial tension. Based on the three-dimensional field equations and the traction-free boundary conditions, by using a coupled series-asymptotic expansion method, we manage to express the total elastic potential energy of the cylinder in terms of the leading order term of the axial strain. We further consider the rate-independent dissipation effect in a purely one-dimensional setting. The mechanical dissipation functions are also expressed in terms of the axial strain. The equilibrium configuration of the cylinder is then determined by using the principle of maximizing the total energy dissipation. An illustrative example with some special chosen material constants is further considered. Free end boundary conditions are proposed at the two ends of the cylinder. By conducting a phase plane analysis and through some calculations, we obtain the analytical solutions of the equilibrium equation. We find that the engineering stress–strain curves corresponding to the obtained solutions can capture some important features of the experimental results. It appears that the analytical results obtained in this paper reveal the multiple solutions nature of the problem and shed certain light on the instability phenomena during the phase transition process.     

一类时变分岔问题与Duffing—Van der Pol振子

用量级平衡方法分析一类时变分岔问题,得出正反两个方向的分岔转迁滞后且具有对称性,将Duffing-Van derPol振子的相图是一动态滞后环。     

The existence of codimension-two bifurcation in a discrete SIS epidemic model with standard incidence

In this paper, we investigate the dynamical complexity of a discrete SIS epidemic model with standard incidence by the qualitative analysis and numerical simulations. It is verified that there are the codimension-two bifurcations associated with 1:2 and 1:4 strong resonances and chaos phenomena. The results are established by using the bifurcation theory and the normal form method. Furthermore, the numerical simulations are obtained by the phase portraits, the codimension-two bifurcation diagrams, and the maximum Lyapunov exponents diagrams for two different varying parameters in a 3-dimension space. The results obtained in this paper show that a discrete SIS epidemic model can have very rich dynamical behaviors.