陶瓷衬管与双层钢套过盈配合后的应力分析

本文利用ＭＳＣ／ＮＡＳＴＲＡＮ通用程序和过盈接触面有限元柔度间接法，对于陶瓷衬管与双层过盈套管配合后的轴对称结构进行了应力分析，给出了具有实际意义的结论     

MAS 5．0结构分析和优化设计系统

ＭＡＳ是一个兼有结构分析、优化设计和图形处理的现代有限元程序系统，适用于多部门进行工程项目和产品的现代设计．本文简要介绍ＭＡＳ５．０新版软件的组成和功能，系统特点及应用情况．     

膜基组件微硬度量测的数值模拟

采用轴对称弹塑性有限元计算模拟了膜基组件的微硬度量测过程，得到了压头与膜体间无摩擦时组件的变形、塑性区和接触压力分布，针对Ａｌ／Ｓｉ与Ｓｉ／Ａｌ两种膜基组件得到了微硬度和压下量的关系曲线。     

圆杆中弹性应力波的傅立叶弥散分析

基于Ｐｏｃｈｈａｍｍｅｒ和Ｃｈｒｅｅ关于无限长圆杆中纵向谐波的三维弹性解析解，得到了关于圆杆中应力波弥散效应的快速傅立叶波谱分析方法和程序（ＦＦＴＤＳＰ），并利用二维轴对称动力学有限元分析程序（ＡＤＩＮＡ），论证了弥散分析方法和程序的有效性。利用这一弥散分析方法和程序（ＦＦＴＤＳＰ），研究了圆杆的物理和几何参数的变化对弹性波在圆杆中传播的弥散效应的影响。     

圆杆中弹性应力波的傅立叶弥散分析

基于Ｐｏｃｈｈａｍｍｅｒ和Ｃｈｒｅｅ关于无限长圆杆中纵向谐波的三维弹性解析解，得到了关于圆杆中应力波弥散效应的快速傅立叶波谱分析方法和程序（ＦＦＴＤＳＰ），并利用二维轴对称动力学有限元分析程序（ＡＤＩＮＡ），论证了弥散分析方法和程序的有效性。利用这一弥散分析方法和程序（ＦＦＴＤＳＰ），研究了圆杆的物理和几何参数的变化对弹性波在圆杆中传播的弥散效应的影响。     

粘弹性大变形动力响应的有限元分析

本文基于Ｔｏｔａｌ Ｌａｇｒａｎｇｉａｎ增量叠加方法，采用Ｋｉｒｃｈｈｏｆｆ应力增量和Ｇｒｅｅｎ应变增量表示的动力虚功方程和Ｋｉｒｃｈｈｏｆｆ应力－Ｇｒｅｅｎ应变的单积分型本构关系，导出粘弹性大变形的动力变分方程。依此采用Ｎｅｗｍａｒｋ法和八节点轴对称等参数元与二十节点三维等参数元编制了轴对称及三维问题的动力响应计算程序，典型例题的计算结果表明分析符合结构的物理性质。     

粘弹性大变形动力响应的有限元分析

本文基于ＴｏｔａｌＬａｇｒａｎｇｉａｎ增量叠加方法，采用Ｋｉｒｃｈｈｏｆｆ应力增量和Ｇｒｅｅｎ应变增量表示的动力虚功方程和Ｋｉｒｃｈｈｏｆｆ应力－Ｇｒｅｅｎ应变的单积分型本构关系，导出粘弹性大变形的动力变分方程。依此采用Ｎｅｗｍａｒｋ法和八节点轴对称等参数元与二十节点三维等参数元编制了轴对称及三维问题的动力响应计算程序，典型例题的计算结果表明分析符合结构的物理性质。     

MAS5.0结构分析和优化设计系统

ＭＡＳ是一种兼有结构分析，优化设计和图形处理的现代有限元程序系统，适用于多部门进行工程项目和产品的现代设计，本文简要介绍ＭＡＳ５．０新版软件的组成和功能，系统特点及应用情况。     

SMA短纤维增强复合材料在热载下的相交特性

在形状记忆合金（ＳＭＡ）复合材料研究中,相变特性的研究是一个主要的工作．基于Ｅｓｈｅｌｂｙ的等效夹杂模型和Ｍｏｒｉ和Ｔａｎａｋａ的场平均法,考虑到ＳＭＡ材料的强物理非线性,发展了增量型的等效夹杂模型（ＩｎｃｒｅｍｅｎｔａｌＥｑｕｉｖａｌｅｎｔＩｎｃｌｕｓｉｏｎＭｏｄｅｌ）．考虑在某一温度循环条件下讨论形状记忆合金短纤维增强的铝基复合材料在热载下的相变行为．特别研究了ＳＭＡ短纤维复合材料在变温过程中纤维几何尺寸、体积分数等参数对ＳＭＡ复合材料的相变行为和ＳＭＡ内残余应力等的影响．这些工作对于指导材料设计和了解ＳＭＡ复合材料热机械特性是颇有意义的．     

固体力学边界元分析程序包BESMAP——基本结构功能

要使边界元法象有限元法那样得到广泛应用，必须开发与有限元法相媲美的大型边界元法程序包。国外虽出现少数几个边界元法程序包，但由于结构、功能等方面的原因，还不能成为边界元法广泛应用的工具。针对这种情况，本文借鉴现有的先进的有限元法程序包，研制了大型固体力学边界元法程序包ＢＥＳＭＡＰ，ＢＥＳＭＡＰ在总体设计、计算能力、使用方便和功能齐全等方面作了研究和改进。     

超弹性镍钛形状记忆合金单轴相变棘轮行为的宏观唯象本构模型

超弹性镍钛形状记忆合金因其良好的力学性能以及独特的超弹性和形状记忆效应已广泛应用于土木工程、航空航天和生物医疗等多个领域,在实际服役环境中超弹性镍钛合金元件不可避免地会承受不同应力水平的循环载荷作用,亟待建立描述相变棘轮行为(即峰值应变和谷值应变随着正相变和逆相变循环的进行不断累积)的循环本构模型.为此,基于已有的超弹性镍钛形状记忆合金在不同峰值应力下的单轴相变棘轮行为实验研究结果,在广义黏塑性框架下,对Graesser等提出的通过背应力非线性演化方程反映超弹性镍钛形状记忆合金超弹性行为的一维宏观唯像本构模型进行了拓展,考虑了正相变和逆相变过程中特征变量的差异及其随循环的演化,以非弹性应变的累积量为内变量引入了正相变开始应力、逆相变开始应力、相变应变和残余应变的演化方程,同时通过峰值应力与正相变完成应力的比值来确定演化方程中的相关系数,建立了描述超弹性镍钛合金单轴相变棘轮行为的本构模型.将模拟结果与对应的实验结果进行对比发现,建立的宏观唯像本构模型能够合理地描述超弹性镍钛形状记忆合金的单轴相变棘轮行为及其峰值应力依赖性,模型的预测结果和实验结果吻合得很好.     

形状记忆合金的本构模型及其有限元实施

基于塑性力学中屈服面的概率以及Liang和Brinson提出的马氏体体积百分量和应力,温度间的关系,提出了适用于描述多信形状记忆合金的形状记忆效应和伪弹性效应的本构模型,并用T．T．法对该本构模型进行了非线性有限元实施,算例表明该本构模型与实验结果比较吻合,且只需对现有非线性有限元程度稍做修改就可得到实施,简单易行,有一定的实用价值。     

显式方法精确模拟形状记忆合金循环荷载下的变形行为

本文提出全新的有限弹塑性J2流方程,用来显式、精确地模拟SMAs（形状记忆合金）材料在循环加载-卸载条件下从塑性逐渐转变为伪弹性的变形行为．首先,改进流动法,使得本构方程耦合屈服中心的移动和屈服面的增大,并改进背应力演化方程,使模型可以产生强烈的包辛格效应,从理论上具备模拟SMAs独特变形行为的能力;其次,构造全过程下的统一硬化函数显式表达式,代入本构方程后能得到符合要求的形函数;再次,利用选定的数据点构造统一光滑的上屈服函数,再利用上下屈服应力之间的一种线性关系,推导得到下屈服阶段的形函数;最后,只需要给定一个参数就可以得到单个循环结果,利用拉格朗日插值方法构建参数随循环次数变化的函数,就可以模拟任意循环荷载下的变形行为．通过模型结果和实验数据对比证明新方法的有效性．     

A constitutive theory for shape memory polymers. Part II: A linearized model for small deformations

A constitutive theory is developed for shape memory polymers. It is to describe the thermomechanical properties of such materials under large deformations. The theory is based on the idea, which is developed in the work of Liu et al. [2006. Thermomechanics of shape memory polymers: uniaxial experiments and constitutive modelling. Int. J. Plasticity 22, 279-313], that the coexisting active and frozen phases of the polymer and the transitions between them provide the underlying mechanisms for strain storage and recovery during a shape memory cycle. General constitutive functions for nonlinear thermoelastic materials are used for the active and frozen phases. Also used is an internal state variable which describes the volume fraction of the frozen phase. The material behavior of history dependence in the frozen phase is captured by using the concept of frozen reference configuration. The relation between the overall deformation and the stress is derived by integration of the constitutive equations of the coexisting phases. As a special case of the nonlinear constitutive model, a neo-Hookean type constitutive function for each phase is considered. The material behaviors in a shape memory cycle under uniaxial loading are examined. A linear constitutive model is derived from the nonlinear theory by considering small deformations. The predictions of this model are compared with experimental measurements.     

A constitutive theory for shape memory polymers. Part I: Large deformations

A constitutive theory is developed for shape memory polymers. It is to describe the thermomechanical properties of such materials under large deformations. The theory is based on the idea, which is developed in the work of Liu et al. [2006. Thermomechanics of shape memory polymers: uniaxial experiments and constitutive modeling. Int. J. Plasticity 22, 279-313], that the coexisting active and frozen phases of the polymer and the transitions between them provide the underlying mechanisms for strain storage and recovery during a shape memory cycle. General constitutive functions for nonlinear thermoelastic materials are used for the active and frozen phases. Also used is an internal state variable which describes the volume fraction of the frozen phase. The material behavior of history dependence in the frozen phase is captured by using the concept of frozen reference configuration. The relation between the overall deformation and the stress is derived by integration of the constitutive equations of the coexisting phases. As a special case of the nonlinear constitutive model, a neo-Hookean type constitutive function for each phase is considered. The material behaviors in a shape memory cycle under uniaxial loading are examined. A linear constitutive model is derived from the nonlinear theory by considering small deformations. The predictions of this model are compared with experimental measurements.     

A non-local implicit gradient-enhanced model for unstable behaviors of pseudoelastic shape memory alloys in tensile loading

In this paper, a gradient-enhanced 3-D phenomenological model for shape memory alloys using the non-local theory is developed based on a 1-D constitutive model. The method utilizes a non-local field variable in its constitutive framework with an implicit gradient formulation in order to achieve results independent of the finite element discretization. An efficient numerical approach to implement the non-local gradient-enhanced model in finite element codes is proposed. The model is used to simulate stress drop at the onset of transformation, and its performance is evaluated using different experimental data. The potential of the presented numerical approach for behavior of shape memory alloys in eliminating mesh-dependent simulations is validated by conducting various localization problems. The numerical results show that the developed model can simulate the observed unstable behaviors such as stress drop and deviation of local strain from global strain during nucleation and propagation of martensitic phase.     

NONLINEAR LARGE DEFORMATION BENDING PROPERTIES OF THE TRACHEA1)

研究了人工气管和生物气管拉伸和弯曲的力学性能及仿真方法。根据气管拉伸实验数据,拟合建立了人工气管的线弹性和生物气管的非线性幂函数本构模型,其与实验的最大误差为18.8%。根据非线性弯曲理论,建立了气管大变形的弯曲变形方程,并得到了其解析解,计算的弯曲载荷与实验的最大误差为8.7%。基于显式有限元法提出了气管弯曲变形的有限元仿真方法,犬气管的弯曲角度的有限元计算结果与实验的误差为3%。     

A finite element model for shape memory alloys considering thermomechanical couplings at large strains

In the present work we propose a new thermomechanically coupled material model for shape memory alloys (SMA) which describes two important phenomena typical for the material behaviour of shape memory alloys: pseudoelasticity as well as the shape memory effect. The constitutive equations are derived in the framework of large strains since the martensitic phase transformation involves inelastic deformations up to 8%, or even up to 20% if the plastic deformation after the phase transformation is taken into account. Therefore, we apply a multiplicative split of the deformation gradient into elastic and inelastic parts, the latter concerning the martensitic phase transformation. An extended phase transformation function has been considered to include the tension–compression asymmetry particularly typical for textured SMA samples. In order to apply the concept in the simulation of complex structures, it is implemented into a finite element code. This implementation is based on an innovative integration scheme for the existing evolution equations and a monolithic solution algorithm for the coupled mechanical and thermal fields. The coupling effect is accurately investigated in several numerical examples including pseudoelasticity as well as the free and the suppressed shape memory effect. Finally, the model is used to simulate the shape memory effect in a medical foot staple which interacts with a bone segment.     

Differential and integrated form consistency in 1-D phenomenological models for shape memory alloy constitutive behavior

Shape memory alloys are being explored increasingly for developing smart structures and devices in aerospace, automotive and other application areas. The material behavior is highly nonlinear with coupled thermomechanical response involving temperature and/or stress induced phase transformations. Modeling the constitutive behavior of these materials poses several challenges and a few phenomenological models exist that provide a quick and reasonable approach to assess their behavior. Due to phenomenological approach, several assumptions are made in order to simplify the model and some of them introduce inconsistencies or anomalies into the model. In this paper, a frequently used approach, namely, Brinson [Brinson, L.C., 1993. One dimensional constitutive behavior of shape memory alloys: thermomechanical derivation with non-constant material functions and redefined martensite internal variable. J. Intell. Mater. Syst. Struct. 4(2), 229–242.] model, is investigated. The constitutive equation is usually expressed at the outset in the differential form and the integrated form of the same is obtained. It is shown that the two forms of equations are not consistent in the Brinson [Brinson, L.C., 1993. One dimensional constitutive behavior of shape memory alloys: thermomechanical derivation with non-constant material functions and redefined martensite internal variable. J. Intell. Mater. Syst. Struct. 4(2), 229–242.] model, given the assumed form of material functions. In the present work, the nature and implications of the inconsistency are highlighted. The cause of incompatibility is the inconsistent material definitions. A modified consistent constitutive model is proposed by redefining the material function which satisfies the compatibility condition. The advantages in using the proposed modified model are highlighted with numerical case studies involving hysteretic stress–strain behavior.