Deformation Behavior Modeling of SMAs Under Cyclic Loading Based on Rational Interpolation北大核心CSCD

提出了一个有限弹塑性模型,用来模拟形状记忆合金(shape memory alloys,SMAs)在循环荷载下的变形行为.首先,通过分析上下屈服阶段形函数的特点,利用有理插值方法给出循环荷载下的应力-应变形函数显式表达,可以精确匹配任意形状的实验数据;其次,基于对数客观率,构建了有限弹塑性J2流模型,耦合了屈服中心的移动和屈服面的增大;再次,从单轴情况出发,推导得到了单个循环下的三个硬化函数显式表达,再引入局部因子和多轴扩展不变量,构造了光滑统一且多轴有效的硬化函数;最后,将模型得到的结果与经典实验结果比较,证明了新方法的有效性.该文创新点如下:第一,通过改进传统的背应力演化方程,使得新模型产生强烈的Bauschinger效应,从而使新方法具备模拟SMAs特殊变形行为的能力;第二,新的光滑统一硬化函数在单个循环下会自动退化,得到精确符合实验数据的结果;第三,利用本构方程推导得到有效塑性功演化规律,而有理插值得到的形函数中包含依赖有效塑性功的参数,给出这些参数方程以后使得模型具备了预测变形的能力.     

有限变形下的混凝土动态本构关系研究

讨论有限变形和小变形假设下本构关系的区别,并将其运用于混凝土的弹-粘塑性本构关系研究,提出了一个应变率相关的动态力学模型．模型基于Ottosen的4参数屈服准则,分别考虑混凝土在硬化阶段和软化阶段加载面的不同变化规律,建立冲击荷载下的混凝土本构关系．该模型可以应用于冲击载荷下混凝土材料响应的模拟．引进Green-Naghdi客观率建立有限变形的混凝土模型．根据大量实验结果对应变率和材料强度的关系提出合理假设,使模型可以反映混凝土大变形的动态力学行为,为相关工程问题的研究提供有益的思路和有效的工具．     

一种基于无屈服概念的粘塑性模型

结合位错运动的热激活理论,基于无屈服概念,提出了一组描述金属材料变形规律的弹/粘塑性本构方程.方程从总体上考虑了应变率、应变历史、应率变历史、硬化和温度等效应,具有较强的物理基础.恒温单轴条件下商业纯钛的力学性能的理论预测与实验结果相比较,存在着良好的一致性.     

Ti-6242S钛合金高温循环粘塑性行为有限元模拟

采用ANSYS提供的粘塑性流动准则下的双线性各向同性硬化本构模型,考虑材料参数的温度相关性,通过单个单元有限模型对4种温度下施加相同平均应力和不同应力幅值的应力循环工况进行有限元模拟。实验与模拟结果的对比表明,该模型能够较好的地模拟高温450℃以下Ti-6242S钛合金粘塑性变形的循环累积。此外,由于该模型没有考虑循环过程中背应力的演化,对滞回环的预测不够理想,且过高预测了520℃下的粘塑性累积变形。     

超塑性板料的成形极限

根据超塑变形过程中的损伤演变方程和超塑性变形的特点，本文将基于粘塑性势的热粘塑性损伤势函数与Ｈｉｌｌ描述板料变形的各向异性材料屈服行为有机地结合起来，考虑了起塑变形过程中损伤与失稳的交互作用．将起塑变形全过程分为稳定变形。准稳定变形、应变路径飘移和集中性失稳发展四个阶段，用数值方法建立了超塑性板料的损伤失稳模型．然后在此基础上，以集中性失稳发生（ｄε２＝０）或临界空洞体积分数（ｆｃ）作为破坏判据，预测了板料超塑变形时的成形极限。     

混凝土材料的粘塑性损伤本构模型

基于不可逆热力学,引入运动硬化、等向硬化和损伤内变量,构造了相应的自由能函数和流动势函数,推导出了混凝土材料的粘塑性损伤本构模型．数值模拟的结果表明,该模型能够避开屈服面和破坏准则的基本假设来描述混凝土材料的以下特性:压缩载荷作用下的体积膨胀现象;应变率敏感性;峰值后由损伤和破坏引起的应力软化和刚度退化现象A·D2由于此模型避开了根据各种变形阶段选择与其相应的本构模型的繁琐计算,因此更便于纳入复杂工况下应力分析有限元程序中．     

基于有限变形弹塑性模型模拟伪弹性合金全程变形行为

提出一个J2流的有限弹塑性本构方程来显式、全面地模拟了形状记忆合金(SMAs)在3个不同阶段加载并卸载所表现出来的应力-对数应变关系.这3个阶段包括变形完全恢复的伪弹性阶段、变形部分恢复的塑性阶段以及软化破坏阶段.该文的主要思想在于从实验数据的形函数出发,得到用形函数表达的多轴硬化函数,进而代入到本构方程,建立一个能模拟任意形状应力-对数应变关系,多轴有效的本构方程.该文方法的优势在于避免考虑微观到宏观的平均方法、相变条件等一系列复杂处理,大大减少了计算量.所得到的数值结果可以精确匹配实验数据.     

韧性金属大变形拟流动角点理论及应用

本文提出韧性金属弹塑性大变形拟流动角点理论（ｑｕａｓｉ－ｆｌｏｗｃｏｒｎｅｒｔｈｅｏｒｙ）．该理论从塑性变形正交法则出发，将”模量衰减函数”及屈服面的尖点效应引入本构模型，从而实现了由正交法则本构模型向非正交法则本构模型以及从塑性加载向物理弹性却载的光滑过渡，使一般无角点各向异性硬化屈服函数与有角点硬化情形相结合成为可能．用于数值模拟各向异性金属薄板单向拉伸失稳与剪切带分析并与实验结果作比较，表明本文理论的有效性．     

正交各向异性材料的混合硬化弹塑性本构方程

建立了混合硬化正交各向异性材料的屈服准则,进而推导了与之相关的塑性流动法则.根据简单应力状态的实验曲线,可得到广义等效应力-应变关系.初始屈服曲面与材料的弹性常数有关,材料退化为各向同性且只考虑各向同性硬化时,屈服函数退化为Huber-Mises屈服函数,相关的本构方程退化为Prandtl-Reuss方程.     

非线性塑性材料内部空洞闭合模型的研究

基于典型体元(RVE)模型和Rayleigh-Ritz法,对材料内部空洞从球形闭合成裂纹的过程进行了定量研究.基体材料的本构关系采用幂次粘性方程.通过研究材料变形过程中内部球形空洞和圆形裂纹的演化规律,得到了各自的体积应变率的表达式.采用插值近似,建立了空洞闭合的解析模型,发现空洞变形的主要机理来自于空洞周围基体材料的塑性流动.空洞闭合模型反映了材料属性、远场应力三轴度、远场等效应变对空洞闭合的定量规律.空洞闭合模型的预测结果与文献中的数值结果和有限元计算结果相吻合.空洞闭合模型与CAE(computer-aided engineering)技术相结合可对材料加工工艺进行优化设计,为消除材料内部空洞提供了一条有应用前景的新途径.     

模糊随机桁架结构的动力特性双因子分析法

针对模糊随机桁架结构的动力特性分析,提出了一种新的模糊随机有限元方法．当结构的物理参数和几何尺寸同时具有模糊随机性时,利用模糊因子法和随机因子法建立了结构刚度矩阵和质量矩阵;从结构振动的Rayleigh商表达式出发,利用区间运算推导出结构动力特性模糊随机变量的计算表达式;之后利用随机变量的矩法和代数综合法,推导出结构特征值的数字特征的计算式．通过算例分析了模糊随机桁架结构参数的模糊随机性对其动力特性的影响．该方法的优点是能准确反映结构某一参数的模糊随机性对结构特征值及其数字特征的影响．     

模糊运算和模糊有限元静力控制方程的求解

根据模糊数的区间形式表达和区间运算的性质,给出了模糊数和模糊变量的运算规则.据此并依据区间有限元理论,提出了结构模糊有限元静力控制方程的几种求解方法.方法可根据输入模糊数的隶属函数,给出结构响应量的可能性分布.且计算量小,易于实施.算例分析说明了方法是实用和可行的.     

Propagation of infinitesimal thermo-mechanical waves during the finite-deformation loading of a viscoelastic material: general theory

We study the theory of propagation of infinitesimal thermo-mechanical waves in a special class of nonlinear viscoelastic materials under homogeneous and inhomogeneous finite static and time-varying deformations. These results are based on a thermodynamically consistent finite-deformation nonlinear viscoelastic model that reduces to a general linear viscoelastic model of integral form. On a thermo-mechanically deforming body, we impose a thermo-mechanical perturbation history and obtain the equations to solve for the perturbation parameters from the constitutive model and the balance laws. We use these equations to study the characteristics of different perturbations. We develop the special equations for both time-harmonic and time-damping plane waves for homogeneous pre-loads.     

A flexible approach to the simulation of hybrid multibody systems

The present works deals with the incorporation of both flexible beam and shell structures into the realm of flexible multibody dynamics. Geometrically exact beam formulations based on classical Simo-Reissner kinematics are suitable for modelling beam-type flexible components in the context of finite-deformation multibody dynamics. So geometrically exact shell formulations are based on Reissner-Mindlin kinematics. In [2], a flexible framework for dealing with flexible structural elements in a multibody context is described. A specific isoparametric finite element discretization of a shell formulation leads to semi-discrete equations of motions assuming the form of differential-algebraic equations (DAEs). A compatible isoparametric formulation of beams has already been developed in [1]. The uniform DAE framework makes possible the incorporation of alternative finite element formulations. In addition to that, various time-stepping schemes such as energy-momentum methods or variational integrators can be applied. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Comportamiento dinámico de viaductos cortos considerando la interacción vehículo-vía-estructura-suelo

The dynamic vehicle-track-bridge-soil interaction is studied on high speed lines. The analysis is carried out using a general and fully three dimensional multi-body-finite element-boundary element model, formulated in the time domain to predict vibrations due to the train passage over the bridge. The vehicle is modelled as a multi-body system, the track and the bridge are modelled using finite elements and the soil is considered as a homogeneous half-space by the boundary element method. Usually, moving force model and moving mass model are employed to study the dynamic response of bridges. In this work, the multi-body system allows one to consider the quasi-static and dynamic excitation mechanisms. Soil-structure interaction is taken into account on the dynamic structure behaviour on simply-supported short span bridges. The influence of soil-structure interaction is analysed in both resonant and non-resonant regimes.     

二维非饱和土壤水分运动问题的半离散有限体积元模拟

本文利用基于重心对偶剖分的有限体积元法建立了二维非饱和土壤水分运动问题的数值逼近格式,讨论了离散有限体积元解的存在唯一性,并给出了最优误差估计的证明.最后给出数值算例,模拟结果表明,利用有限体积元格式来求解二维非饱和土壤水分运动问题是可靠的,且该格式具有稳定性和可实用性.     

Computational Excavation Analysis of a Single Cutting Tool using a Hypoplastic Constitutive Model

We propose a computational model for the numerical analysis of the dynamic interaction between a single excavation tool and the surrounding soil. An incremental non-linear (hypoplastic) constitutive model is employed to capture the complex response of soft soils. Large displacements and deformations are handled by an Updated Lagrangian formulation, the particle finite element method (PFEM). (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A beam segment element for dynamic analysis of large aqueducts

Large aqueduct structure is a complex structure that is commonly used in hydraulic engineering, especially in large-scale water conveying projects. The analysis of dynamic response for an aqueduct structure is necessary if the aqueduct is built in an earthquake area. Traditional 3D finite element analysis is time consuming and the existing simplified response method cannot take into account all the effects, such as the bending-torsion coupling effect and the constrained torsion, of the deformations of the thin wall structure of the aqueduct body. For this special structure, a simple and yet accurate model for dynamic analysis is needed. In this paper, a beam segment element is developed and used for the calculation of dynamic response for aqueduct structures. With the frame of the aqueduct being modeled using beam element, the proposed model can calculate the dynamic response of the whole aqueduct structures. Results are compared with that of a general purpose finite element analysis software using 3D finite element model. Good agreement is achieved between the two models. However, the proposed model needs less elements and much less computing time.     

A Hardening Description based on a Finite-Deformation Gradient Crystal Plasticity Model: Formulation and Numerical Implementation

In this study, a well-defined finite-deformation gradient crystal plasticity is employed to study size-dependence strengthening behavior of a single crystal under simple shear loading. The constitutive model is implemented in the FEM software ABAQUS via a user-defined element subroutine (UEL). Effect of gradient strengthening, latent hardening and scale-variation in mechanically plastic response of a single crystal subjected to isothermal quasi-static loading is studied and discussed. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dynamic pricing model and algorithm for perishable products with fuzzy demand

This paper studies the dynamic pricing problem of selling fixed stock of perishable items over a finite horizon, where the decision maker does not have the necessary historic data to estimate the distribution of uncertain demand, but has imprecise information about the quantity demand. We model this uncertainty using fuzzy variables. The dynamic pricing problem based on credibility theory is formulated using three fuzzy programming models, viz.: the fuzzy expected revenue maximization model, α‐optimistic revenue maximization model, and credibility maximization model. Fuzzy simulations for functions with fuzzy parameters are given and embedded into a genetic algorithm to design a hybrid intelligent algorithm to solve these three models. Finally, a real‐world example is presented to highlight the effectiveness of the developed model and algorithm. Copyright © 2009 John Wiley & Sons, Ltd.