基于应力的广义Jaumann导数的大变形本构关系

研究了用实心圆轴扭转实验标定大变形弹塑性本构关系的问题.首先进行了A3钢的单向拉伸和纯扭转实验,分析了两种实验的应力应变曲线特性,给出了实心圆轴扭转实验中变形率d、相对旋率Ω和广义Jaumann导数的具体形式.然后以应力的广义Jaumann导数作为客观导数,应用等向强化J2流动塑性理论,建立了由扭转实验的Υ-γ曲线标定的大变形本构关系形式.结果表明,对应广义Jaumann应力导数的扭转大变形本构关系与对应Jaumann应力导数的本构关系形式相同.     

基于扭转试验的大变形本构关系分析

研究采用实心圆轴扭转试验标定大变形弹塑性本构关系时客观应力导数的影响问题.给出了在实心圆轴扭转试验中,几种常用旋率的具体形式.应用等向强化的J2流动塑性理论,建立了以扭转试验的应力-应变曲线为基准的,分别由Oldroyd、广义Jaumann应力导数和相对于变形率标架旋率的应力导数表述的大变形弹塑性本构关系.所得各本构关系中的塑性刚度函数与由Jaumann客观应力导数给出的塑性刚度函数形式相同,说明用扭转试验标定大变形弹塑性本构关系时,塑性刚度函数不受客观应力导数的影响,本构形式相对稳定.     

基于变形率标架旋率的大变形本构关系

选用扭转实验标定大变形弹塑性本构关系,讨论在实心圆轴扭转实验中,变形率标架旋率Ωd的具体形式.以应力相对于变形率标架旋率Ωd的导数tobj0[Ωd]作为客观导数,应用各向同性硬化的J2流动塑性理论,建立由扭转实验的τ-γ曲线标定的大变形本构关系形式.所得结果与由Jaumann客观应力导数给出的结果相同,从而说明用扭转实验标定大变形本构关系时,本构形式相对稳定.     

两种约束圆轴扭转实验确定大应变本构关系

针对大应变本构关系的参数标定问题,采用实心圆轴扭转实验进行了研究.分别对一端自由实心圆轴和两端固定实心圆轴的大应变扭转变形和扭转应力进行了分析.对于大应变等向强化弹塑性本构模型,基于Kirchhoff应力的Jau-mann应力导数,采用实心圆轴扭转实验标定了弹塑性本构模型中的塑性刚度函数.对一端自由实心圆轴扭转实验,讨论了轴向伸长变形和径向变形对塑性刚度函数的影响.对于两端固定实心圆轴扭转实验,讨论了轴向正应力对塑性刚度函数的影响.结果表明,实心圆轴扭转时的Swift效应对大应变本构关系有影响,影响程度与轴向和径向变形及轴向正应力相对于剪应变的变化率有关.     

实心圆轴扭转问题中的旋率分析

给出由实心圆轴扭转实验标定大变形本构关系时的各种旋率张量.由于实心圆试件在扭转过程中变形具有较好的均匀性,所以用于标定大变形本构关系问题比拉伸试验更为合理.在圆柱坐标系下讨论实心圆轴扭转试验中用于表述客观应力率张量的各种旋率形式,给出有意义的理论结果.扭转问题中旋率的分析为今后建立基于扭转试验的各种大变形本构关系打下基础.     

沥青混合料粘弹塑性本构关系及大变形有限元分析一般理论

应用Perzyna’s理论和Mises屈服准则建立沥青混合料粘弹塑性本构方程,并扩展到三维方程;应用Newton-Raphson迭代程序的逐步积分方法,获得了小变形粘弹塑性本构理论增量形式和有限元数值方程。基于小变形本构理论,把其应力应变、应力偏量和等效应力分别改用Cauchy应力的Jaumann导数、变形率、应力偏量和等效应力,推导出大变形粘弹塑性增量形式的本构方程和数值方程,建立了沥青混合料粘弹塑性理论体系。     

欧拉描述的有限应变固结控制方程之矩阵表述

采用Voigt规则建立了欧拉描述的有限应变固结控制方程的矩阵表述形式.同时将Truesdell率型本构关系引入到欧拉描述的有限应变固结理论中,阐明了Truesdell率与常用的Jaumann率之间的关系.结果表明,欧拉描述的有限应变固结控制方程的矩阵形式要比T.L.和U.L.两种物质描述方法的矩阵形式简洁;当忽略Truesdell率型本构矩阵中的某子矩阵时,就退化为Jaumann率型本构矩阵.可供有限元编程分析参考.     

粘土数值建模方法与Duncan模型的对比研究

以塑性体应变与塑性剪应变之间的相互作用原理为指导,对粘土本构关系的数值建模方法进行了研究。采用包含应力路径函数的两个本构泛函作为模型基本框架,可以反映出应力路径相关性。应力应变增量关系的表达式包含两个偏导数的交叉项,用于反映塑性体应变与塑性剪应变的相互作用。利用三轴试验结果建立了粘土的弹塑性本构模型,该模型能够反映出土的三大基本力学特性:压硬性、剪胀性和应力路径相关性。通过可视化,分别给出在整个应力场中剪切和体积的三维变形曲面。此外,从模型的理论基础、基本框架和预测结果等方面与Duncan模型进行对比,显示出数值建模方法优于传统方法。     

基于试验非拟合混凝土本构方程

目的建立混凝土单轴拉伸和压缩应力-应变方程．方法基于混凝土单轴拉伸和压缩的试验数据,研究应力-应变变化规律,抛弃传统的拟合方法,直接由混凝土基本性能（初始弹性模量、峰值应力、峰值应变和应变软化性态）导出应力-应变方程．结果全程应力-应变方程由强化方程和软化方程给出,在峰值应力之前,强化方程为单调增且二阶导数为负的曲线,与试验结果曲线相符．在峰值应力之后,用不同的软化方程表示试验软化曲线．结论笔者提出的混凝土本构方程与很多实验数据相符,方程中的参数具有明显的力学意义,形式简单,便于理解,能很好的应用于混凝土本构关系的研究中．     

散煤的大变形应力应变关系试验研究

为了得到散煤的本构关系,设计了散煤在侧限条件下的大尺寸轴向压缩试验以测定其在轴向分级受压时的应力应变关系,应力和应变的度量分别采用Cauchy应力和对数应变.分析了燃煤的本构关系特点,整理得出:体积应力的对数和体积应变之间近似呈线性关系,偏应力的对数与偏应变之间也近似呈线性关系,此关系符合多孔介质弹性理论中所指出的材料的应力应变关系.基于多孔介质弹性本构模型,通过线性回归分析得到了散煤的体积模量和剪切模量的一般表达式.     

土体有限变形理论的弹性本构关系之辨析

根据有限变形理论 ,针对土体变形的运动描述形式不同 ,具有不同类型的应力、应变定义及其相应的本构关系构成形式 ,考虑到固结理论耦合分析对本构关系的要求 ,讨论了将土体视为弹性或非线性弹性条件下本构关系的客观性与适用性     

Modeling uniaxial tensile deformation of polycrystalline AI using CPFEM

The crystal plasticity finite element modeling （CPFEM） is realized in commercial finite element code ABAQUS with UMAT subroutine on the basis of the crystal plasticity theory of rate dependent polycrystal constitutive relations in the mesoscopic scale. The initial orientations obtained by electron backscatter diffraction （EBSD） are directly input into the CPFEM to simulate the mechanical response of polycrystalline 1050 pure Al in uniaxial tensile deformation. Two polycrystal models and two tensile strain rates were used in the simulations. The stress-strain curves of tensile deformation were analyzed. The predictions and the corresponding experiment result show reasonable agreement and slight deviation with experiments. The flow true stress of strain rate 0.01 s^-1 is higher than that of strain rate 0.001 s^-1. At the strain less than 0.05, the stress saturated rate of the experiment is higher than the simulated results. However, the stress saturated rate of the experiment becomes gentler than the corresponding simulated predictions at the strain over 0.05. Also, necking was simulated by the two models, but the necking strain is not well predicted. Tensile textures at strain 0.25 were predicted at the low strain rate of 0.001 s^-1. The predictions are in good accord with the experimental results. 2008 University of Science and Technology Beijing. All rights reserved.     

Modeling uniaxial tensile deformation of polycrystalline Al using CPFEM

The crystal plasticity finite element modeling (CPFEM) is realized in commercial finite element code ABAQUS with UMAT subroutine on the basis of the crystal plasticity theory of rate dependent polycrystal constitutive relations in the mesosocpic scale. The initial orientations obtained by electron backscatter diffraction (EBSD) are directly input into the CPFEM to simulate the mechanical response of polycrystalline 1050 pure AI in uniaxial tensile deformation. Two polycrystal models and two tensile strain rates were used in the simulations. The stress-swain curves of tensile deformation were analyzed. The predictions and the corre-sponding experiment result show reasonable agreement and slight deviation with experiments. The flow true stress of strain rate 0.01 s-1 is higher than that of strain rate 0.001 s-1. At the strain less than 0.05, the stress saturated rate of the experiment is higher than the simulated results. However, the stress saturated rate of the experiment becomes gentler than the corresponding simulated predictions at the strain over 0.05. Also, necking was simulated by the two models, but the necking strain is not well predicted. Tensile textures at swain 0.25 were predicted at the low strain rate of 0.001 s-1. The predictions are in good accord with the experimental results.     

钢管混凝土三维非线性梁单元的研究与应用

为研究钢管混凝土构件的力学性能。建立可承受压弯剪（扭）的三维钢管混凝土梁单元，用双线性随动硬化模型模拟外钢管的本构关系，对核心受拉和受压混凝土采用不同的非线性材料特性。利用自行编制的程序，对各种钢管混凝土构件荷载－变形全过程分析，计算结果与试验数据符合较好。     

Constitutive Modeling and Dynamic Recrystallization Mechanisms of an Ultralow-carbon Microalloyed Steel During Hot Compression Tests

The hot deformation behavior of an ultralow-carbon microalloyed steel was investigated using an MMS-200 thermal simulation test machine in a temperature range of 1 073-1 373 K and strain rate range of 0.01-10 s~(-1).The results show that the flow stress decreases with increasing deformation temperature or decreasing strain rate.The strain-compensated constitutive model based on the Arrhenius equation for this steel was established using the true stress-strain data obtained from a hot compression test.Furthermore,a new constitutive model based on the Z-parameter was proposed for this steel.The predictive ability of two constitutive models was compared with statistical measures.The results indicate the new constitutive model based on the Z-parameter can more accurately predict the flow stress of an ultralow-carbon microalloyed steel during hot deformation.The dynamic recrystallization (DRX) nucleation mechanism at different deformation temperatures was observed and analyzed by transmission electron microscopy (TEM),and strain-induced grain boundary migration was observed at 1 373 K/0.01 s~(-1).     

薄膜元理论在钢筋混凝土纯扭构件计算中的应用

对薄膜元理论在受扭构件中的应用进行了探讨，以软化变角空间桁架理论为基础，考虑混凝土的“软化效应”，通过建立应力平衡方程、应变协调方程、本构关系方程，用反复迭代的数值分析方法，模拟构件受力的全过程。用此方法对纯扭构件作了全过程分析，对构件的破坏荷载和变形进行了计算，理论分析结果与试验结果吻合较好。     

Dynamic analysis of fault rockburst based on gradient-dependent plasticity and energy criterion

Fault rockburst is treated as a strain localization problem under dynamic loading condition considering strain gradient and strain rate. As a kind of dynamic fracture phenomena, rockburst has characteristics of strain localization, which is considered as a one-dimensional shear problem subjected to normal compressive stress and tangential shear stress. The constitutive relation of rock material is bilinear (elastic and strain softening) and sensitive to shear strain rate. The solutions proposed based on gradientdependent plasticity show that intense plastic strain is concentrated in fault band and the thickness of the band depends on the characteristic length of rock material. The post-peak stiffness of the fault band was determined according to the constitutive parameters of rock material and shear strain rate. Fault band undergoing strain softening and elastic rock mass outside the band constitute a system and the instability criterion of the system was proposed based on energy theory. The criterion depends on the constitutive relation of rock material, the structural size and the strain rate. The static result regardless of the strain rate is the special case of the present analytical solution. High strain rate can lead to instability of the system.     

一种考虑多种强化机制的黄土本构关系

将黄土材料的含水量和变形历史引入到内时定义中,利用与热力学相一致的简单机械模型发展了黄土的偏应力应变本构关系。用所建立的本构方程分别描述了马兰黄土在不同围压和不同含水量条件下的应力应变响应特性,取得与现有实验相吻合的结果。所提出的考虑围压和含水量的黄土本构模型对黄土在各种复杂载荷作用下变形与破坏现象的研究具有一定参考价值。