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。     

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.     

考虑附加强化效应的多轴稳态循环塑性本构模型

已有试验结果表明,非比例循环加载下应变主轴连续旋转,导致多滑移系开动,阻碍材料内部形成稳定的位错结构,使非比例加载下的应力-应变曲线高于比例加载下的应力-应变曲线,从而产生非比例附加强化现象.由此,从应力空间表述的塑性增量本构模型一般形式出发,建立一个能够反映非比例附加强化效应的稳态循环塑性本构模型.在Armstrong-Frederick模型背应力演化方程的基础上,新模型通过引入非比例度因子和附加强化系数,构建了一个新的背应力演化方程.然后,通过一致性条件建立塑性模量方程与背应力之间的关系.同时,利用最小法向应变范围,提出一种计算非比例度因子的新方法,并针对一般的多轴加载情形,明确最小法向应变范围的计算步骤.新模型从加载路径和材料本身两个方面来考虑非比例附加强化效应的影响,克服Armstrong-Frederick模型中材料常数确定方法繁琐,且通过单轴疲劳试验数据确定的材料常数不能很好地反映材料非比例附加强化现象的不足.应用新模型时,仅仅需要3个独立的常规力学参量和2个疲劳参数,便于工程应用.利用多种多轴加载路径下S460N钢和304不锈钢的试验结果对模型进行验证,预测结果与试验结果吻合良好.     

关于弹塑性应力应变集中关系的探讨

本文分析了Neuber关系的推导过程,描出Neuber关系,即使对Ⅲ型加载问题也不是解析解。本文根据弹塑性断裂力学理论,对幂强化材料,导出了Ⅲ型加载裂纹问题弹塑性应力应变集中关系。同时分折了Ⅰ型缺口弹塑性应力应变集中关系。     

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.     

基于σ=C（e^p,e^.p,T）热弹塑性本构关系矩阵

高温下的材料流动应力通常是应变总量、温度和应变速率的函数。考虑为三个因素对流动应力的影响，建立了高温感化材料的弹塑性本构关系矩阵。     

Mises等向强化材料的薄壁圆管的拉扭联合变形

本文根据文献中所得到的用于Mises等向强化材料的薄壁圆管拉扭联合变形时的增量理论和全量理论的应力应变关系,提出了一个明确的Mises等向强化条件,并给出了在线性等向强化条件下沿阶梯加载路径和线性比例加载路径的具体解答.     

冻土粘弹塑性参数的测试方法

根据已有冻土试验资料,建立描述冻土粘弹塑性特征的本构模型,给出本构参数的确定方法。首先,推导本构模型的微分列式并根据不同加载条件求解微分方程。其次,设计不同加载条件的冻土试验,以测定应力应变曲线,或应力随时间、或应变随时间曲线。然后,根据以等应变率下的试验曲线为例研究讨论了在不同条件下确定本构参数的方法。包括:在等应变率加载条件下,根据应力应变曲线或应力时间曲线确定本构参数;在等应力加载条件下,根据应力应变曲线或应变时间曲线确定本构参数;在应变率为零时,利用松弛曲线确定本构参数;在应力率为零的条件下,利用蠕变曲线确定本构参数。     

岩石塑性应变损伤模型的建立及应用

岩石塑性变形和损伤变量的微观机制都是岩石中微裂纹的萌生和发育,塑性变形与损伤在岩石材料中是同时出现的,它们的演化规律是相互耦合的.本文采用基于塑性应变的损伤变量,定义岩石在破坏过程中塑性应变增量与损伤增量成正比关系,并把极限塑性应变归一于岩石的临界损伤值,建立了岩石塑性应变损伤模型和本构模型.实验曲线与利用所建立的塑性应变损伤模型计算的应力-应变曲线吻合较好,岩石塑性应变损伤模型能较好地描述岩石整个加载过程中的损伤与应力、应变的关系.并根据岩石塑性应变损伤模型,分析了单轴压缩荷载作用下岩石的应力和应变与损伤的演化规律.     

强化—弱化材料的本构关系

本文从岩土类材料的变形和破坏机理出发,建议在应力空间中用一个不断收缩的“边界面”来描述材料的弱化过程。给出了强化一弱化材料的本构方程。加载准则采用应力和应变混合判据。这种方法能同时吸取应力空间描述和应变空间描述两种方法的优点。     

超固结土的蛋形弹塑性本构模型

为了描述超固结软土在不同应力条件下的强度变形特征,以蛋形函数为基本框架,建立并发展适用于超固结土体的弹塑性本构模型. 通过对一系列超固结土应力路径三轴压缩试验结果的分析,探讨土体在超固结状态下塑性应变的发展规律(剪胀/剪缩). 在先前提出的旋转塑性势面流动法则基础上对其进行发展与改进,引入峰值应力比,构建剪胀状态下归一化塑性势面旋转角与应力状态参数之间的近似线性关系,以满足超固结土的塑性变形特性. 结合基于等效硬化参量的广义塑性功硬化原理构建超固结软土的蛋形弹塑性本构模型. 将三轴压缩试验数据与数值预测结果进行对比以验证模型有效性,结果表明该模型可以有效反映超固结软土在不同加载条件下的应力应变特性,比如软化与剪胀.     

考虑应变强化的高压缩性黏土修正双曲线模型

研究了武汉地区高压缩性黏土弹塑性本构模型。基于Duncan E～v双曲线模型,对等压固结条件下CTC应力路径三轴实验数据进行了数据拟合,得到了该条件下的非线性应力应变关系,并将卸载-再加载试验曲线的平均斜率作为卸载模量,引入了加卸载函数作为判定加卸载的准则。将该模型嵌入有限元程序对三轴压缩试验进行数值模拟,并与Duncan模型数值解及试验曲线作对比。结果表明,该模型较Duncan模型能更好的体现正常固结黏土在CTC路径下的应力应变关系,特别是加载后期的应变强化效应,与试验曲线的最大相对误差不超过5％。     

基于增量本构关系弹塑性分析的无网格伽辽金法

在无网格伽辽金法的基础上，采用增量形式的无网格伽辽金法的插值方法，并利用应力应变增量形式表征材料的弹塑性本构关系，在小变形假设的前提下，提出了基于增量本构关系的弹塑性分析的无网格伽辽金法；采用罚参数修正了能量变分方程式，方便地实现了无网格伽辽金法的本质边界条件．对二维平面问题及轴对称问题的计算结果表明：运用增量形式的无网格伽辽金法进行弹塑性问题的数值分析，具有较高的计算精度，且适应性强，从而为材料的弹塑性分析计算提供了一种实用方法。     

Mean-field homogenization of elasto-viscoplastic composites based on a new mapping-tangent linearization approach

In this work, a new homogenization method of elasto-viscoplastic composites is developed. Using the fully implicit backward Euler's integration algorithm, the nonlinear ordinary differential equations in the constitutive laws of the matrix and inclusion phases are discretized. Three classical incremental linearization approaches, i.e., direct, secant and tangent ones are adopted and an affine relationship between the stress and strain increments is deduced. In order to reduce the interaction between the inclusion and matrix phases, a second-ordered mapping tensor is introduced and a new mapping-tangent linearization approach is proposed. Different linearization approaches are implemented by the incremental self-consistent scheme to predict the overall stress-strain response of particle-reinforced composites. It is shown that the predicted stress-strain curves given by the proposed mapping-tangent linearization approach are softer than that by other three classical ones, and are much closer to that from a fullfield finite element simulation. Moreover, the linearized elasto-viscoplastic constitutive equation based on the proposed mapping-tangent approach has the same mathematical structure as the rate-independent elasto-plastic constitutive law. In this sense,the homogenization problems faced in the elasto-plastic and elasto-viscoplastic heterogeneous materials can be unified.     

循环荷载三面本构模型及与实验结果比较

为探求形式简洁,参数较少,便于工程应用的循环本构模型,本文基于边界面模型和多面模型理论,建立了一个可描述金属材料三轴循环加载力学行为的三面本构模型.把塑性应变分解成塑性应变1和塑性应变2,塑性应变1对应于一套屈服面-边界面模型,塑性应变2对应于一套单屈服面模型.提出了当前应力点与边界面上对偶点之间距离的演变公式,基于一致性条件得出边界面模型中塑性模量的计算与运动硬化准则的联系.采用塑性应变作为硬化参数,应用关联流动法则计算塑性应变.相比于经典的边界面模型,本文模型形式简明;相比于前人修正随动硬化准则模型,本文模型需要的材料参数较少.结合金属稳定材料U71Mn的单轴循环实验结果,对其4种力学行为进行模拟,分析了非对称应力循环下平均应力和应力幅值对稳定材料棘轮效应的影响,以及对称应变循环下材料的最大应变幅值记忆效应.研究结果表明,本文模型的模拟结果与前人文献的实验结果一致性较好,可为研究材料的本构行为提供一条新的途径.     

Experimental investigation and numerical modeling for elasto-plastic notch-root stress/strain analysis under monotonic loadings

Experimental investigation and numerical modeling on elasto-plastic notch-root stress/strain distributions under monotonic loadings of both the Ni-based directionally solidified (DS) superalloy and Titanium alloy were carried out simultaneously. For measuring inhomogeneous deformation fields at notch roots, an optical-numerical full-field surface deformation measurement system was developed based on the digital image correlation (DIC) method. The obtained strain distributions were then verified with reasonable accuracy by finite element simulation, where an anisotropic elastic-viscoplastic constitutive model was developed for DS superalloy and a simple isotropic stress-strain relationship was adopted for Titanium alloy. Meanwhile, factors affecting elasto-plastic notch-root stress/strain distributions were systematically investigated numerically, where the emphasis was placed on temperature, loading stress rate, sample shape, anisotropy and notch features. The results show that stress/strain behavior at notch root is significantly affected by the mentioned factors, which are concretely embodied in the distribution of tensile stress/strain, equivalent stress and accumulative equivalent plastic strain.     

Elasto-plastic analysis of masonry with anisotropic plastic material model

This paper establishes an anisotropic plastic material model to analyze the elasto-plastic behavior of masonry in plane stress state.Being an anisotropic material,masonry has different constitutive relation and fracture energies along each orthotropic axes.Considering the unique material properties of masonry,a new yield criterion for masonry is proposed combining the Hill’s yield criterion and the Rankine’s yield criterion.The new yield criterion not only introduces compression friction coefficient of shear but also considers yield functions for independent stress state along two material axes of tension.To solve the involved nonlinear equations in numerical analysis,several nonlinear methods are implemented,including Newton-Raphson method for nonlinear equations and Implicit Euler backward mapping algorithm to update stresses.To verify the proposed material model of masonry,a series of tests are operated.The simulation results show that the new developed material model implements successfully.Compared with isotropic material model,the proposed model performs better in elasto-plastic analysis of masonry in plane stress state.The proposed anisotropic model is capable of simulating elasto-plastic behavior of masonry and can be used in related applications.     

Cyclic constitutive equations of rock with coupled damage induced by compaction and crackingOA

In this paper, the cyclic constitutive equations were proposed to describe the constitutive behavior of cyclic loading and unloading. Firstly, a coupled damage variable was derived, which contains two parts,i.e., the compaction-induced damage and the cracking-induced damage. The compaction-induced damage variable was derived from a nonlinear stress–strain relation of the initial compaction stage, and the cracking-induced damage variable was established based on the statistical damage theory.Seco...     

冲压成形过程的弹粘塑性有限元数值模拟

应用单轴应力状态下的弹粘塑性本构关系和J2 流动理论及等向强化准则建立起适用于多轴应力状态的普遍的弹粘塑性本构关系 ,并将其引入增率型虚功率原理建立了弹粘塑性有限元列式。用基于该组列式编制的大变形有限元程序对单拉过程和方盒件深拉延成形过程进行了数值模拟 ,并与单拉实验结果进行了比较。数值模拟结果表明 :本文建立的弹粘塑性材料的本构关系是有效的 ,同时说明根据增率型虚功率原理建立的弹粘塑性有限元列式可以有效地对弹粘塑性变形过程进行数值模拟。