几种循环塑性模型的剖析和比较研究

首先阐明循环塑性模型需满足的力学条件：连续与光滑条件，曼辛效应与棘轮效应。基于这些条件，对多面、无限多面、两面、单面、边界面、次加载面模型等几种常见的循环塑性模型的基本特性进行深入而系统的剖析，对它们预测材料循环加载特性的能力进行分析与比较。结果表明：多面模型与无限多面模型反映的是过强的滞回效应，无法反映变形的积累性；两面、单面与边界面模型反映的是较弱的滞回效应与较大的积累变形；次加载面模型满足循环塑性模型所要求的力学条件，可以控制曼辛系数，能较好地反映材料的循环加载特性，将次加载面思想与广义塑性力学结合，可望建立更合理的循环塑性模型。     

基于数字图像相关法的A7N01-T4铝合金焊接接头循环变形行为实验研究

为研究A7N01铝合金MIG焊焊接接头单轴拉伸性能和循环变形特征,采用数字图像相关方法(DIC)分析A7N01铝合金焊接接头在单调拉伸和循环加载下的应变场分布,结合焊接接头显微硬度获取焊接接头整体、焊缝、热影响区和母材的平均应力-应变曲线。实验结果表明:焊接接头母材在单调拉伸和循环变形中一直处于弹性变形,焊接接头整体的塑性变形由焊缝和热影响区主导,体现出循环稳定特征和棘轮安定状态,焊接接头的棘轮应变值依赖于当前的应力水平和加载历史。     

合金钢的高温单轴棘轮效应实验研究1.25Cr0.5Mo

利用MTS810电液伺服试验机在300℃温度下对1.25Cr0.5Mo合金钢进行了单轴棘轮效应实验研究,探讨了温度、应力幅值、应力峰值、平均应力以及加载历史对材料棘轮效应的影响.以0.1%/s及0.2%/s两种不同的应变加载速率分别对材料进行单轴拉伸实验,结果表明1.25Cr0.5Mo合金钢在所研究的温度范围内的变形行为是率无关的;在0.4%应变幅值下进行了单轴应变循环实验,响应应力幅值随循环次数几乎没有变化,可视为循环稳定材料;单轴棘轮效应实验表明棘轮应变速率随平均应力、应力幅值及温度的升高而增大;棘轮变形依赖于加载历史,先前较大的循环应力对后继较小的循环应力下的棘轮变形起抑制作用.     

长期循环荷载下饱和软黏土安定性模型

鉴于传统显式、隐式模型计算饱和软黏土长期循环荷载下轴向塑性累积应变的不足,在建立饱和软黏土总应力弹塑性模型基础上,考虑软黏土在长期小动应力比循环荷载作用下具有安定性特点,结合过应力模型及安定性理论提出计算饱和软黏土长期循环荷载下轴向塑性累积应变安定性本构模型。安定性模型能合理描述饱和软黏土循环荷载下的变形特性,模型只考虑最大塑性变形包络线故可采用任意积分步长,适用于大数目循环加载的累积变形计算及长期交通荷载下地基的沉降计算。     

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.     

Cyclic deformation behaviour of natural K_0-consolidated soft clay under different stress paths

Characteristic of cyclic loading due to passing wheels is associated with one-way loading without stress reversal,which includes a simultaneous cyclic variation of vertical normal stress and horizontal normal stress lasting for a long period of time and generally takes place in partially-drained conditions.Therefore,it is of great practical relevance to study the deformation behaviour according to the characteristic of traffic loading.In this work,a series of one-way stress-controlled cyclic triaxial tests with a simultaneous variation of the vertical and horizontal stress components during cyclic loading were conducted to investigate the deformation behaviour of natural K_0-consolidated soft clay in partially-drained conditions.Test results demonstrate that not only the deviator part of the stress rules accumulation but also the volumetric part significantly contributes.While the deviator part of the stress amplitude is held constant,the increase amplitude of cyclic confining pressure will promote the development of both permanent volumetric strain and axial strain significantly.Furthermore,the effects of cyclic confining pressure on the deformation of natural K_0-consolidated soft clay was quantified.Finally,an empirical formula for permanent axial strain considering the effects of cyclic confining pressure was proposed which can be used for feasibility studies or for the preliminary design of foundations on K_0-consolidated soft clay subjected to traffic loading.     

长期交通荷载作用下粉砂土累积变形本构模型构建及数值积分格式

因目前在模拟长期交通荷载作用下粉砂土路基不均匀变形时尚缺乏一套严谨、高效的计算模型,在室内静力及动三轴试验的基础上,通过引入安定性理论,基于弹塑性本构理论框架,提出了一个能合理反映粉砂土复杂变形机理的双屈服面等效黏塑性本构模型。对粉砂土动三轴试验结果的模拟表明,该模型采用完全隐式的积分方法,可任意选取积分步长,计算效率高,模拟效果良好。最后,将该模型在有限元程序中进行了实现,可应用于路基不均匀累积变形的计算。     

SSUH model: A small-strain extension of the unified hardening model

A small strain unified hardening (SSUH) model is proposed in the present study to tackle the small strain behavior of clay. The model is an extension of the unified hardening (UH) model for overconsolidated (OC) clays accounting for the small strain stiffness. The new features of the SSUH model over the UH model include: (a) a new elastic hysteretic stress-strain relationship to evaluate the stiffness degradation at small strains and to generate the hysteresis loop under cyclic loading condition; (b) a revised unified hardening parameter to enhance the plastic stiffness at small strains; and (c) a new overconsolidation parameter, which is crucial to make the UH model working with the elastic hysteretic stress-strain relationship effectively. With these enhancements, the SSUH model can describe a high initial stiffness and the highly nonlinear stress-strain relationship at small strains, in addition to the shear dilatancy and strain hardening/softening behaviors of OC clays at large strains. In comparison with the Modified Cam-clay (MCC) model, the proposed model needs two more small strain related parameters, which can be easily obtained from laboratory tests. Finally, some drained triaxial compression tests at large strains, drained triaxial compression/extension tests at small strains, an undrained compression test at small strains and a drained cyclic constant radial stress test are employed to validate the new model.     

混凝土的一种梨形边界面本构模型

为研究混凝土材料在多轴循环荷载作用下的非线性特性,基于经典塑性力学理论和边界面模型理论,提出一个改进的边界面模型.模型中,屈服面为封闭、光滑曲面,在子午面内为梨形;边界面与屈服面的形状相似;选择应力的第一不变量和应变偏量作为屈服面函数中的自变量;相应的加卸载判据中的微分变量也是上述两种变量;根据屈服面和边界面形状的相似性,通过比例关系定义映射法则;对于处在屈服面上的任意一个当前应力点,根据此法则,都能够找到与之对应的处在边界面上的映射点,两个点对应的曲面法线方向相同;采用非相关流动法则描述塑性变形.对沿着偏平面上的压缩方向,对混凝土试块分别进行单调加载和循环加载时的试验结果,用本构模型进行模拟,模型计算结果与试验结果吻合.模型能够统一地描述应力-应变曲线的上升-下降段,能够描述剪胀现象.     

General Analytical Shakedown Analysis of a Structure Subjected to Combined Loading with Constant and Cyclic Loads

恒定载荷和循环载荷共同作用时结构的安定性一般解析分析

邹宗园,郭宝峰,金淼

（燕山大学 先进锻压成形技术与科学教育部重点实验室）

创新点说明：

推导得到了结构在恒定载荷和循环载荷共同作用时安定极限载荷的一般解析解,揭示了恒定载荷和循环载荷共同作用下结构安定性的影响因素以及影响规律。

研究目的：

揭示恒定载荷和循环载荷共同作用对结构安定性的影响规律。

研究方法：

（1）通过理论推导,得到结构在恒定载荷和循环载荷共同作用时安定极限载荷的一般解析解;

（2）将所得到的一般解析解应用于两个具体的例子,所得到的结果与文献中的结果一致,从而验证本文研究结果的正确性。

结果：

应用Polizzotto的适用于恒定载荷和循环载荷共同作用的安定定理,通过解析推导,得到结构安定极限载荷的一般解析解。据此得到如下研究结果：

1) 当结构受到恒定载荷和循环载荷共同作用时,结构是否安定,取决于循环载荷的幅度、恒定载荷和循环载荷的峰值共同作用时的应力与循环载荷单独作用时的弹性参考应力之间的夹角。

2) 在结构中,若恒定载荷和循环载荷的峰值共同作用所产生的应力与循环载荷单独作用产生的弹性参考应力之间的夹角为零,则循环载荷幅度不超过弹性极限载荷的2倍时,结构安定。此时,安定极限载荷幅度等于循环载荷单独作用下结构弹性极限载荷的2倍。

3) 在结构中,若由恒定载荷和循环载荷的峰值共同作用所产生的应力,与循环载荷单独作用产生的弹性参考应力之间的夹角为锐角时,则当循环载荷幅度不大于该夹角的余弦与其弹性极限载荷的2倍的乘积时,结构安定。此时,安定极限载荷的幅度小于结构弹性极限载荷的2倍。

4) 在结构中,若由恒定载荷和循环载荷的峰值共同作用所产生的应力,与循环载荷单独作用产生的弹性参考应力之间的夹角等于或大于90°,则结构不安定。

结论：

应用本文得到的一般解析解,分别对受恒定拉伸和对称循环扭转共同作用的理想弹塑性薄壁管,和受到水平的恒定均匀拉伸和竖直的循环均匀拉伸共同作用的带中心圆孔方板进行安定性分析,得到的结果与其它文献中所给出的结果一致。验证了本文得到的一般解析解,该解析解普遍适用于恒定载荷和循环载荷共同作用时结构的安定性分析,揭示了此种加载情况下结构安定性的一般性规律。

关键词：弹塑性;安定极限载荷;一般解析解;组合加载

     

Experimental study on permanent deformation characteristics of coarse-grained soil under repeated dynamic loading

Practical assessment of subgrade settlement induced by train operation requires developing suitable models capable of describing permanent deformation characteristics of subgrade filling under repeated dynamic loading. In this paper, repeated load triaxial tests were performed on coarse-grained soil (CGS), and the axial permanent strain of CGS under different confining pressures and dynamic stress amplitudes was analysed. Permanent deformation behaviors of CGS were categorized based on the variation trend of permanent strain rate with accumulated permanent strain and the shakedown theory. A prediction model of permanent deformation considering stress state and number of load cycles was established, and the ranges of parameters for different types of dynamic behaviors were also divided. The results indicated that the variational trend of permanent strain rate with accumulated permanent strain can be used as a basis for classifying dynamic behaviors of CGS. The stress state (confining pressure and dynamic stress amplitude) has significant effects on the permanent strain rate. The accumulative characteristics of permanent deformation of CGS with the number of load cycles can be described by a power function, and the model parameters can reflect the influence of confining pressure and dynamic stress amplitude. The study’s results could help deepen understanding of the permanent deformation characteristics of CGS.

     

An improved hypoplastic constitutive model of rockfill considering effect of stress path

An incrementally nonlinear hypoplastic constitutive model was introduced, which was developed without recourse to the concepts in elastoplasticity theory such as yield surface, plastic potential and the decomposition of the deformation into elastic and plastic parts. Triaxial drained tests on rockfill were conducted on a large scale triaxial apparatus under two types of stress paths, which were the stress paths of constant stress ratio and the complex stress paths with transitional features. Motivated by the effect of stress path, the Gudehus-Bauer hypoplastic model was improved by considering the parameter variations with different ratios of stress increment. Fitting parameter α presents a piecewise linear relationship with cosine of the slope angle θ determined by instantaneous stress path. The improved hypoplastic model can present peak stress increasing and volumetric strain changing from dilatancy to contractancy with the increase of transitional confining pressure σ _3t and the decrease of slope angle θ of stress path. Compared with the test data, it is shown that the model is capable of fully considering the effect of stress path on rockfill.     

钢筋混凝土框架结构安定性分析

对钢筋混凝土框架结构安定性分析的必要性及原理进行了初步论述，推导出计算公式并编制了计算程序，通过实例分析获得了结构的安定域。结果表明当反复荷载为对称循环变化时结构所能承受的最大荷载值与静力极限荷载值差别最大，而非对称循环时差别较小。     

循环荷载下考虑滞回效应的混凝土损伤模型

针对高混凝土坝地震过程中复杂的材料非线性问题,建立循环荷载下考虑滞回效应的混凝土损伤模型。模型分别选取符合混凝土实际变形特性的拉伸与压缩骨架线以考虑材料拉压异性,骨架线中含有软化段系数以适应试验结果的离散性。采用不依赖于骨架线形状的滞回效应加卸载特征点表达式,搭建能够反映混凝土循环荷载作用下软化段滞回效应的卸载路径与重新加载路径,并建议设立残余应变临界值解决残余塑性应变与卸载应变比值随应变增长的持续发散问题。模型将复杂多轴问题转化至单轴等效应变空间中求解,计算参数少,数学表达式简单,并通过混凝土循环荷载试验与Koyna重力坝的震害模拟验证了模型在非线性问题求解上的正确性与高效性。     

水平循环荷载下砂土中斜单桩累积变形特性

研究斜单桩在风、浪、洋流等循环荷载作用下的累积特性. 通过用户开发子程序将砂土刚度衰减模型嵌入桩-土体系有限元模型中,实现了单桩循环受荷特性的数值分析,研究不同循环幅值及循环次数下斜单桩的变形累积规律. 研究结果表明,当桩身倾斜角由?25°逐渐过渡到25°时,在相同的静力荷载作用下,斜单桩桩顶位移及桩身相同位置处弯矩会不断增加,但在循环荷载作用下,桩顶位移与桩身最大弯矩的累积速度会逐渐下降. 当循环荷载幅值较大时,负斜桩的桩顶位移和桩身位移段深度均小于竖直桩,正斜桩的桩顶位移和桩身位移段深度均最大. 基于数值计算结果,对不同循环幅值和循环次数下的斜单桩桩顶累积位移和桩身最大弯矩进行拟合分析,提出适用于斜单桩的累积变形特性预测方法.     

交通荷载作用下软土地基的累积沉降分析

针对交通荷载作用下软土地基的累计沉降问题,提出采用土体刚度衰减修正公式计算累计塑形变形的方法.基于饱和软土循环三轴试验数据,建立刚度衰减系数与循环次数间的关系.对有限元软件ABAQUS进行二次开发,将刚度衰减模型嵌入到有限元分析程序中去,再通过数值分析计算出任意循环周数后土体的累积塑性变形.采用该方法对交通荷载作用下典型上海软土地基的累积沉降进行预测.计算结果表明,路面结构层的存在有助于减小软土地基的沉降,交通荷载所引起的沉降主要发生在软土地基的浅层,并且随着深度的增加而迅速减小.     

反复荷载作用下剪切板阻尼器的抗剪极限强度

为了使剪切板阻尼器具有稳定的滞回耗能特性,避免其腹板发生局部屈曲,提出了一种考虑翼缘抗弯承载力贡献的剪切板阻尼器抗剪极限强度计算公式,为剪切板阻尼器的设计与应用提供了参考.剪切板阻尼器作为消能减震装置应用于建筑和桥梁等工程结构,可有效减轻地震破坏作用.基于通用有限元程序ABAQUS,对反复荷载作用下单侧布置1、2或3对双向加劲肋的剪切板阻尼器进行了一系列的精细化有限元计算与分析.计算模型考虑了初始变形和残余应力两种初始缺陷,采用修正双屈服面模型描述反复荷载下的钢材料本构关系.研究结果表明,翼缘所承担的剪力约占总抗剪承载力的13%~28%,设计时不能忽略.     

基于蠕变试验下的海相黏性土蠕变模型研究

为了研究海相黏性土的蠕变规律,采用三轴流变仪,在变动围压与分级加载下,对某大型人工岛下不同深度处海相黏性土原状样进行了三轴固结排水蠕变试验。基于耦合Adachi-Oka模型与Biot固结理论控制方程的推导,编写了二维有限元计算程序CFEM 2D。由常规试验结果,给出不同土层海相黏性土的Adachi-Oka模型参数,采用上述程序对蠕变试验进行了数值模拟,得出Adachi-Oka模型适用于描述该地区海相黏性土的蠕变特性。在验证模型的基础上,采用程序CFEM 2D对该人工岛深厚黏性土地基的长期沉降特性进行了计算,计算结果表明,在荷载施加初期,人工岛沉降速率较大。100年时,超孔压已基本消散完成,地表沉降量达到了88.5cm。通过与分层总和法结果的对比得出,二者误差约为2.5%,表明数值计算结果具有一定的精度,从而验证了计算程序的可靠性。     

A critical state subloading surface model of sands with shear hardening

Based on the framework of critical state soil mechanics,a subloading surface plastic model for sand, being applicable to cyclic loading, was proposed. The model can be used to describe strain softening behaviour of sand under monotonic loading when the similarity-ratio equals to unity. The characteristics of the model are as follows: 1) A reverse bullet-shaped yield surface is adopted to ensure accurate prediction of the behavior of sand, instead of bullet-shaped or elliptical yield surface in Cam-Clay mode...     

砂土动应力-应变发展特性试验

对福建标准砂和南沙群岛珊瑚砂进行了不同初始固结条件下的循环剪切试验.试验结果表明,在不同固结条件下动应力-应变发展模式显著不同.在均等固结条件下,动应力-应变关系的循环效应和对称累积特性均十分显著,随着砂土强度的完全丧失累积变形迅速发展;而在非均等固结条件下,当动应力作用平面上具有扭剪应力预剪作用时,剪应变则以单向累积变形为主,当动应力作用平面上只有轴向应力作用时,剪应变循环效应相对较大,累积变形并不显著,即使在循环扭剪荷载作用下,变形仍以轴向变形为主.这种特征似乎与中主应力系数没有显著的依赖关系.