考虑材料损伤时厚壁圆筒的承载能力

本文采用摩尔-库仑屈服条件,考虑材料损伤后的应变软化特性,对岩土类介质的厚壁圆筒的承载能力进行分析,并给出有关的结果.     

软化梁的动力行为

由于材料的应变软化，或是由于薄壁梁在挠曲变形时的截面畸变，梁的弯矩一曲率关系可能呈现先强化后软化的性态。近几年来北京大学一个研究组的工作证实，具有软化特性的半无限长梁在自由端受常速度冲击时，软化可能发展为一个有限长的区段，并在梁内移动，同时，英国ＵＭＩＳＴ的一个研究组以核电站中的管道甩动问题为工程背景，集中研究了具有软化特性的有限长梁的动力行为。提出了计及弹性、强化、软化和梁的几何大变形的理论模型，并发展了相应的有限差分程序。这一理论模型能够预报软化区的萌生、发展和局部化，同管道甩动实验观测极为符合。     

40钢非比例循环塑性行为研究

对４０钢在拉扭循环复杂应变路径下的硬化特性和流动特性进行了实验研究。研究表明：４０钢材料的循环硬／软化不但依赖于应变路径形状，而且依赖于等效应变幅值，还具有路径历史效应；材料的塑性流动几乎不受先前路径历史的影响，仅依赖于当前应变路径形状和等效奕变幅值。     

脆性固体损伤和局部软化的有限元分析

本文研究混凝土、岩石一类工程中常用的应变软化材料的有限元分析方法。在作者以往有关粘塑性损伤本构模型的工作基础上，给出了一组便于有限元计算的本构方程表达式。包括损伤弹性矩阵和局部损伤软化矩阵，分别运用于计算硬化和软化阶段的有限元刚度矩阵；对所提出的本构方程的实验验证计算和一些算例的有限元数值分析，表明文中给出的本构方程是可行的，相应的有限元算法能较好地对损伤固体的局部软化效应进行数值分析，并可成功地追踪应力应变响应的软化曲线     

考虑材料应变软化的弹塑性有限元解法研究

指出了已有初应力法多种加速方案在对考虑材料应变软化特性的非线性有限元进行求解时，并不能保证求解过程的收敛性。借鉴整体割线刚度送代法的思想，提出了一种新的初应力加速方案，该方案不仅可以有效地提高初应力法的求解效率，而且即使考虑材料的应变软化，也可以保证在结构达到最大承载能力前的求解过程是收敛的。     

非均质材料弹塑性破裂过程的数值模拟研究

阐述了岩土类材料的非均质特性，根据这种特性提出了对材料参数进行随机赋值的方法。为了对非匀质类材料的弹塑性破裂过程进行数值模拟研究，必须在有限元计算中实现材料的参数随机赋值。还给出了实例－－平面应力状态下试样的弹塑性破裂过程的数值模拟分析。     

类橡胶材料变形直到破坏的显式本构模型

本文通过直接、显式的方法提出一个多轴可压缩应变能弹性势来模拟类橡胶材料受载荷直到软化破坏的变形行为．首先，我们提出一个多轴可压缩应变能函数；其次，通过特定的不变量，该多轴应变能函数在单轴拉伸，平面应变和等双轴拉伸三个基准实验的情况下，可以退化为各自的单轴形函数形式；再次，我们显式给出带有软化破坏特性的形函数；最后，模型结果和试验数据可以精确匹配，同时可以预测材料临近破坏以后，接下来的变形行为．     

一个综合模糊裂纹和损伤的混凝土应变软化本构模型

本文研究就变软化材料的本构关系，提出了一个考虑损伤的粘塑性模型，损伤不仅影响材料的临界应力，而且影响材料的粘塑性，为模拟材料的应变软化行为，假设受损混凝土的破坏局部区域由模糊裂纹和损伤所统治，软化模量和局部区域尺度参量依赖于模糊裂纹扩展时释放的断裂能的参变量，用文中提出的模型计算了混凝土单轴压缩时不同应变速率下的瞬时应力应变响应以及等应力长期作用下的徐变，均得到很的结果。     

显式模拟类橡胶材料应力软化引起的不可恢复变形及其各向异性特征

类橡胶材料在经过初次加载后会产生应力软化现象, 也就是Mullins效应. 实验证明应力软化现象会导致材料产生不可恢复变形, 同时引入各向异性特征. 本文基于对数应变构造一个多轴可压缩应变能函数, 先引入耗散来表征应力软化现象, 再引入依赖耗散大小的不可恢复变形量以及各向异性特征量, 使得新模型既可以表征Mullins效应, 又能模拟应力软化作用下产生的不可恢复变形和各向异性特征. 本文在各向同性形函数的基础上, 通过球坐标系的思想, 进一步发展并提出了一个任意方向适用的各向异性形函数. 新模型在材料尚未发生软化(耗散为0)的情况下, 表现出各向同性; 一旦发生应力软化(耗散大于0), 则变为各向异性. 随着加载?卸载循环的累积, 耗散逐渐变大, 不可恢复变形也随之变大直到达到一个稳定的值, 各向异性特性也逐渐变得明显. 新方法得到的结果可以精确匹配经典的实验数据, 并预测不同方向的应力软化现象以及由此产生的不可恢复变形和各向异性特征.      

铝锂合金材料的极限应变率软化特性研究

通过系列准静态与动态力学实验得到了铝锂合金材料的基本力学参数。证实了该种材料具有独特的应变率软化特性 ,并揭示了材料应变率软化效应的极限性特征 ,提出了极限应变率软化材料的概念 ,从而对突加载荷下粘塑性材料中也会出现双波结构的现象给出了合理的解释。为便于实际应用 ,还对实验得到的材料应力 应变曲线进行了拟合 ,提出了一种便于实际应用的材料本构关系的具体形式 ,即双幂次应变硬化 极限幂次应变率软化本构关系。     

统一强度准则下厚壁圆筒的弹脆塑性承载能力分析

应用统一强度准则和弹脆塑性变形模型，研究材料具有软化效应的厚壁圆筒的承载力。分别导出在内压及外压作用下厚壁圆筒弹脆塑性承载力的计算公式。这些公式不仅给出了以往基于Mohr-Coulomb准则和广义双剪准则的结果，而且给出了一系列新的结果，因而本文的结果可适用于多种材料。实例表明材料软化效应以及分析中所选用的强度准则对厚壁圆筒承载力具有重要影响。因此，在确定厚壁圆筒承载力时，应该合理地选用材料的软化参数及强度准则。     

The dynamic response of a strain-softening beam

The dynamic response of a strain-softening beam subjected to a transverse impulsive on its tip is investigated. A softening moment-curvature relation is assumed for the beam and a closed form solution is obtained for a special kind of load, which shows that there exists a softening region in the beam and this region propagates along the beam. This result indicates that, except for the possible discrete softening points with rotation discontinuity caused by the deformation localization^[1], the existence of the softening region and its travelling along the beam are the essential features of the dynamic response of a strain-softening beam. The results also show that the failure of the beam should take place under a special load and the critical condition on which the dynamic failure occurs is given. The project supported by National Natural Science Foundation of China     

DAMAGE MODEL FOR HARDENING AND SOFTENING MATERIAL IN GENERAL STATE OF STRESS

The present paper is aimed to simulate progression of damage,hardeningand softening response in brittle materials such as concrete or rock in general state ofstress.Similar shape of surfaces for yield,failure and damage progressing areavailable,and softening strain is treated as plasticity.Then,the proposed model isapplied to solving several boundary value problems.     

Modelling of stress softening in elastomeric materials: foundations of simple theories

This work is concerned with formulation of constitutive relations for materials exhibiting the stress softening phenomenon (known as the Mullins effect) typical observed in elastomeric and other amorphous materials during loading–reloading cycles. It is assumed that microstructural changes in such materials during the deformation process can be represented by a single scalar-valued softening variable whose evolution is accompanied by microforces satisfying their own law of balance, besides the classical laws of mechanics underlying macroscopic deformation of a material. The constitutive equations are then derived in consistency with thermodynamics of irreversible processes with the restriction to purely mechanical theory. The general form of the derived constitutive equations is subsequently simplified through introduction of additional assumptions leading to various models of the stress softening phenomenon. As an illustration of the general theory, it is shown that the so-called pseudo-elastic model proposed in the literature may be derived without an ad hoc postulate of the variational principle.     

MICROMECHANICAL MODELLING OF STRAIN SOFTENING IN MICROCRACK-WEAKENED QUASI-BRITTLE MATERIALS

By using the concept of domain of microcrack growth(DMG),themicromechanisms of damage in quasi-brittle materials subjected to triaxial either tensileor compressive loading are investigated and the complete strew-strain relation includingfour stages is obtained from micromechanical analysis.The regime of pre-peaknonlinear hardening corresponds to the distributed damage,i.e.the stable propagationof microcracks.After the attainment of the ultimate strength of load-bearing capacity,some microcracks experience the second unstable growth and the distributed damage istransmitted to the localization of damage.These analyses improve our understanding ofthe hardening and softening behaviors of quasi-brittle materials.     

Near tip quasi-static crack growth behavior in strain hardening and softening material

Analyzed in this work is a semi-infinite crack that grows slowly in a steady-state. The assumed constitutive relation for the material permits strain hardening and softening as it is damaged in time. Four distinct regions divided angularly are identified for the asymptotic expressions of the quasi-static crack-tip stress field. They refer to material degraded in front of the crack; undergone elastic unloading; reloading of degraded material; and material completely by exhausted in its load carrying capacity.     

Application of a stress triaxiality dependent fracture criterion in the finite element analysis of unnotched Charpy specimens

Nonlinear dynamic finite element analysis (FEA) is conducted to simulate the fracture of unnotched Charpy specimens of steel under pendulum impact loading by a dedicated, oversized and nonstandard Bulk Fracture Charpy Machine (BFCM). The impact energy needed to fracture an unnotched Charpy specimen in a BFCM test can be two orders of magnitude higher than the typical impact energy of a Charpy V-notch specimen. To predict material failure, a phenomenological, stress triaxiality dependent fracture initiation criterion and a fracture evolution law in the form of strain softening are incorporated in the constitutive relations. The BFCM impact energy results obtained from the FEA simulations compare favorably with the corresponding experimental data. In particular, the FEA predicts accurately the correlations of the BFCM impact energy with such factors as specimen geometry, impactor tup width and material type. The analyses show that a specimen’s progressive deterioration through the thickness dimension displays a range of shear to ductile fracture modes, demonstrating the necessity of applying a stress state dependent fracture initiation criterion. Modeling the strain softening behavior helps to capture the residual load carrying capability of a ductile metal or alloy beyond the onset of damage. The total impact energy can be significantly under predicted if a softening branch is not included in the stress-strain curve. This research supports a study of the puncture failure of railroad tank cars under dynamic impact loading. Applications of the presented fracture model in failure analyses of other structures are further discussed.