弹塑性损伤本构关系的显式积分算法研究

首先引入弹塑性损伤本构关系,分别从材料软化与残余应变两个方面,描述伪脆性材料的非线性行为.针对结构动力分析中的强非线性问题,给出了弹塑性损伤本构关系的显式积分算法.算法中引入算子分解的思想,将弹塑性本构关系分成塑性与损伤两个模块.首先求解塑性模块,根据有效应空间塑性演化公式,采用前进欧拉算法,直接构造塑性演化的预测值,并且根据屈服函数的漂移构造了误差限公式,作为衡量显式算法精度的指标.将塑性模块求解的结果代入损伤模块,可以方便地求得损伤变量的演化,并最终得到更新后的应力.整个求解过程不需要迭代,可最大程度的算法稳定性.将论文建立的本构关系显式算法与结构分析显式算法结合,构造了结构显式分析方法,并模拟了两个经典算例,算例结果验证了论文方法的有效性.     

室温下镁合金板循环塑性随动强化本构模型研究

本文在具有各向异性屈服强度和拉压不对称的CPB06屈服准则的基础上,建立了基于随动强化的循环塑性本构模型．通过引入滑移、孪晶以及去孪等不同变形模式下的背应力演化方程,对室温下镁合金板材异常循环硬化行为进行了模拟．选取了AZ31B-O和AZ31B两种镁合金板材,通过拉伸-压缩-拉伸(T-C-T)和压缩-拉伸(C-T)等不同加载路径下的部分实验曲线确定模型的参数,采用三次插值多项式建立了背应力参数与上一变形模式中累积的等效塑性应变（即预应变）之间的函数关系．使用本模型对剩下的实验曲线进行了预测,发现预测结果与实验结果有良好的一致性,说明了当前模型的正确性．     

SS304不锈钢高温非比例多轴循环变形行为的粘塑性本构描述

在350℃和700℃下SS304不锈钢的非比例多轴循环变形行为进行了系统的实验研究。在此基础上,在统一粘塑性本构理论的框架下改进和发展了一个新的循环本构模型。该模型给出了新的背应力演化方程,引入了非比例度参量,考虑了温度效应和最大塑性应变幅值记忆效应,能够对材料的高温非比例多轴应变循环变形行为和棘轮行为进行统一描述。模型的模拟结果与实验结果比较表明:该模型对SS304不锈钢高温非比例多轴循环变形行为的描述比较合理。     

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．     

96.5Sn-3.5Ag 钎料合金的含非比例度的多轴时相关本构模型研究

基于96.5Sn-3.5Ag钎料合金的多轴时相关变形行为,提出了一个考虑其多轴变形特性的本构模型.在该模型背应力演化方程中,引入了非比例度对背应力演化率的影响,并提出了模型参数的确定方法.在室温下对96.5Sn-3.5Ag钎料合金进行了十字形、双三角形及椭圆形等拉扭组合非比例循环应变路径下的变形行为的本构模拟,并将预言结果与实验结果进行了比较.预言结果表明,该模型对于96.5Sn-3.5Ag钎料合金的多轴应变循环变形行为具有很好的预言能力.     

显式方法精确模拟形状记忆聚合物热力学行为

通过构建一个热耦合的多轴可压缩应变能函数,得到应力-应变、应力-温度和应变-温度之间的函数关系,建立形状记忆聚合物的本构方程.本文引入三个基于对数应变的不变量使得模型（i）可以模拟可压缩情况;（ii）适用于单轴拉伸和等双轴拉伸至少两个基准实验;（iii）多轴有效.通过显式方法（i）给出自由能和熵的具体表达,证明模型热力学定律;（ii）给出应变-应力,温度-应力以及,温度-应变的形函数具体表达.多轴模型在特定的情况下可以自动退化到各自的单轴情况. 通过调节形函数的参数,最终得到的模型结果和实验结果能够精确匹配.新方法建立的本构模型得到的结果能更加准确地指导形状记忆聚合物的工程设计。     

显式方法精确模拟形状记忆聚合物热力学行为

通过构建一个热耦合的多轴可压缩应变能函数,得到应力-应变、应力-温度和应变-温度之间的函数关系,建立形状记忆聚合物的本构方程.本文引入三个基于对数应变的不变量使得模型（i）可以模拟可压缩情况;（ii）适用于单轴拉伸和等双轴拉伸至少两个基准实验;（iii）多轴有效.通过显式方法（i）给出自由能和熵的具体表达,证明模型热力学定律;（ii）给出应变-应力,温度-应力以及,温度-应变的形函数具体表达.多轴模型在特定的情况下可以自动退化到各自的单轴情况. 通过调节形函数的参数,最终得到的模型结果和实验结果能够精确匹配.新方法建立的本构模型得到的结果能更加准确地指导形状记忆聚合物的工程设计。     

SnPb钎料合金的粘塑性Anand本构方程

采用统一型粘塑性本构 Anand方程描述了电子封装焊点 Sn Pb钎料合金的非弹性变形行为 ,基于 Sn Pb 合金的弹塑性蠕变本构方程和实验数据 ,确定了6 2 Sn36 Pb2 Ag、6 0 Sn40 Pb、96 .5 Sn3.5 Ag和 97.5 Pb2 .5 Sn四种钎料合金 Anand方程的材料参数 ,验证了粘塑性 Anand本构方程对 Sn Pb合金在恒应变速率和稳态塑性流动条件下应力应变行为的预测能力。结果表明 ,Anand方程能有效描述 Sn Pb钎料的粘塑性本构行为 ,并可应用于电子封装 Sn Pb焊点的可靠性模拟和失效分析     

非定常微分型黏弹性本构模型

在应力作用下, 材料的力学参数随着微观结构的变化而变化, 需要考虑参数的时间效应. 利用黏滞系数随时间变化的黏性元件, 构造出非定常Maxwell模型、非定常Kelvin模型和非定常Zener模型. 求解非定常模型的微分型本构方程得到它们的松弛模量、蠕变柔量和卸载方程. 结果表明, 可以把常见的经验松弛函数和经验蠕变函数视为非定常微分型本构模型.      

各向异性本构关系在板料成形数值模拟中的应用

对几种能表达面内各向异性的屈服准则Hill、Barlat-Lian、Barlat进行了比较。以弹性变形服从各向同性广义虎克定律的情况下，给出了基于张量算法推导的弹塑性本构关系的一般表达式，并由此导出了相应屈服准则的弹塑性本构关系的显式表达。借助ABAQUS软件本构模块用户子程序接口，分别实现了这些屈服准则在ABAQUS的嵌入。以模拟方形盒的拉延过程为例，分析了不同的屈服准则在板料成形过程数值模拟中的应用。模拟结果表明，基于弹塑性本构关系一般表达所列出的相应屈服准则的显式表达式是正确的；在采用壳元来模拟板料成形时，采用Barlat准则的模拟结果和采用Barlat-Lian准则的结果差别不大。     

形状记忆合金的一种基于经典塑性理论的两相混合本构模型

形状记忆合金由马氏体相和奥氏体相动态组成,其行为实质上是两相各自行为的动态组合,根据实验现象,假设在一定的变形范围内,马氏体相为弹塑性而奥氏体相为线弹性,基于经典塑性理论和混合物理论,结合Tanaka的相变描述,得到了形状记忆合金的一种本构描述,对不同温度下形状记忆合金Au-47．5at．％Cd的铁弹性、拟弹性和形状记忆特性进行了分析,取得了与实验相吻合的结果。     

NiTi 形状记忆合金热-力耦合循环变形行为宏微观实验和理论研究进展

本文对NiTi形状记忆合金热-力耦合循环变形行为研究的最新进展进行综述和评价。首先总结NiTi形状记忆合金在循环加载条件下的单轴、非比例多轴循环变形特性以及强烈的热-力耦合特性,阐述NiTi形状记忆合金在循环变形过程中出现功能性劣化的微观机理;然后,讨论在宏观和细观尺度上建立的三类NiTi形状记忆合金典型的循环本构模型,并评述代表性模型的预测能力;最后,总结已有研究存在的不足,对相关问题的进一步研究提出建议。在本构模型方面主要介绍了作者及其合作者在基于晶体塑性的热-力耦合循环本构模型方面的工作,突出了多种非弹性变形机制和强烈热-力耦合行为对形状记忆合金循环变形行为的影响。     

A multi-dimensional composite model for plastic continua under polyaxial loading condition

By replacing a medium with reinforcing components oriented and distributed uniformly in a multi-dimensional space, a constitutive model is constructed. The components are extended/compressed compatibly with the strain and the resultant of load exerted on them to balance the stress. Their load-elongation relation can be determined from a conventional material test. Each component undergoes different elongation history depending on its own orientation during deformation, so that the model can simulate elasto-plastic behavior of materials under polyaxial loading conditions. The incremental constitutive matrix has been derived for application in numerical analysis and a yield criterion is also introduced. A few subsequent yield surfaces have been predicted and compared with experiments.     

Thermomechanical behavior of shape memory alloy under complex loading conditions

The thermo-mechanical behavior of polycrystalline shape memory alloy (SMA) under multi-axial loading with varying temperature conditions has been studied by experiments. Recently the research has been extended theoretically and a mechanical model of polycrystalline SMA and the corresponding mesoscopic constitutive equations have been developed. The model presented in this paper is constructed on the basis of the crystal plasticity and the deformation mechanism of SMA. The variants in the crystal grains and the orientations of crystal grains in the polycrystal are considered in the proposed model; the constitutive equations are derived on the basis of the proposed model. The volume fraction of the martensite variants in the transformation process and the influence of the stress state on the transformation process are also considered. Some calculated results obtained by the constitutive equations are presented and compared with the experimental results. It is found that the deformation behavior of SMA under complex loading conditions can be well reproduced by the calculation of the constitutive equations.     

A viscoplastic model combined smedamage and smeared crack for softening of concrete

A viscoplastic model accounting for developing damage in concrete is proposed by assuming the rate of damage to be dependent on viscous strain and stress rates. The damage is measured by a scalar parameter affecting both the yield stress and the material viscosity. For a post-critical range of deformation, the localized mode occurs for which additional constitutive equations are specified. The model is applied to simulate uniaxial strain rate controlled and creep response for the concrete.     

A three-dimensional constitutive model for shape memory alloys

Shape memory alloys (SMAs) are materials that, among other characteristics, have the ability to present high deformation levels when subjected to mechanical loading, returning to their original form after a temperature change. Literature presents numerous constitutive models that describe the phenomenological features of the thermomechanical behavior of SMAs. The present paper introduces a novel three-dimensional constitutive model that describes the martensitic phase transformations within the scope of standard generalized materials. The model is capable of describing the main features of the thermomechanical behavior of SMAs by considering four macroscopic phases associated with austenitic phase and three variants of martensite. A numerical procedure is proposed to deal with the nonlinearities of the model. Numerical simulations are carried out dealing with uniaxial and multiaxial single-point tests showing the capability of the introduced model to describe the general behavior of SMAs. Specifically, uniaxial tests show pseudoelasticity, shape memory effect, phase transformation due to temperature change and internal subloops due to incomplete phase transformations. Concerning multiaxial tests, the pure shear stress and hydrostatic tests are discussed showing qualitatively coherent results. Moreover, other tensile–shear tests are conducted modeling the general three-dimensional behavior of SMAs. It is shown that the multiaxial results are qualitative coherent with the related data presented in the literature.     

A phenomenological description of shape memory alloy transformation induced plasticity

Transformation induced plasticity is defined as the plastic flow arising from solid state phase transformation processes involving volume and/or shape changes without overlapping the yield surface. This phenomenon occurs in shape memory alloys (SMAs) having significant influence over their macroscopic thermomechanical behavior. This contribution presents a macroscopic three-dimensional constitutive model to describe the thermomechanical behavior of SMAs including classical and transformation induced plasticity. Comparisons between numerical and experimental results attest the model capability to capture plastic phenomena. Both uniaxial and multiaxial simulations are carried out.     

Finite elasto-viscoplastic modeling of polymers including asymmetric effects

Asymmetric effects between compression and tension are a pronounced behavior for glassy polymers such as polycarbonate. For its simulation an elasto-viscoplastic framework is formulated within a geometrically nonlinear theory. Here a new approach within the concept of stress mode dependent weighting functions is used, where each material parameter is additively decomposed into a sum of weighted stress mode-related quantities. The characterization of the stress modes is obtained in the octahedral plane of the deviatoric stress space in terms of the mode angle, such that stress mode dependent scalar weighting functions can be constructed. The constitutive equations are formulated for large strains in terms of logarithmic Hencky strains and its work conjugated Hill stresses. The resulting evolution equations are updated using a semi-implicit Euler scheme, and the algorithmic tangent operator is derived for the finite element equilibrium iteration. The numerical implementation is also used to identify the material parameters thus resulting into a good agreement with experimental data. Furthermore, the model is used to simulate the cold drawing processes for a dumbbell-shaped specimen in tension and a perforated strip in compression and tension.