准脆性材料的弹塑性各向异性损伤耦合本构模型研究

针对准脆性材料的非线性特征：强度软化和刚度退化、单边效应、侧限强化和拉压软化、不可恢复变形、剪胀及非弹性体胀,在热动力学框架内,建立了准脆性材料的弹塑性与各向异性损伤耦合的本构关系。对准脆性材料的变形机理和损伤诱发的各向异性进行了诠释,并给出了损伤构形和有效构形中各物理量之间的关系。在有效应力空间内,建立了塑性屈服准则、拉压不同的塑性随动强化法则和各向同性强化法则。在损伤构形中,采用应变能释放率,建立了拉压损伤准则、拉压不同的损伤随动强化法则和各向同性强化法则。基于塑性屈服准则和损伤准则,构建了塑性势泛函和损伤势泛函,并由正交性法则,给出了塑性和损伤强化效应内变量的演化规律,同时,联立塑性屈服面和损伤加载面,给出了塑性流动和损伤演化内变量的演化法则。将损伤力学和塑性力学结合起来,建立了应变驱动的应力-应变增量本构关系,给出了本构数值积分的要点。以单轴加载-卸载往复试验识别和校准了本构材料常数,并对单轴单调试验、单轴加载-卸载往复试验、二轴受压、二轴拉压试验和三轴受压试验进行了预测,并与试验结果作了比较,结果表明,所建本构模型对准脆性材料的非线性材料性能有良好的预测能力。     

聊聊动态塑性和黏塑性

固体力学研究者致力于具有应力-应变本构关系（以下简称为形变型本构关系）的变形体的力学响应研究，而流体力学研究者致力于具有应力-应变率本构关系（以下简称为流动型本构关系）的流动体的力学响应研究。当涉及结构和材料的动态塑性时，到底应该用“塑性变形”还是“塑性流动”来表示？本文从宏观塑性本构理论和微观位错动力学机理两个角度，分别讨论并指出塑性本构关系属于流动型黏塑性率相关本构关系，且同时适用于加载和卸载；因而不应该用应力-应变图来描述塑性加-卸载过程。弹塑性本构关系则是一种形变型和流动型本构关系的耦合。     

时间无关不可逆过程及不可逆系统的稳定性

在不可逆热力学框架内引入了四条基本假设，建立了宏观本构关系的新的逻辑系统．在假设3中通过引入一种新的运算，把内变量演化方程定义在时间的点集上．结合讨论C1ausius-Dubem不等式，得到了假设4，它把时间点集的性质与系统状态联起来．以此为基础，证明了一致性条件成立的判别准则和加卸载准则，并成功地解释了实验现象存在有一个应变速率的临界值，当加载应变速率低于该值时，材料的应力—应变关系基本上与速率无关；当高于该值时，则明显与速率相关、更富有力学含义地给出了不可逆系统稳定性的一种定义，并证明了判别稳定性的一个准则．此外，还得出系统稳定是不可逆行为与时间无关的前提条件．     

塑性力学的Drucker公设和Ильюшин公设

本文介绍和评述了塑性理论的Drucker公设和公设,并从这些公设出发,分别在应力空间和应变空间讨论了加载函数的外凸性,正交法则和加载准则,以及本构关系。对比在两个空间中得到的相应关系,可以看出公设以及相应地在应变空间表述本构性质具有更广泛的适用性。     

含损伤材料的热粘塑性本构关系和柱壳破裂研究

以含内变量的本构关系理论为基础 ,结合材料损伤演化方程 ,并考虑了温度和损伤对材料参数的影响 ,得到了增量形式的热粘塑性本构关系的普适显式表达式。然后使用Bodner幂函数型粘塑性模型 ,具体推导了其增量形式的热粘塑性本构方程。接着结合在实践中有重要意义的内部爆炸载荷作用下的柱壳破裂问题 ,建立了含损伤热粘塑性柱壳破裂问题的完备方程组 ,使用有限差分方法 ,完成了对问题的数值模拟 ,并对结果进行了分析。计算结果与实验结果符合良好。     

一种混凝土损伤模型和数值方法

Ｏｔｏｓｅｎ准则在准静态时和实验结果有很好的一致性，但是混凝土的动态力学性质和准静态相比有明显的变化。此时，需要用应变率相关的本构模型来描述混凝土的力学行为。从Ｏｔ－ｔｏｓｅｎ的四参数混凝土破坏准则出发，考虑损伤、静水压和应变率对本构关系的影响，建立了混凝土的粘塑性本构模型。同时给出了基于该本构模型的混凝土的有限元计算方法:在积分内变量时采用改进的龙格－库塔格式，在时间方向上的积分使用带有步长控制的ｇｅｎｅｒａｌｉｚｅｄ－方法，有效地保证了积分的稳定和精度，给混凝土的进一步研究提供了方便。     

多轴加载下混凝土细观破坏模拟的强度准则探讨

实际工程结构中混凝土材料大多处于双轴或三轴的复杂应力状态,已有的细观力学数值研究工作大多针对单轴加载问题,对于双轴或者三轴加载条件下混凝土破坏模拟的研究相对较少。复杂受力条件下的混凝土材料破坏模拟中,细观组分强度准则选取的合理与否将成为混凝土破坏模式及宏观力学性能数值研究准确和成功与否的关键。本文旨在探讨单轴强度准则,如最大拉应变准则在多轴加载条件下混凝土破坏过程研究中运用的合理性。鉴于此,首先在细观尺度上建立了混凝土试件的二维随机骨料模型,分别采用弹性损伤本构关系模型及塑性损伤本构关系模型来描述细观组分(即砂浆基质)的力学性能,对双轴加载条件下混凝土的细观破坏过程进行数值模拟,对比了单轴强度准则和多轴强度准则下混凝土试件破坏路径及宏观应力-应变关系的差异。数值结果表明,简单的单轴强度准则难以反映双轴加载下混凝土内部应力状态的复杂性,不宜采用单轴强度准则来描述多轴加载下混凝土的破坏行为。     

非比例循环塑性和循环粘塑性本构描述的某些新进展

金属材料循环塑性本构方程和循环粘塑性本构方程是固体力学中近１０多年来一个十分重要的领域。本文评述了金属材料非比例循环塑性界限面本构理论、内时理论和循环粘塑性本构理论及其某些进展，对某些模型中非比例度定义，材料在复杂应变幅值历史、非比例循环加载历史以及其它历史下的强化规则和流动规则进行了分析与评价，在此基础上对循环本构理论的发展趋势提出自己的看法。     

具有体膨胀和剪切效应的结构陶瓷相变塑性细观本构模型:Ⅰ.非比例加载历史

本文在对结构陶瓷的四方至单斜(t→m)马氏体相变进行细观力学、热力学和微观机制分析的基础上,导出了在非比例加载条件下考虑材料的体膨胀和剪切效应的相变塑性细观本构模型。作者首次采用 Mori-Tanaka 方法以自洽的方式导出了材料构元的 Helmho-ltz 自由能及余能函数的解析表达式,它是外加宏观应力(或应变)、温度、相变夹杂体积分数以及夹杂内平均相变应变的函数,其中夹杂体积分数和平均相变应变为描述材料构元微结构变化的内变量。最后按 Hill-Rice 本构理论框架导出相变塑性屈服面方程及增量本构关系。     

具有体膨胀和剪切效应的结构陶瓷相变塑性细观本构模型:Ⅰ.非比例加载历史

本文在对结构陶瓷的四方至单斜(t→m)马氏体相变进行细观力学、热力学和微观机制分析的基础上,导出了在非比例加载条件下考虑材料的体膨胀和剪切效应的相变塑性细观本构模型。作者首次采用 Mori-Tanaka 方法以自洽的方式导出了材料构元的 Helmho-ltz 自由能及余能函数的解析表达式,它是外加宏观应力(或应变)、温度、相变夹杂体积分数以及夹杂内平均相变应变的函数,其中夹杂体积分数和平均相变应变为描述材料构元微结构变化的内变量。最后按 Hill-Rice 本构理论框架导出相变塑性屈服面方程及增量本构关系。     

无耦合条件下的多子系统静动态统一本构关系(下)--铝的双子系统静动态统一本构模型

构造了标量形式的无耦合条件下双子系统静动态统一本构模型.推导出第1和第2子系统中加载应变速率临界值ε·c1和ε·c2,当应变速率ε·分别低于和高于某个临界值时,相应子系统中的不可逆行为分别是与时间无关的和与时间相关的.由于当ε·跨越ε·c1和ε·c2时,内变量的求解公式发生变化,所以动态强度随ε·变化的规律发生变化.经与铝的实验结果比较确认,本构模型能够描述材料的多种静动态力学行为.     

Plastic spin: necessity or redundancy?

The plastic spin concept in large deformation anisotropic elastoplasticity theories with tensorial internal variables, is proved to be a necessary constitutive ingredient. Different inaccurate notions about the plastic spin are dispelled, and its presence in the theory is demystified as something very simple and straightforward. To this extent it is necessary to disassociate the plastic spin concept and the conjugate notion of constitutive spin from the foundation of kinematics, which caused confusion in the past, and define it only in relation to the constitutive equations of evolution of the tensorial internal variables. There, the plastic spin is related to the orientation aspect of such constitutive equations, and the multiplicity of the different internal variables suggests the necessity to have a different spin for each variable. In the process, a straightforward constitutive framework is developed which is based on classical hyperelasticity, yield criteria and invariance requirements of the constitutive functions under superposed rigid body rotation. Ad-hoc assumptions about stress corotational or convected rates and other fuzzy suggestions for different spins are not part of this development. Other topics such as the concept and simplifying effect of the spinless unstressed configuration and its comparison with the isoclinic configuration, some computational aspects, and the effect of small elastic strains are discussed, and all along the significance of plastic spin in the different equations is evaluated.     

Fluctuation relation based continuum model for thermoviscoplasticity in metals

A continuum plasticity model for metals is presented from considerations of non-equilibrium thermodynamics. Of specific interest is the application of a fluctuation relation that subsumes the second law of thermodynamics en route to deriving the evolution equations for the internal state variables. The modelling itself is accomplished in a two-temperature framework that appears naturally by considering the thermodynamic system to be composed of two weakly interacting subsystems, viz. a kinetic vibrational subsystem corresponding to the atomic lattice vibrations and a configurational subsystem of the slower degrees of freedom describing the motion of defects in a plastically deforming metal. An apparently physical nature of the present model derives upon considering the dislocation density, which characterizes the configurational subsystem, as a state variable. Unlike the usual constitutive modelling aided by the second law of thermodynamics that merely provides a guideline to select the admissible (though possibly non-unique) processes, the present formalism strictly determines the process or the evolution equations for the thermodynamic states while including the effect of fluctuations. The continuum model accommodates finite deformation and describes plastic deformation in a yield-free setup. The theory here is essentially limited to face-centered cubic metals modelled with a single dislocation density as the internal variable. Limited numerical simulations are presented with validation against relevant experimental data.     

Mean-field homogenization of elasto-viscoplastic composites based on a general incrementally affine linearization method

We propose a general formulation – which we believe to be new – for the mean-field homogenization of inclusion-reinforced elasto-viscoplastic composites assuming small strains. Our proposal is based on an interplay between constitutive equations and numerical algorithms, and the key ideas behind it are the following. The evolution equations for inelastic strain and internal variables at the beginning of each time interval are linearized around the ending time of the same interval. The linearized equations are then numerically integrated using a fully implicit backward Euler scheme. The obtained algebraic equations lead to an incrementally affine stress–strain relation which involves two important terms. The first one is the algorithmic tangent operator, obtained by consistent linearization of the time discretized constitutive equations. The second term is a new one and called an affine strain increment. The proposal leads to thermoelastic-like relations directly in the time domain, and not in the Laplace–Carson (L–C) one. There is no need for viscoelastic-type integral rewriting of the evolution equations, for L–C transforms, or for numerical inversion back from L–C to time domains. The proposed method can be readily applied to sophisticated elasto-viscoplastic models with an arbitrary set of scalar or tensor internal variables, and is valid for multi-axial, non-monotonic and non-proportional loading histories. The theory is applied in detail to a well-known constitutive model, and verified against finite element simulations of representative volume elements or unit cells, for a number of composite materials.     

On thermodynamic potentials in thermoelasticity under small strain and finite thermal perturbation assumptions

Expressions for thermodynamic potentials (internal energy, Helmholtz energy, Gibbs energy and enthalpy) of a thermoelastic material are developed under the assumption of small strains and finite changes in the thermal variable (temperature or entropy). The literature provides expressions for the Helmholtz energy in terms of strain and temperature, most often as expansions to the second order in strain and to a higher order in temperature changes, which ensures an affine stress–strain relation and a certain temperature dependence of the moduli of the material. Expressions are here developed for the four potentials in terms of all four possible pairs of independent variables. First, an expression is obtained for each potential as a quadratic function of its natural mechanical variable with coefficients depending on its natural thermal variable that are identified in terms of the moduli of the material. The form of the coefficients’ dependence on the thermal variable is not specified beforehand so as to obtain the most general expressions compatible with an affine stress–strain relation. Then, from each potential expressed in terms of its natural variables, expressions are derived for the other three potentials in terms of these same variables using the Gibbs–Helmholtz equations. The paper provides a thermodynamic framework for the constitutive modeling of thermoelastic materials undergoing small strains but finite changes in the thermal variables, the properties of which are liable to depend on the thermal variables.     

A constitutive model for magnetostrictive and piezoelectric materials

This paper is concerned with a macroscopic nonlinear constitutive law for magnetostrictive alloys and ferroelectric ceramics. It accounts for the hysteresis effects which occur in the considered class of materials. The uniaxial model is thermodynamically motivated and based on the definition of a specific free energy function and a switching criterion. Furthermore, an additive split of the strains and the magnetic or electric field strength into a reversible and an irreversible part is suggested. Analog to plasticity, the irreversible quantities serve as internal variables. A one-to-one-relation between the two internal variables provides conservation of volume for the irreversible strains. The material model is able to approximate the ferromagnetic or ferroelectric hysteresis curves and the related butterfly hysteresis curves. Furthermore, an extended approach for ferrimagnetic behavior which occurs in magnetostrictive materials is presented. A main aspect of the constitutive model is its numerical treatment. The finite element method is employed to solve the coupled field problem. Here the usage of the irreversible field strength permits the application of algorithms of computational inelasticity. The algorithmic consistent tangent moduli are developed in closed form. Hence, quadratic convergence in the iterative solution scheme of governing balance equations is obtained.     

Micromechanics of ferroelectric domain switching behavior: Part II: Constitutive relations and hysteresis

A constitutive relation is developed to describe the nonlinear behavior of ferroelectric ceramics subjected to external stress and electric field. The theoretical development considers each domain as an inclusion. The Helmholtz and Gibbs free energy of the constituent element are derived by using a micromechanics approach. They are functionals of the orientation distribution function (ODF) that represents the domain distribution patterns. By applying the internal variable theory and expanding ODF in Fourier series, the yield condition, evolution of ODF, and constitutive relation are obtained. Theoretical results agree with experiments.     

热粘塑性体的积分－微分型本构关系

应用　　　关于应力是五维偏应变空间变形历史的泛函的概念和Ｖａｌａｎｉｓ有关内＊时理论的描述，本文提出，对热粘塑性体，应力可设为应变、应变率和温度历史的泛函；并应用Ｍｉｌｌｅｒ和其它一些作者有关内变量演化方程的描述，由此建立了热粘塑性体的积分－微分到本构方程．这一积分－微分型本构关系大体和Ｍｉｌｌｅｒ微分型模型等价．对１０２０钢的单轴本构响应进行了数值模拟，和Ｔａｎａｋａ与Ｍｉｌｌｅｒ的分析及一些实验结果符合较好．     

土的本构方程与热力学

介绍一种基于热力学理论建立土力学本构方程的一般性理论框架. 这一方法利用两个势函数即自由能势函数和耗散势函数(或屈服函数)以及固定的过程和框架, 建立土的本构方程. 简要介绍了建立热力学本构方程中所用到的热力学内变量理论, 利用Legendre变换建立了热力学势函数之间以及各耗散函数与屈服函数之间的关系;利用自由能势函数和耗散势函数(或屈服函数)建立土的本构方程及其具体步骤. 最后讨论了土力学本构方程研究的意义以及它和应用之间的关系.