材料生长与变形的连续介质模型:平衡方程与边界条件

本文探讨了生长变形体连续介质模型的平衡理论框架。文中首先证明了广义输运定理，根据这个定理，推导了生长变形体广义平衡方程的一般形式及其生长边界条件，并导出反映生长边界面对平衡影响的生长耦合函数。在此基础上，具体讨论了质量、动量、动量矩以及能量平衡方程，并对其中相伴出现的一些新的物理量进行了评述；此外，还根据非平衡热力学理论的局域平衡假设建立了描述生长变形体热力学过程的熵不等式。这些方程唯象反映了生长变形体在运动、变形与生长过程中各物理量之间的耦合关系与平衡规律。     

结构阻尼时域本构模型及其应用

阻尼合金作为一种新型结构功能材料在不少领域已获应用，由于其阻尼值较大且随频率呈复杂交化关系，传统的线性粘性阻尼理论或经典的非频变结构阻尼理论难以精确地描述其耗能行为。本文应用粘弹性阻尼理论，根据阻尼合金储能模量和损耗因子在频域的实测数据．应用最优化方法拟合出标准线性体模型中的本构参数；根据积分形式的三参量本构关系和变形体虚功原理，推导出了有限元形式的动力学方程；讨论了三参数初值的选取；对包含卷积积分的有限元动力学方程通过数学推导将其化为三阶线性微分方程组，再转化为标准状态变量方程，应用数值求解。数值计算实例证明了所提方法的正确和有效性。     

复本构理论中的对偶原则

复本构理论中的对偶原则何钟怡（哈尔滨建筑工程学院，１５０００６）关键词复本构方程，对偶原则，强迫振动１复本构的对偶原则材料的本构方程完全可以不用复数形式表达，概括性很强的Ｎｏｌｌ泛函就是以实变量表示的．但是对于线性本构，采用复变量表示优越性很大．例如...     

Sn—Pb共晶钎料合金的Bodner—Partom本构方程

采用Ｂｏｄｎｅｒ－Ｐａｒｔｏｍ粘塑性本构理论研究了Ｓｎ－Ｐｂ共晶合金的本构方程。在应变速率１０－５—１０－２Ｓ－１、温度为－５５—１２５℃的外部变量范围内进行了单轴拉伸和稳态蠕变数值模拟，结果与实验吻合良好。同时讨论了该本构方程用于ＳＭＴ焊点热循环寿命预测的实际意义。     

蠕变损伤问题的有效模量法及差分解

本文在蠕变损伤问题中，以有效模量法将损伤变量引入本构方程，给出相应非线性问题的差分解；并将结果与一维实验数据及有效应力法的结果进行了比较。     

热粘塑性体的积分—微分型本构关系

应用ИЛЪЮШИН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、应变率和温度历史泛；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－微分型本构方程这一积分－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     

无耦合条件下的多子系统静动态统一本构关系(上)--基本理论

引入了同步性的概念。按照是否同步对所有的内变量进行分组，得到了整个系统的子系统结构。证明了子系统间无耦合时各子系统内部一致性条件成立的判别准则，从而得到了可以统一描述子系统内部的时间相关、时间无关不可逆行为的内变量演化方程和加卸载准则。本构关系既适用于静态加载，也适用于动态加载。经典塑性本构关系、多屈服面本构关系及过应力型粘塑性本构关系只是本文的特例。     

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．     

考虑损伤的内变量黏弹--黏塑性本构方程

基于Rice不可逆内变量热力学框架,在约束构型空间中讨论材料的蠕变损伤问题.通过给定具体的余能密度函数和内变量演化方程推导出考虑损伤的内变量黏弹--黏塑性本构方程.通过模型相似材料单轴蠕变加卸载试验对一维情况下的本构方程进行参数辨识和模型验证,本构方程能很好地描述黏弹性变形和各蠕变阶段.不同的蠕变阶段具有不同的能量耗散特点.受应力扰动后,不考虑损伤的材料系统能自发趋于热力学平衡态或稳定态.在考虑损伤的整个蠕变过程中,材料系统先趋于平衡态再背离平衡态发展.能量耗散率可作为材料系统热力学状态偏离平衡态的测度;能量耗散率的时间导数可用于表征系统的演化趋势;两者的域内积分值可作为结构长期稳定性的评价指标.     

考虑损伤的内变量黏弹-黏塑性本构方程

基于Rice 不可逆内变量热力学框架,在约束构型空间中讨论材料的蠕变损伤问题. 通过给定具体的余能密度函数和内变量演化方程推导出考虑损伤的内变量黏弹-黏塑性本构方程. 通过模型相似材料单轴蠕变加卸载试验对一维情况下的本构方程进行参数辨识和模型验证,本构方程能很好地描述黏弹性变形和各蠕变阶段.不同的蠕变阶段具有不同的能量耗散特点. 受应力扰动后,不考虑损伤的材料系统能自发趋于热力学平衡态或稳定态. 在考虑损伤的整个蠕变过程中,材料系统先趋于平衡态再背离平衡态发展. 能量耗散率可作为材料系统热力学状态偏离平衡态的测度;能量耗散率的时间导数可用于表征系统的演化趋势;两者的域内积分值可作为结构长期稳定性的评价指标.      

The equilibrium equations and constitutive equations of the growing deformable body in the framework of continuum theory

In this paper, a general framework of continuum theory for a growing deformable body is established. Firstly, the so-called material accretion derivative is defined. Based on this definition, a general form of the equilibrium equation and its growing boundary condition describing motion of the growing deformable body are deduced in detail. From the process of deduction, the concept of coupling function of growth is derived, which reflects the influence of the accretive boundary surface. Then, the equilibrium equations, including the equation of mass, momentum, moment of momentum and energy, are discussed. Also, the entropy inequality is given according to the assumption of local equilibrium of non-equilibrium thermodynamics. In the meantime, the related constitutive equations are deduced. All these equations constitute a group of closed equations characterizing the growth and motion of the body.     

计及表面能的应变梯度理论本构参数识别

本文提出利用静态位移信息对一种计及表面能的应变梯度理论本构参数进行识别的求解策略.基于Vardoulakis和Sulem的计及表面能的简单线性应变梯度理论,文献[13]给出了伯努力-欧拉梁弯曲问题的正演解析模型,本文将其反演归结为两个带有不等式约束的非线性规划问题.在此基础上,采用黄金分割一维搜索方法进行求解,给出了数值验证,讨论了信息误差对反演结果的影响.结果显示,这种方法可以用来对应变梯度理论本构参数进行识别,即使在体积和表面能常数非常小的情况下,仍然能够得到满意的结果.     

Effective constitutive relations for inelastic composites

The first special boundary value problem in the mechanics of deformable solids is considered to derive the effective constitutive relations for a heterogeneous inelastic body. The problem is reduced to a number of auxiliary boundary value problems for functions dependent on the shape of the body and on the form of constitutive relations. In the case of a layer of nonuniform thickness, the problem of finding the effective constitutive relations is reduced to an operator equation whose solution is sought by an iterative method of successive approximations. An approximate analytical formula is proposed to find the effective constitutive relations for a laminated composite on the basis of known inelastic constitutive relations for its components. This approximate formula takes into account the character of structural anisotropy in a laminated composite and, in the elastic case, yields the exact values of the effective elastic modulus.     

Temperature-rate dependent constitutive theory in thermo-viscoplastic media

In this paper, a temperature-rate dependent constitutive theory in thermo-viscoplastic media is proposed. On the basis of Clausius-Duhem (C-D) entropy inequality and the generalized Helmholtz free energy defined by Green and Lindsay, it is shown under some reasonable assumptions that the constitutive models in classical thermo-plasticity theory can be extended to the temperature-rate dependent (TRD) media provided that the temperature-rate effect is taken into account and the absolute temperatureT taken as an independent constitutive variable is replaced by coldness function T^* introduced by Müller, and discussed in detail by Ru and Duan.     

CONSTITUTIVE RELATION OF UNSATURATED SOIL BY USE OF THE MIXTURE THEORY(Ⅰ)—NONLINEAR CONSTITUTIVE EQUATIONS AND FIELD EQUATIONS

IntroductionSoilisthemostcommonlyusedconstructionmaterialincivilengineeringandhydraulicengineering .Thecharacteristicsofsoilhavebeeninvestigatingfornearlyonehundredyears.Butbecauseofitscomplexstructure,changeableenvironmentandbeingsensitivetotheoutsideconditions,thesoiloftenshowsvariedproperties[1,2 ].Themaindifficultytothedevelopmentofgeotechnicalmechanicsishowtosetupconstitutiveequationswhichcouldsatisfactorilyaccountforengineeringpropertiesofsoil[3].Manyconstitutivemodelshavebeenformedinth…     

Constitutive structure in coupled non-linear electro-elasticity: Invariant descriptions and constitutive restrictions

A constitutive framework for electro-sensitive materials in the context of non-linear elasticity is analyzed. Constitutive equations are given in terms of energy functions that depend on several invariants. The study includes both the analysis of the invariants, which are present in the energy functions, and the analysis of constitutive restrictions that have to be obeyed by the constitutive functions. Isotropic as well as non-isotropic electro-sensitive elastomers are studied. The set of invariants that describe each material model is analyzed under two homogeneous deformations: (i) an uniaxial elongation and (ii) a simple shear deformation. These deformations are chosen since they are relevant to specific experiments, from which one may try to fit constitutive equations. The constitutive restrictions developed are based on classical ones used for isotropic non-linear elastic materials, in particular, are based on the Baker–Ericksen inequality and the ellipticity condition.     

On a distributed derivative model of a viscoelastic bodySur un model de corps viscoélastique de dérivé distribué

We study a viscoelastic body, in a linear stress state with fractional derivative type of dissipation. The model was formulated so that it takes into account, with a weighting factor, all derivatives of stress and strain between zero and one. We derive restrictions on the model that follow from Clausius–Duhem inequality. Several known constitutive equations are derived as special cases of the model proposed here. Two examples are discussed. To cite this article: T.M. Atanackovic, C. R. Mecanique 331 (2003).     

A unified residual-based thermodynamic framework for strain gradient theories of plasticity

A unified thermodynamic framework for gradient plasticity theories in small deformations is provided, which is able to accommodate (almost) all existing strain gradient plasticity theories. The concept of energy residual (the long range power density transferred to the generic particle from the surrounding material and locally spent to sustain some extra plastic power) plays a crucial role. An energy balance principle for the extra plastic power leads to a representation formula of the energy residual in terms of a long range stress, typically of the third order, a macroscopic counterpart of the micro-forces acting on the GNDs (Geometrically Necessary Dislocations). The insulation condition (implying that no long range energy interactions are allowed between the body and the exterior environment) is used to derive the higher order boundary conditions, as well as to ascertain a principle of the plastic power redistribution in which the energy residual plays the role of redistributor and guarantees that the actual plastic dissipation satisfies the second thermodynamics principle. The (nonlocal) Clausius-Duhem inequality, into which the long range stress enters aside the Cauchy stress, is used to derive the thermodynamic restrictions on the constitutive equations, which include the state equations and the dissipation inequality. Consistent with the latter inequality, the evolution laws are formulated for rate-independent models. These are shown to exhibit multiple size effects, namely (energetic) size effects on the hardening rate, as well as combined (dissipative) size effects on both the yield strength (intrinsic resistance to the onset of plastic strain) and the flow strength (resistance exhibited during plastic flow). A friction analogy is proposed as an aid for a better understanding of these two kinds of strengthening effects. The relevant boundary-value rate problem is addressed, for which a solution uniqueness theorem and a minimum variational principle are provided. Comparisons with other existing gradient theories are presented. The dissipation redistribution mechanism is illustrated by means of a simple shear model.