缺陷连续统理论及其在本构方程研究中的应用 Ⅱ.缺陷的规范场理论

详细评述了缺陷连续统的规范场理论,该理论是近代材料科学和固体力学中新发展起来颇有意义的一个分支。首先强调了Noether定理及其逆定理在构造缺陷规范场理论中的重要性。同时基于Yang-Mills普适规范场构造,包括对SO(3)T(3)群的最小替换和最小耦合原理,系统地介绍了Golebiewska-Lasota,Edelen,Kadic和Edelen等人的原始性工作及他们的贡献。本文表明,Kadic和Edelen的理论是基于一组缺陷动力学的线性连续性方程发展起来的,不能和关于缺陷场的现有几何理论完全协调起来。考虑到这一点,本文提供了另一种方法来建立非线性弹性规范场的相应理论,这里考虑了Poincaré规范群SO(3)T(3).采用类似于研究引力场理论的Kibble方法,导出了缺陷连续统的拉氏密度。非完整坐标变换和非欧联络系数在数学上完全等价于子Poincaré群SO(3)T(3)的规范场。因此,本文的规范场理论和4维物质流形的缺陷场的非线性几何理论是完全一致的,并证明在弱缺陷条件下,可以简化到Kadic和Edelen的结果。     

变形体非协调理论的理性理论

本文介绍Noll和Wang等人用理性力学观点建立的变形体非协调理论(即缺陷的连续统理论)。这理论表明,本构方程完全确定物质流形的几何结构。因而,几何结构是理论的自然结果,而不是作为理论出发点的最初假设。      

具有非局部体力矩的非局部弹性理论

本文基于非局部连续统场论的公理系统,建立了具有非局部体力矩作用的非局部弹性理论,我们证明了,在非局部弹性固体中存在着非局部体力矩,非局部体力矩引起了应力的非对称和非局部体力矩是由材料中的共价键产生的。     

弹性理论方程的不变解

基于李群和李代数理论,分析了固体力学中微分方程的群分析的基本原理和应用.总结了群分析在弹性理论领域取得的一些重要成果,特别是弹性动力学中的拉梅方程和非线性弹性理论方程方面,得到了弹性理论方程的一系列不变解.预测了群分析在弹性理论领域的进一步发展方向.     

含单排周期微裂纹平板结构中的弹性波传播

受损伤固体中含有的微裂纹或微孔洞往往具有周期性，对含周期性缺陷结构中的弹性波分析是力学研究中的重要课题，它直接关系到结构的强度和使用寿命。目前对损伤固体中弹性波散射与透射研究结果主要是弹性动力学平面问题。1995年。Scarpetta和Sumbatyan采用解析法研究了平面波在双周期裂纹弹性介质中的传播问题。并推出显式分析结果。本文基于弹性动力学理论，分析研究了含有单排横向周期裂纹的平板中弯曲波的反射与透射问题。给出了含单排裂纹时反射波与透射波系数的数值结果。对于多排裂纹情况，可采用具有退化核第一类Fredholm积分方程方法分析求解，在求解中给出相应的无量纲数，例如无量纲波数、裂纹尺寸比等。本文分析结果可望能在工程振动控制中应用。     

理性连续统力学国外发展概况

古代埃及由于当时的客观实际需要形成了土地测量术,以后通过希腊的公理学逐渐发展成了几何学。事实证明,几何学是一门非常有用的学科。由于生产发展的需要,已经形成了诸如材料力学、弹性力学、流体力学、热力学、土壤力学等许多力学分支,并已发展到了相当高的水平。像把土地测量术通过合理化变成几何学那样把连续统力学各个分支也通过公理化变成数学的想法,就是理性连续统力学所要达到的目的。理性连续统力学,主要是提供和研究描述物质位置和形状变化的数学模型的学科。它是数学的一部分,而且是连续统物理学的基础。      

关于塑性动力学问题

塑性动力学是固体力学的一个较新的分支,它研究固体材料和各种结构物在短时强载荷作用下的弹塑性动力性态和应力与变形传播的规律。由于塑性动力学问题来自生产实践的各个领域,所以它和航空、造船、工业与民用建筑、水工建筑、矿山建筑、机械制造等工业的飞速发展有着直接的关系。同时由于塑性动力学是在弹塑性静力学和弹性动力学基础上引伸发展起来的,所以它和弹性、塑性理论,以及爆炸力学、地震力学、实验力学、计     

艾林根教授在华讲学

美国普林斯顿大学连续统物理学教授 A·C·Eringen 应邀于1980年夏来我国,在兰州大学及中国科学院力学研究所进行为期一个月的讲学.A.C.Eringen 教授是国际有声望的科学家.他在理性连续统力学,连续统物理学,极性场论,局部和非局部理论,以及液晶理论等方面都作出了重要的贡     

艾林根教授在华讲学

美国普林斯顿大学连续统物理学教授 A·C·Eringen 应邀于1980年夏来我国,在兰州大学及中国科学院力学研究所进行为期一个月的讲学.A.C.Eringen 教授是国际有声望的科学家.他在理性连续统力学,连续统物理学,极性场论,局部和非局部理论,以及液晶理论等方面都作出了重要的贡 ...     

帕普科维奇对力学的贡献

帕普科维奇是苏联著名的力学家, 他在船舶结构力学的杆系理论、板的弯曲、板架分析、弹性体系的稳定性以及结构振动和动力学等各个方面都有重要成就, 特别是他推出了弹性力学基本方程的通解, 这对弹性力学是一个突破性的贡献. 他的《船舶结构力学》和《弹性力学》等著作是力学领域的名著. 本文对他在力学的各个方面主要的创新性成果作了全面的系统的介绍.     

Finite element approximation of field dislocation mechanics

A tool for studying links between continuum plasticity and dislocation theory within a field framework is presented. A finite element implementation of the geometrically linear version of a recently proposed theory of field dislocation mechanics (J. Mech. Phys. Solids 49 (2001) 761; Proc. Roy. Soc. 459 (2003) 1343; J. Mech. Phys. Solids 52 (2004) 301) represents the main idea behind the tool. The constitutive ingredients of the theory under consideration are simply elasticity and a specification of dislocation velocity and nucleation. The set of equations to be approximated are non-standard in the context of solid mechanics applications. It comprises the standard second-order equilibrium equations, a first-order div-curl system for the elastic incompatibility, and a first-order, wave-propagative system for the evolution of dislocation density. The latter two sets of equations require special treatment as the standard Galerkin method is not adequate, and are solved utilizing a least-squares finite element strategy. The implementation is validated against analytical results of the classical elastic theory of dislocations and analytical results of the theory itself. Elastic stress fields of dislocation distributions in generally anisotropic media of finite extent, deviation from elastic response, yield-drop, and back-stress are shown to be natural consequences of the model. The development of inhomogeneity, from homogeneous initial conditions and boundary conditions corresponding to homogeneous deformation in conventional plasticity, is also demonstrated. To our knowledge, this work represents the first computational implementation of a theory of dislocation mechanics where no analytical results, singular solutions in particular, are required to formulate the implementation. In particular, a part of the work is the first finite element implementation of Kröner's linear elastic theory of continuously distributed dislocations in its full generality.     

A theory of the adaptive growth of biological materials

Summary In this paper, a new theory of the adaptive growth of biological materials is presented. The theory is derived from the basic laws of continuum mechanics. The material is described as a classical mixture of solid material and fluid. It will be shown that several well-known models of the adaptive growth are embedded in this more general theory. In addition, it is clarified on which material assumptions these models are based. Finally, a solution procedure for the new theory is developed, and several examples are given. Received 31 March 1999; accepted for publication 1 June 1999     

A continuum approach to the second-sound effect

Standard techniques of continuum mechanics are used to describe the flow of certain microscopic excitations which are believed to give rise to the second-sound phenomena in some materials at low temperatures. Appropriate balance laws are formulated, and constitutive equations for an elastic solid are postulated. The propagation of small-amplitude second-sound waves is discussed and the results compared with those predicted by the theory of Lord and Shulman [1].     

Elasto-viscoplastic-viscous theories of granular and porous media

The mechanics of granular and porous media is considered in the light of the modern theories of structured continuum. The basic laws of motion are presented and several constitutive relations are derived. The special case of elastic porous media is considered in detail and the basic field equations are derived and the possible application of the results to soil dynamics is pointed out. The theory of the flow of granular media is also considered and basic equations of motion are derived where the results of Goodman and Cowin are recovered. The viscoplastic flow of porous media is studied and the possible application to soil mechanics is also discussed.     

Neglected transport equations: extended Rankine–Hugoniot conditions and <Emphasis Type="Italic">J</Emphasis> -integrals for fracture

Transport equations in integral form are well established for analysis in continuum fluid dynamics but less so for solid mechanics. Four classical continuum mechanics transport equations exist, which describe the transport of mass, momentum, energy and entropy and thus describe the behaviour of density, velocity, temperature and disorder, respectively. However, one transport equation absent from the list is particularly pertinent to solid mechanics and that is a transport equation for movement, from which displacement is described. This paper introduces the fifth transport equation along with a transport equation for mechanical energy and explores some of the corollaries resulting from the existence of these equations. The general applicability of transport equations to discontinuous physics is discussed with particular focus on fracture mechanics. It is well established that bulk properties can be determined from transport equations by application of a control volume methodology. A control volume can be selected to be moving, stationary, mass tracking, part of, or enclosing the whole system domain. The flexibility of transport equations arises from their ability to tolerate discontinuities. It is insightful thus to explore the benefits derived from the displacement and mechanical energy transport equations, which are shown to be beneficial for capturing the physics of fracture arising from a displacement discontinuity. Extended forms of the Rankine–Hugoniot conditions for fracture are established along with extended forms of J -integrals.     

Analytical modelling of thermal stresses in anisotropic composites

This paper represents a continuation of the author's previous work which deals with an analytical model of thermal stresses which originate during a cooling process of an anisotropic solid elastic continuum. This continuum consists of anisotropic spherical particles which are periodically distributed in an anisotropic infinite matrix. The infinite matrix is imaginarily divided into identical cubic cells with central particles. This multi-particle–matrix system represents a model system which is applicable to two-component materials of the precipitate–matrix type. The thermal stresses, which originate due to different thermal expansion coefficients of components of the model system, are determined within the cubic cell. The analytical modelling results from fundamental equations of continuum mechanics for solid elastic continuum (Cauchy's, compatibility and equilibrium equations, Hooke's law). This paper presents suitable mathematical procedures which are applied to the fundamental equations. These mathematical procedures lead to such final formulae for the thermal stresses which are relatively simple in comparison with the final formulae presented in the author's previous work which are extremely extensive. Using these new final formulae, the numerical determination of the thermal stresses in real two-component materials with anisotropic components is not time-consuming.     

On the block element method in nonstationary problems

The block element method is used to study and solve the boundary-value problems of continuum mechanics for materials with time-varying characteristics. An example of constructing a block element is given for a boundary-value problem related to nonstationary behavior of a continuum in a four-dimensional space, with time taken into account. Pseudodifferential equations describing the block element parameters are derived. It is shown that, in the theory of block elements, the difference between the boundary and initial conditions in a nonstationary boundary-value problem disappears.     

An asymmetric theory of nonlocal elasticity—Part 2. Continuum field

In this paper, an asymmetric theory of nonlocal elasticity with nonlocal body couple is developed on the basis of the axiom system in nonlocal continuum field theory. The Galileo invariance is used for determining the explicit form of the constitutive equations. It is shown that both continuum field theory and quasicontinuum theory give the same constitutive equations and field equations for the general theory of nonlocal elasticity. Finally, the relations among nonlocal theory, couple stress theory, and higher gradient theory are investigated.     

压电介质损伤、断裂力学研究的现状

压电介质的损伤与断裂力学是现代固体力学的重要课题．本文简要地综述了压电介质损伤与断裂力学研究的现状,集中讨论了：（１）裂纹面电边界条件的不同模型及其求解的结果;（２）宏观连续力学与细观力学用于压电介质的损伤与断裂的静力学分析;（３）压电介质动态断裂分析的某些新结果．文末,指出了今后在压电介质损伤与断裂研究的某些有吸引力的研究方向     

Wave propagation through an interface between viscoelastic media in the presence of defects

The propagation of plane harmonic waves through an interface between viscoelastic media is considered using the equations of field theory of defects, the kinematic identities for an elastic continuum with defects, and the dynamic equations of gauge theory. The reflection and refraction coefficients of elastic displacement waves and the waves of a defect field characterized by a dislocation density tensor and a defect flux tensor are determined. Dependences of the obtained quantities on the parameters of the interfacing media are analyzed.