Some exact solutions for a class of compressible non-linearly elastic materials

In this paper we consider exact solutions for plane and axisymmetric deformations for a class of compressible elastic materials we call coharmonic. The coharmonic materials are derived from the harmonic materials by using Shield's inverse deformation theorem. The governing equations for the coharmonic material show the same kind of simplification associated with the harmonic materials. The equations reduce to first-order linear equations depending on an arbitrary harmonic function. They are intractable in general, so various ansätze are investigated. Boundary value problems for the coharmonic materials are compared with the same problems for harmonic materials. For certain boundary value problems, the harmonic materials exhibit well-known problematic behaviour which limits their use as models of material behaviour. The corresponding solutions for the coharmonic materials do not display these non-physical features.     

Development of a Hybrid Method of Reflection Photoelasticity for Crack Problems in Anisotropic Plates

Reflection type photoelastic experiment can be used more effectively than a transmission type photoelastic experiment especially in industrial fields. Moreover, composite materials have been widely used in engineering applications and structures because of their outstanding advantages which individual isotropic components do not have. The development of these materials requires a promising technique such as reflection photoelasticity to analyze their behaviors in service. Unfortunately, there are few experimental studies based on this technique. Therefore, a hybrid method based on this technique was developed in this research to analyze the fracture behavior of opaque anisotropic materials. The application of this method will help to understand the fracture behaviors of anisotropic materials used in engineering components and structures. The validity of this method was verified by comparison of the results obtained from this method with ones obtained from the hybrid methods for isotropic material on the same isotropic specimen. The reflection type photoelastic experiment for orthotropic materials was then applied to orthotropic plates with a central crack of various inclination angles. Using this hybrid method for anisotropic materials, stress intensity factors and separated stress components were obtained at the vicinity of the crack-tip in orthotropic plates from only the isochromatic fringe patterns of the isotropic coating material.     

The role of mechanics in biological and biologically inspired materials

In the development of new materials, researchers have recently turned to nature for inspiration and assistance. A special emphasis has been placed on understanding the development of biological materials from the traditional correlation of structure to property, as well as correlating structure to functionality. The natural evolution of structure in biological materials is guided by the interaction between these materials and their environment. What is most notable about natural materials is the way in which the structure is able to adapt at a wide range of length scales. Much of the interaction that biological materials experience occurs through mechanical contact. Therefore, to develop biologically inspired materials it is necessary to quantify the mechanical behavior of and mechanical influences on biological structures with the intention of defining the natural structure-property-functionality relationship for these materials. In particular, the role mechanics has assumed in understanding biological materials, and the biologically inspired materials developed from this knowledge, will be clarified. The following will serve to elucidate on this role: the helical structure of fibrous tissue, the multi-scale structure of wood, and the biologically inspired optimal structure of functionally graded materials.     

Green's function solution and displacement potentials for Transformed Transversely Isotropic materials

A totally non-degenerate expression for the Green's function of infinite Transversely Isotropic (TI) materials is first deduced from the solutions given by Pan and Chou [Pan, Y.-C., Chou, T.-W., 1976. Point force solution for an infinite transversely isotropic solid. Trans. ASME, J. Appl. Mech. 43 (4), 608–612]. Then this solution and also the displacement potentials for TI materials are extended by a linear transformation to a larger family of anisotropic materials (Transformed Transversely Isotropic or TraTI materials). This family depends on 12 independent parameters and contains non-orthotropic materials and in this way a first explicit analytical solution for the Green's function for a non-orthotropic material is obtained. The TraTI materials which have orthotropic Symmetry (StraTI materials) constitute a sub-family depending on 6 independent parameters in the symmetry basis of the material. These materials present a 3D anisotropy (different stiffnesses in three orthogonal directions). General displacement potentials and the Green's function solution for STraTI materials can be deduced by a simple change and introducing one additional parameter in the well-known TI solutions.     

复合材料和粘弹性材料中的应力奇异性

在各种材料中,出现的应力奇异性已为工程技术人员的科学研究提供了丰富的素材,本文的主要目的在于对粘弹性材料的应力奇异性进行探讨,利用对应性原理从弹性材料导出粘生材料的应力奇异分布。     

负泊松比材料和结构的研究进展

负泊松比材料和结构具有特殊的力学性能,在单轴压力(拉力)作用下发生横向收缩(膨胀).其在抗剪承载力、抗断裂性、能量吸收和压陷阻力等方面比传统材料更有优势,因而负泊松比材料在医疗设备、传感器、防护设备、航空航海及国防工程等领域有广泛的应用前景,但目前负泊松比材料的应用与普及仍面临一些挑战.本文广泛讨论了国内外关于负泊松比材料的研究成果并介绍了负泊松比材料的最新进展,将负泊松比材料大体概括为以下4类:天然负泊松比材料、胞状负泊松比材料、金属负泊松比材料、多重和复合负泊松比材料.主要介绍了各种负泊松比材料的内部结构、负泊松比机理、力学性能以及在各行各业的新发明、新应用.针对目前负泊松比材料研究理论和实验成果多,而实际应用仍然较少的情况,指出了负泊松比材料的缺点及其推广所面临的挑战.目前负泊松比材料面临的主要问题是制造成本高、孔隙率大而承载力不足以及仅适用于小应变情况等.本文针对此情况详细介绍了金属负泊松比材料及其设计和制作的方法,改善负泊松比材料的不足并推广其应用.      

磁敏智能软材料及磁流变机理

磁敏智能软材料是一类将微米或纳米尺度的磁性颗粒分散在不同基体中制备而成的多功能复合材料.由于其流变性能在外磁场的调控下可以实现连续、快速、可逆的改变,因此在建筑、振动控制和汽车工业等领域得到了广泛地应用.本文首先介绍了磁敏智能软材料发展历史及分类,分析了不同种类的磁敏智能软材料的特点和存在的科学问题;然后从实验和理论两个方面讨论了磁流变机理的研究现状;最后从实际应用的角度对这类材料未来的发展方向进行了展望.      

微孔压电弹性动力学的能量原理

根据古典阴阳互补和现代对偶互补的基本思想,通过作者早已提出一条简单而统一的新途径,系统地建立了微孔压电弹性动力学的能量原理,给出一个重要的以卷积表示的积分关系式,可以认为,在力学上它是广义虚功原理的表式,从该式出发,不仅能得到微孔压电弹性动力学的虚功原理和互等定理,而且通过作者所给出的一系列广义Legendre变换,能系统地导出成互补关系的11类变量、9类变量、6类变量和3类变量简化Gurtin型变分原理的泛函,同时,通过这条新途径,还能清楚地阐明这些原理之间的内在联系。     

Superposition of Generalized Plane Strain on Anti-Plane Shear Deformations in Isotropic Incompressible Hyperelastic Materials

The purpose of this research is to investigate the basic issues that arise when generalized plane strain deformations are superimposed on anti-plane shear deformations in isotropic incompressible hyperelastic materials. Attention is confined to a subclass of such materials for which the strain-energy density depends only on the first invariant of the strain tensor. The governing equations of equilibrium are a coupled system of three nonlinear partial differential equations for three displacement fields. It is shown that, for general plane domains, this system decouples the plane and anti-plane displacements only for the case of a neo-Hookean material. Even in this case, the stress field involves coupling of both deformations. For generalized neo-Hookean materials, universal relations may be used in some situations to uncouple the governing equations. It is shown that some of the results are also valid for inhomogeneous materials and for elastodynamics.     

固体跨尺度压痕标度律的研究与展望

压痕标度律是对通过压痕试验方法测定固体材料力学性能参量问题所给出的一般性结论, 具有重要的理论意义, 是探寻材料力学性能潜在规律的方法论研究. 本综述论文系统而简要地介绍如下主要内容: 采用传统理论对传统固体材料压痕标度律的研究回顾; 采用跨尺度力学理论对先进固体材料的跨尺度压痕标度律的研究回顾. 总结并得到了如下主要结论: 传统固体材料压痕标度律可由一空间曲面完整描绘, 若进一步已知某类无量纲独立参量的取值范围, 则该空间曲面可退化为系列平面曲线族; 先进固体材料(新材料)的跨尺度压痕标度律可由一个三维函数关系完整描绘, 若存在某类独立无量纲参量取值范围已知, 则该三维函数关系将退化为系列空间曲面族. 压痕标度律的未来研究发展仍将重点集中在建立新材料的跨尺度压痕标度律上, 以试图从根本上解决新材料力学性能标准规范难以建立的理论问题. 除此之外也将重点关注建立各类功能新材料的多尺度及跨尺度压痕标度律规律.      

多尺度复合材料力学研究进展

多尺度复合材料力学是运用多尺度分析思想研究空间分布非均匀材料力学性能的学科, 近年来,多 组分、多层级先进材料的蓬勃发展和微纳米实验观测手段的不断进步,有力地推动了该学科的研究,论文围绕非均 匀材料力学性能的多尺度分析,首先从微纳米尺度到宏观尺度综述了常用的理论分析方法;接着分别针对非均匀 连续介质和离散体系介绍了常用的多尺度计算模拟方法;然后结合本课题组在纳米复合材料、抗冲击吸能材料、随 机网络材料和多层级自相似材料等方面的研究工作,举例说明了如何综合运用多种方法对各种复杂材料系统进行 多尺度分析;最后,展望了该领域还需进一步发展和完善的若干方向。     

Strain gradient plasticity by internal-variable approach with normality structure

This paper presents a constitutive formulation for materials with strain gradient effects by internal-variable approach with normality structure. Specific micro-structural rearrangements are assumed to account for the inelasticity deformations for this class of materials, and enter the constitutive formulations in form of internal variables. It is further assumed that the kinetic evolution of any specific micro-structural rearrangement may be fully determined by the thermodynamic forces associated with that micro-structural rearrangement, by normality relations via a flow potential. Macroscopic gradient-enhanced inelastic behaviours may then be predicted in terms of the microscopic internal variables and their conjugate forces, and thus a micro–macro bridging formulation is available for strain-gradient-characterised materials. The obtained formulations are first applied to crystallographic materials, and a crystal gradient plasticity model is developed to account for the influence of microscopic slip rearrangements on the macroscopic gradient-dependent mechanical behaviour for this class of materials. Micro-cracked geomaterials are also treated with these formulations and a gradient-enhanced damage constitutive model is developed to address the impacts of the evolutions of micro-cracks on the macroscopic inelastic deformations with strain gradient effects for these materials. The available formulations are further compared with other thermodynamic approaches of constitutive developing.     

白光DSCM方法用于岩石变形观测的研究

本文分析了白光DSCM（数字散斑相关测量）方法用于岩石材料表面变形观测的可行性及优越性，并根据岩石材料变形的特点将普通DSCM方法进行改进。DSCM方法应用于岩石变形观测中，使观测过程得到简化，同时有助于解决岩石力学中一些难题。文中的实验结果证实了该方法的可行性和优越性。     

Analysis of residual stresses in bars and tubes of cylindrically orthotropic materials

One of the most frequently used techniques of determining residual stresses in cylindrical bodies of elastically isotropic materials is the Mesnager-Sachs boring-out method. This method is adequate for many engineering materials; however, certain materials possess elastic properties which vary with direction. Materials having one fairly common kind of directional variation are known as cylindrically orthotropic materials. Heretofore, no means has been available for determining the residual stresses from strain data taken after successive borings of members made of such materials. This paper gives the derivation of equations for this purpose along with graphs depicting the error to be expected if the data had been reduced by the Sachs equations.     

Experimental analysis of the pressure drop and heat transfer through metal foams used as volumetric receivers under concentrated solar radiation

The main objective of this work was to evaluate the behavior of porous materials, when treated as volumetric receivers under concentrated solar radiation. For this reason various porous metallic and ceramic materials have been tested as potential receivers for concentrated solar radiation. The experimental investigation showed that their efficiency was depending on both materials parameters and flow conditions. In this work, a variety of foam materials such as Ni and Ni alloy, inconel, copper, aluminum and SiC with different open cell porosity were tested as potential media to be used as volumetric receivers and heat exchangers. However, since the results were similar, for space economy, only the results of two of them, nickel and inconel were presented in detail and compared with each other.     

ANALYTICAL SOLUTIONS FOR A ONE-DIMENSIONAL CHEMO-MECHANICAL COUPLING PROBLEM

Chemo-mechanical coupling exists in a lot of intelligent materials including hy- drogels, biological tissues and other soft materials. These materials are able to respond to ex- ternal stimulus, such as temperature, chemical concentration, and pH value. In this paper, a one-dimensional theoretical model for chemo-mechanical coupling is proposed for analyzing the uniaxial stress/strain state of coupling materials. Based on the chemo-mechanical coupled gov- erning equation, the displacement function and concentration function are derived and the stress and chemical potential are obtained. It is shown that the present chemo-mechanical theory can characterize the chemo-mechanical coupling behavior of intelligent materials.     

An integral representation of the surface-impedance tensor for incompressible elastic materials

A fundamental result in anisotropic elasticity and surface-wave theory is the integral representation for the surface-impedance tensor first derived by Barnett and Lothe in 1973. However, this representation is only valid for compressible materials but not valid for incompressible materials. In this paper the corresponding integral representation for the surface-impedance tensor valid for incompressible materials is derived and is used to establish the uniqueness of surface-wave speed and to obtain an expression for the tensor Green's function for the infinite space. Mathematics subject classifications (2000) 74B05, 74B15, 74B20, 74J15     

弹性力学的一种正交关系

在弹性力学求解新体系中，将对偶向量进行重新排序后，提出了一种新的对偶微分矩阵，对于有一个方向正交的各向异性材料的三维弹性力学问题发现了一种新的正交关系．将材料的正交方向取为z轴，证明了这种正交关系的成立．对于z方向材料正交的各向异性弹性力学问题，新的正交关系包含弹性力学求解新体系提出的正交关系。     

Application of the least-squares method to elastic and photoelastic calibration of orthotropic composites

New experimental methods continue to be proposed for determining the in-plane elastic constants of orthotropic composite materials, as no single method has been found completely satisfactory. In particular, the in-plane shear modulus is difficult to measure. In this paper, an orthotropic half-plane subjected to a concentrated edge load is proposed as a calibration specimen. Photoelastic calibration of orthotropic-birefringent composites is also difficult due to the need to conserve the commercially unavailable, difficult-to-make model materials and the absence of many closed-form solutions. In this paper, the orthotropic half-plane specimen is proposed for photoelastic calibration of birefringent-orthotropic model materials also. For elastic and photoelastic calibration of orthotropic materials, the least-squares procedure is used for processing the experimental data.