Bounds on the Elastic Moduli of Completely Random Two-Dimensional Polycrystals

Explicit bounds on the elastic moduli of completely random planar polycrystals, the shape and crystalline orientations of the constituent grains of which are uncorrelated, are derived and calculated for a number of crystals of general two-dimensional anisotropy. The bounds on the elastic two-dimensional bulk modulus happen to coincide with the simple third order (in anisotropy contrast) bounds for the subclass of idealistic circular cell polycrystals. The bounds on the shear modulus are close to the much simpler bounds for circular cell polycrystals, which approximate aggregates of equiaxed grains.     

On the Existence of Longitudinal Plane Waves in General Elastic Anisotropic Media

We give a new proof of Kolodner's result that longitudinal waves can propagate in at least three directions in a hyperelastic anisotropic medium. We give examples of an orthotropic hyperelastic tensor with exactly three such directions, of a monoclinic elastic (but not hyperelastic) tensor with only one, and of a monoclinic elastic (elliptic, but not uniformly elliptic) tensor with no direction for longitudinal waves. This revised version was published online in August 2006 with corrections to the Cover Date.     

含有随机夹杂非均匀体的有效弹性模量

在对含有随机夹杂的非均匀体求有效弹性模量时,一般多根据Eshelby的等效夹杂法,但由于该方法没有充分考虑非均匀体内部的微结构,所以其理论具有一定的局限性。本文认为Kunin的微结构理论与Eshelby的等效夹杂法相比更具一般性,因而本文采用了文[9]中一些合理的思想,摒弃了其中不合理的假设,并且建立了一种新的理论模型.最后,本文针对球夹杂的情况给出了非均匀体有效弹性模量依赖于夹杂体积份数的关系,并将该结果与文[10]中的结果进行了比较.     

Revised Bounds on the Elastic Moduli of Two-Dimensional Random Polycrystals

Our earlier derived bounds on the elastic moduli of two-dimensional random polycrystals [1, 2] involve a geometric restriction through an assumption on the form of an isotropic eight-rank tensor. The general form of the tensor is used in this study to reconstruct the bounds, which are expected to approach the scatter range for the moduli of the irregular aggregate.     

Bounds on the Effective Anisotropic Elastic Constants

Hill [12] showed that it was possible to construct bounds on the effective isotropic elastic coefficients of a material with triclinic or greater symmetry. Hill noted that the triclinic symmetry coefficients appearing in the bounds could be specialized to those of a greater symmetry, yielding the effective isotropic elastic coefficients for a material with any elastic symmetry. It is shown here that it is possible to construct bounds on the effective elastic constants of a material with any anisotropic elastic symmetry in terms of triclinic symmetry elastic coefficients. Similarly, it is then possible to specialize the triclinic symmetry coefficients appearing in the bounds to those of a greater symmetry. Specific bounds are given for the effective elastic coefficients of cubic, hexagonal, tetragonal and trigonal symmetries in terms of the elastic coefficients of triclinic symmetry. These results are obtained by combining the approach of Hill [12] with a representation of the stress-strain relations due, in principle, to Kelvin [25,26] but recast in the structure of contemporary linear algebra. This revised version was published online in August 2006 with corrections to the Cover Date.     

Kelvin结构开孔泡沫材料的弹性性能研究

采用一修正的十四面体结构模型(Kelvin结构模型)对开孔泡沫金属的弹性性能进行研究,对低密度开孔泡沫材料表现出不可压的特性进行了分析。该模型考虑作用在泡沫筋条上的弯矩、剪力和轴向力,以及轴向力的平衡。修正模型的数值计算结果与实验结果及其他模型的结果进行了对比,结果表明修正模型计算的杨氏模量比原有模型的略有提高,筋条截面为星形的修正模型计算的结果与实验比较符合。在密度等同的条件下,筋条截面惯性矩越大的开孔泡沫材料,其弹性模量也越大,而泊松比则越小。Kelvin结构的开孔泡沫材料的泊松比随相对密度的减小而趋于0.5。     

拉压不同弹性模量结构的动力特性分析

研究了拉压不同弹性模量结构动力问题的计算方法,建立了不同模量板壳结构动力特性的有限元算法,编制了相应的计算程序,并通过例题计算及分析得出了有价值的结论。     

Stability of n-covered Circles for Elastic Rods with Constant Planar Intrinsic Curvature

A stability index is computed for the n-covered circular equilibria of inextensible-unshearable elastic rods with constant planar intrinsic curvature û and constant values for the twisting stiffness and two bending stiffnesses. A simple expression is derived for the index as a function of û, (the ratio of bending stiffness out of the plane of curvature to bending stiffness in the plane of curvature), and (the ratio of twisting stiffness to bending stiffness in the plane of curvature). In particular, for intrinsically straight rods (û = 0) we prove that the 1-covered circle is stable if and only if 1, and the n-covered circle (n>1) is stable if and only if >1, >1, and

不同模量壳体理论广义弹性定律的普遍表达式

本文研究了拉伸和压缩不同模量材料制成的壳体弱矩理论的本构关系,导出了广义弹性定律的普遍表达式,即中曲面法向坐标的各任意幂次项系数的公式,并指出文献[1]中最终公式保留的线性项,仅为本文普遍表达式的一个较简单的特殊情形,因此,可以不顾文献[1]中关于应力沿壳厚按线性规律变化的基本假设。     

Effective elastic moduli of an inhomogeneous medium with cracks

In the present paper, the effective elastic moduli of an inhomogeneous medium with cracks are derived and obtained by taking into account its microstructural properties which involve the shape, size and distribution of cracks and the interaction between cracks. Numerical results for the periodic microstructure of different dimensions are presented. From the results obtained, it can be found that the distribution of cracks has a significant effect on the effective elastic moduli of the material. The project supported by the National Education Committee for Doctor     

Effective Medium Analysis of Random Lattices

Calculations of effective conductivities of generalized random bond lattices representing porous media are compared to approximations using effective medium theory (EMT). We use numerical simulations of flow through 2D and 3D random lattice models, which allow for variable lattice densities and a lognormal distribution of local conductivities, to compare effective conductivities to effective medium approximations. We find that the analytical expressions provide good agreement to the simulations in 2D systems, but are in significant error in 3D systems when the standard deviation of the local conductivities is large.     

倾斜内锁型三维机织陶瓷基复合材料的细观力学模型

利用平均化方法提出了倾斜内锁型三维机织陶瓷基复合材料弹性性能分析的三维细观力学模型,对材料的弹性性能进行了预测。这个力学模型考虑了倾斜内锁型三维机织陶瓷基复合材料经向纤维束的弯曲和纬向纤维束的平直,纤维束的横截面形状尺寸和相邻纤维束之间的孔洞以及材料制造过程中碳纤维性能下降对弹性性能的影响。基于层合板理论,提出两种单胞应变状态假设分别对材料的九个弹性常数进行了推导计算,结果表明两种方法理论的预测值非常接近。计算结果与实验值比较吻合,表明所提出的细观力学模型是合理的,可以为纺织陶瓷基复合材料的优化设计提供有价值的参考。     

Effective elastic moduli of inhomogeneous solids by embedded cell model

An embedded cell model is presented to obtain the effective elastic moduli for three-dimensional two-phase composites which is an exact analytic formula without any simplified approximation and can be expressed in an explicit form. For the different cells such as spherical inclusions and cracks surrounded by sphere and oblate ellipsoidal matrix, the effective elastic moduli are evaluated and the results are compared with those from various micromechanics models. These results show that the present model is direct, simple and efficient to deal with three-dimensional two-phase composites. The project supported by the National Natural Science Foundation of China (No. 19704100) and the National Natural Science Foundation of Chinese Academy of Sciences (No. KJ951-1-201)     

拉压不同弹性模量薄板上圆孔的应力分析

采用弹性理论研究了拉压不同弹性模量薄板上圆孔的孔边应力集中问题．采用广义虎克定律推导出了拉压不同弹性模量薄板上圆孔边的应力平衡方程,并联合利用应力函数及边界条件得到了拉压不同弹性模量薄板上圆孔边的应力表达式．算例分析表明,当薄板材料的拉压弹性模量相差较大时,采用经典弹性理论研究薄板上圆孔的孔边应力是不合适的,当经典弹性理论与拉压不同弹性模量弹性理论的计算结果间的差别超过工程允许误差5%时,应该采用拉压不同弹性模量弹性理论进行计算．     

材料高温力学性能理论表征方法研究进展

随着科学技术的迅猛发展,材料在高温领域的应用越来越广泛.然而高温下材料的力学性能和常温相比有很大差异,材料的高温力学性能研究和表征已成为当前的研究热点.论文对材料在高温下力学行为理论表征方法研究的最新进展进行了总结和回顾.着重介绍了近年来高温陶瓷材料的断裂强度、金属材料的屈服强度、弹性模量与本构关系的温度相关性理论表征方法的研究进展.最后,总结已有研究工作的特点和不足之处,对材料高温力学性能理论表征方法的后续研究进行了展望,就进一步研究提供建议.     

任意平面区域的高质量有限元网格自动剖分

实现了任意平面区域的高质量三角形有限元网格自动剖分。初始化时利用广度优先搜索查找孔及凹槽中需删除的三角形 ,不需定义有向边界 ,可十分方便地定出实际剖分区域 ;给出了一种方便、快捷的点定位法 ,可大大提高程序运行速度 ;利用Delaunay网格优化算法实现了对三角形形状的控制 ,可使三角形最小角达到 35° ;分割坏三角形时 ,按最小角由小到大的顺序处理 ,使三角形网格在满足质量要求的同时网格数量较少     

Effective elastic moduli of two dimensional solids with distributed cohesive microcracks

Effective elastic properties of a defected solid with distributed cohesive micro-cracks are estimated based on homogenization of the Dugdale–Bilby–Cottrell–Swinden (Dugdale–BCS) type micro-cracks in a two dimensional elastic representative volume element (RVE).Since the cohesive micro-crack model mimics various realistic bond forces at micro-scale, a statistical average of cohesive defects can effectively represent the overall properties of the material due to bond breaking or crack surface separation in small scale. The newly proposed model is distinctive in the fact that the resulting effective moduli are found to be pressure sensitive.     

随机剪切柱在地震激励下的演变随机响应

随机剪切柱是指固连于地面的剪切柱的某些物理参数是随机变量 ,该模型在Niigata地震激励下的响应属于演变随机响应。本文将新近发展起来的演变随机响应问题的统一解法 ,推广到用于求解随机结构振动响应问题。首先用这一方法求出每个样本结构的随机响应 ,然后用MonteCarlo法来进一步求随机结构的集合随机响应特性。这样 ,与单纯用Monte Carlo法进行数字模拟相比 ,可使计算工作量大为减少。本文用随机剪切柱的演变随机响应问题加以说明     

Random Fiber Networks and Special Elastic Orthotropy of Paper

We consider a particular in-plane elastic orthotropy observed experimentally for various types of paper, namely: S ₁₁₁₁+S ₂₂₂₂−2S ₁₁₂₂=S ₁₂₁₂, where S _ijkm are components of the in-plane compliance tensor. This is a statement of the invariance of in-plane shear compliance S ₁₂₁₂, which has been observed in some studies but questioned in others. We present a possible explanation of this “special orthotropy” of paper, using an analysis in which paper is modeled as a quasi-planar random microstructure of interacting fiber-beams – a model especially well suited for low basis weight papers. First, it is shown analytically that without disorder a periodic fiber network fails the special orthotropy. Next, using a computational mechanics model, we demonstrate that two-scale geometric disorder in a fiber network is necessary to explain this orthotropy. Indeed, disordered networks with weak flocculation best satisfy this relationship. It is shown that no special angular distribution function of fibers is required, and that the uniform strain assumption should not be used. Finally, it follows from an analogy to the thermal conductivity problem that the kinematic boundary conditions, rather than the traction ones, lead quite rapidly to relatively scale-independent effective constitutive responses. This revised version was published online in July 2006 with corrections to the Cover Date.