Representation surfaces of Young''s modulus and Poisson''s ratio for BCC transition metals

 The general expressions for the compliance , Young's modulus E(h k l) and Poisson's ratio υ(h k l) along an arbitrary direction [h k l] are given for cubic crystals. The representation surfaces, for which the length of the radius vector in the [h k l] direction equals to E(h k l) or υ(h k l), are constructed for seven BCC transition metals Cr, Fe, Mo, Nb, Ta, V and W. Neglecting W, which is isotropic, both representation surfaces of Young's modulus and Poisson's ratio are spherical surfaces. The remaining BCC transition metals may be grouped into two classes. In the first group (Cr, Mo, Nb and V) with negative values of s_A, Young's modulus surface has eight depressed corners and six rounded protuberances at the centers of the faces. In the second group (Fe and Ta) with positive values of s_A, on the contrary, Young's modulus surface has eight rounded protuberance corners and six depressions at the centers of the faces. The contrary conclusions are obtained for Poisson's ratio.     

Point load determination of static elastic moduli using laser speckle interferometry

Electronic speckle interferometry (ESPI) is used to determine the Young's modulus E and Poisson ratio ν of an isotropic material. Micron scale deformations of the surface of the block of polymethyl-methacrylate (PMMA) are induced by normal application of a known near-point force. These deformations are recorded in speckle interferometric fringe patterns. An iterative minimum error inversion technique is developed to obtain the elastic properties from the positions of fringe peaks and troughs observed in the fringe patterns. Sensitivity tests of the method on calculated fringe patterns using measured experimental uncertainties suggest the technique will provide measures of the elastic moduli to better than 5%. In an experimental test on a bloc of PMMA (acrylic) the technique gave values of E and ν that differed from corresponding measures obtained using more conventional strain-gauge methods by less than 4%.     

Cyclic reduction and FACR methods for piecewise hermite bicubic orthogonal spline collocation

Cyclic reduction and Fourier analysis-cyclic reduction (FACR) methods are presented for the solution of the linear systems which arise when orthogonal spline collocation with piecewise Hermite bicubics is applied to boundary value problems for certain separable partial differential equations on a rectangle. On anN×N uniform partition, the cyclic reduction and Fourier analysis-cyclic reduction methods requireO(N ²log₂ N) andO(N ²log₂log₂ N) arithmetic operations, respectively.     

Analysis of the geometrical dependence of auxetic behavior in reentrant structures by finite elements

Materials with a negative Poisson's ratio(PR)are called auxetics;they are characterized by expansion/contraction when tensioned/compressed.Given this counterintuitive behavior,they present very particular characteristics and mechanical behavior.Geometrical models have been developed to justify and artificiall reproduce such materials' auxetic behavior.The focus of this study is the exploration of a reentrant model by analyzing the variation in the PR of reentrant structures as a function of geometrical and base material parameters.It is shown that,even in the presence of protruding ribs,there may not be auxetic behavior,and this depends on the geometry of each reentrant structure.Values determined for these parameters can be helpful as approximate reference data in the design and fabrication of auxetic lattices using reentrant geometries.     

势问题的重构核粒子边界无单元法

将重构核粒子法和势问题的边界积分方程方法结合,提出了势问题的重构核粒子边界无单元法. 推导了势问题的重构核粒子边界无单元法的公式,研究其数值积分方案,建立了重构核粒子边界无单元法的离散化边界积分方程,并推导了重构核粒子边界无单元法的内点位势的积分公式. 重构核粒子法形成的形函数具有重构核函数的光滑性,且能再现多项式在插值点的精确值,所以该方法具有更高的精度. 最后给出了数值算例,验证了所提方法的有效性和正确性. }      

分析热力学的应用：平衡态热力学中温度的相对论变换

用分析热力学的观点和方法研究了温度的相对论变换公式，得到了与Planck，Einstein和de Broglie完全相同的结果：T=1-β²T₀；分析热力学的特色和 优点是，在推演过程 中根本不需要δQ=1-βδQ₀这一可能引起争议的和p=p₀这 一显而易见的相对论变换公式，它们是作为附带结果出现的. 关键词： 分析热力学 相对论热力学 平衡态热力学 热力学基本Poisson括号     

Implications and Constraints of Time-Independent Poisson Ratios in Linear Isotropic and Anisotropic Viscoelasticity

It is proven that time-independent viscoelastic Poisson ratios (PR) can only exist under separation of variable solutions which severely limits the class of applicable problems to quasi-static ones with incompressible homogeneous materials and non-moving boundaries under separable stress or displacement boundary conditions without any thermal expansions. Therefore, composites which are inherently anisotropic and sandwich structures which are nonhomogeneous and anisotropic are generally precluded from having time-independent PRs. Equal time variations for material properties in all directions are shown to be another simultaneous requirement instead of the incompressibility condition for achieving time-independent PRs. However, such restricted models lead to physically unrealistic bulk moduli responses when compared to experimentally determined relaxation moduli and are not generally achievable in current real materials. Consequently, viscoelastic materials are best characterized in terms of relaxation or creep functions, moduli or compliances rather than combinations of the latter with Poisson's ratios. Additionally, the assumption of constant PRs in problems involving thermal and chemical expansions, such as curing and manufacture of viscoelastic composites, is shown to be unjustified and insupportable. The distinct viscoelastic PR definitions, as found in the literature, are examined and classified into five categories. It is further shown that each is inherently unrelated to the others and all are always time-dependent, unless the above extremely limiting conditions are imposed. An extensive literature review indicates that experimental results overwhelmingly confirm the time dependent nature of viscoelastic PRs as no constant experimentally observed PRs were reported.     

Hoeffding's inequality for Markov processes via solution of Poisson's equation

We investigate Hoeffding's inequality for both discrete-time Markov chains and continuous-time Markov processes on a general state space. Our results relax the usual aperiodicity restriction in the literature, and the explicit upper bounds in the inequalities are obtained via the solution of Poisson's equation. The results are further illustrated with applications to queueing theory and reective diffusion processes.     

Direct and inverse measurement of thin films magnetostriction

Two techniques of measurements of thin film magnetostriction are compared: direct, when changes of the substrate curvature caused by the film magnetization are controlled, and inverse (“indirect”), when the modification of the magnetic anisotropy induced by the substrate deformation (usually bending) is measured. We demonstrate how both the elastic strength of the substrate and the effective magneto-mechanical coupling between the substrate deformation and magnetic anisotropy of the film depend on different conditions of bending. Equations to be used for magnetostriction value determination in typical cases are given and critical parameters for the corresponding approximations are identified.     

The limiting case of the Marcinkiewicz integral: growth for convex sets

The Marcinkiewicz integral

plays a well-known and prominent role in harmonic analysis. In this paper, we estimate the growth of it in the limiting case . Throughout, we assume that is convex; it is interesting that this condition cannot be dropped.