A statistical theory of fragmentation processes

The goal of the work reviewed here is a theory of material behavior accounting for the average deformation that results from the opening, shear, growth and coalescence of an ensemble of microcracks. A concomitant is the calculation of permeability from crack structure. The first part of this paper summarizes previous developments. In particular, the initial work on this problem made use of a linear Liouville equation to characterize the change in crack distribution resulting from crack growth and coalescence. Straightforward analytic solutions to this equation were possible because the mean free path of cracks was assumed constant. Though this assumption is useful for the early stages of crack growth, increasing crack size reduces the mean free path in the later stages of fragmentation. This problem is addressed in the second part of this paper. The governing (nonlinear) Liouville equation is derived therein, and it is shown that it can be reduced to an ordinary differential equation of third order involving only a single free parameter, denoted by β. This equation has now been solved numerically to determine the limiting value of the mean free parth as a function of β, and the results are presented in graphical form. In the third part of this paper prospects for further developments are briefly discussed.     

Discussion of a statistical theory of fragmentation processes

Microcracking comes into play in many cases of brittle response of solids to applied load. Since the cracks are readily observable and their behavior is a subject of both common experience and extensive scientific investigation, it is natural that one would try to take explicit account of them in modeling deformation behavior. Several interesting problems arise in devising mathematical representations of crack distributions that are simple enough to use in continuum models and still apply to the entire range of observed behavior. In this note, I compare two conventional mathematical representations of cracks with three observed configurations.     

农业信息工程的理论、方法和应用

21世纪人类将跨入信息农业的时代。信息农业将成为合理开发利用农业资源、提高农作物产量、降低成本、减少环境污染、提高农产品国际市场竞争力的前沿研究领域,并获得实施。专家预见,生物技术和信息技术,将是我国21世纪农业技术革命的两大技术支柱,是实现农业现代化的保证。章对农业信息科学的产生、理论基础、主要研究内容,农业信息的主要技术内容,农业信息工程的理论、技术体系,现阶段农业信息工程主要实施的领域等做了阐述;指出面向21世纪的中国农业信息科学、技术和工程应该瞄准国际前沿,实现跨越式的发展,通过对农业信息工程的开发,加快我国农业现代化的进程。     

Exact theory of fibre fragmentation in a single-filament composite

An exact theory is developed to describe the evolution of fibre fragmentation in a single-filament composite test as a function of the underlying fibre statistical strength and fibre/matrix interfacial shear stress, τ. The fragment distribution is a complicated function of fibre strength and τ because the stress around breaks which do occur recovers to the applied value, σ, over a length δ(σ) determined by τ. Therefore, no other breaks can occur within δ (σ) of an existing break. To account for this effect, the fibre fragment distribution is decomposed into two parts; fragments formed by breaks separated by more than δ (σ) at stress σ, and fragments smaller than δ (σ) which were formed at some prior stress σ′ < σ when a smaller δ(σ′) < δ(σ) prevailed. The distribution of fragments larger than δ (σ) is identical to that of a fibre with a unique non-statistical strength σ and is known exactly. The distribution of fragments smaller than δ(σ) can then be determined from the distribution of the longer fragments. Predictions of the theory are compared to simulations of fibre fragmentation for several common models of stress recovery around fibre breaks with excellent agreement obtained. The present theory can be utilized to thus derive both thein situ fibre strength at short gauge lengths ? δ and the τ from experimentally obtained fragment distributions, and an unambiguous inversion procedure is briefly discussed. The application of the theory to other multiple-cracking phenomena in composites is also discussed.     

Mechanical experiments on the superplastic material ALNOVI-1, including leak information

In subatomic particle physics, unstable particles can be detected with a so-called vertex detector, placed inside a particle accelerator. A detecting unit close to the accelerator bunch of charged particles must be separated from the accelerator vacuum. A thin sheet with a complex 3D shape prevents the detector vacuum from polluting the accelerator vacuum. Therefore, this sheet has to be completely leak tight. However, this can conflict with restrictions concerning maximum sheet thickness of the product. To produce such a complex thin sheet, superplastic forming can be very attractive in cases where a small number of products is needed. In order to predict gas permeability of these formed sheets, many mechanical experiments are necessary, where the gas leak has to be measured. To obtain insight in the mechanical behaviour of the used material, ALNOVI-1, tensile experiments were performed to describe the uniaxial stress-strain behaviour. From these experiments, a high strain rate sensitivity was measured. The flow stress of this material under superplastic conditions was low and the material behaved in an isotropic manner upon large plastic strains. The results of these experiments were used to predict the forming pressure as a function of time in a free bulge experiment, such that a predefined target strain rate will not be exceeded in the material. An extra parameter within these bulging experiments is the application of a hydrostatic pressure during the forming process. Such a pressure postpones the nucleation and growth of internal cavities, which means that higher plastic strains can be reached before failure. Results from these experiments showed that at higher hydrostatic pressures, higher bulges were made. All these bulges were leak tested, showing also that higher hydrostatic pressures lead to a lower void volume fraction at higher hydrostatic pressures, since these bulges were more leak tight at the same bulge height than bulges made without the application of this pressure. This article describes the setup and results of the uniaxial (tensile) and biaxial (bulging) experiments on the superplastic aluminium ALNOVI-1.     

Voronoi cell finite element model based on micropolar theory of thermoelasticity for heterogeneous materials

In this paper, a new ‘Voronoi cell finite element model’ is developed for solving steady-state heat conduction and micropolar thermoelastic stress analysis problems in arbitrary heterogeneous materials. The method is based on the natural discretization of a multiple phase domain into basic structural elements by Dirichlet Tessellation. Tessellation process results in a network of polygons called Voronoi polygons. In this paper, formulations are developed for treating these polygons as elements in a finite element mesh. Furthermore, a composite Voronoi cell finite element model is developed to account for the presence of a second phase inclusion within a polygonal element. Various numerical examples are executed for validating the effectiveness of this model in the analysis of the temperature and stress fields for micropolar elastic materials. Effective material properties are derived for microstructures containing different distributions of second phase.     

On the symmetry,monotonicity and concavity of the creep function in Day's information theory

Day's result on the monotonicity, concavity and symmetry of the creep function in his information theory approach is proved without the assumption on the quadratic form of the functional of loss of information. It is also shown that if in Coleman's theory of materials with memory the strain-history bilinear part of the free energy potential is assumed to be quadratic, the monotonicity, convexity and symmetry of the stress relaxation function may be proved.     

基于弹塑性剪滞理论的单丝复合材料段裂过程的蒙特卡罗模拟

单丝复合材料段裂试验(SFCFT)中,随着外载荷的增加,纤维出现了随机脆断的现象,并在一定的载荷下纤维的段裂数达到饱和状态(即纤维段裂数目不再增加),该试验常用于表征纤维与基体间界面性能。针对该试验,本文中充分考虑了组分材料的真实性能(即基体材料的弹塑性性能),利用弹塑性剪滞理论进行纤维与基体间的应力传递分析,初步获得较真实的纤维轴向应力及界面剪应力分布形式;在此基础上,考虑纤维强度分布的非均匀性,利用蒙特卡罗(Monte Carlo)方法对试验中纤维的随机段裂过程进行了模拟预报,获得载荷与纤维的段裂数的关系。模拟预报与试验结果比较吻合,表明该应力分析及模拟方法的有效性。     

The information approach to the theory of irreversible quasi-equilibrium processes

The principles of the thermodynamics of irreversible quasi-equilibrium processes are derived by means of the formalism of information theory. The quasi-equilibrium analogies of familiar thermostatic concepts are formulated.     

Mie theory, airy theory, and the natural rainbow

Compared with Mie scattering theory, Airy rainbow theory clearly miscalculates some monochromatic details of scattering by small water drops. Yet when monodisperse Airy theory is measured by perceptual (rather than purely physical) standards such as chromaticity and luminance contrast, it differs very little from Mie theory. Considering only the angular positions of luminance extrema, Airy theory's errors are largest for small droplets such as those that dominate cloudbows and fogbows. However, integrating over a realistic drop-size distribution for these bows eliminates most perceptible color and luminance differences between the two theories.     

The information wastage ratio: Towards a theory of rates of information generation and utilization

This paper presents a theoretical framework of the relationships between certain phenomena attendant to an information society, i.e. information explosion, societal information overload, etc. It also attempts to explain and predict the possible effects of these phenomena on information generation, utilization and wastage. A theory of rates of information generation and utilization as well as a wastage ratio is proposed. The initial propositions, axioms and postulates which form the bases of this theory are described in their logical sequence. Hypotheses and conceptual models are also included.