Bridging the Length Scales: Micromechanics of Granular Media

Aristotle's statement that the whole is more than the sum of its parts aptly describes the essence of a granular material's rich and complex behaviour, which ultimately arises from internal mechanisms developed on many length scales. Recently, non-invasive experimental studies have given remarkable insight into the evolution of these mechanisms, thereby providing benchmarks and a unique opportunity for the theoretical modelling of these systems. This paper focuses on the challenges of capturing these multiscale mechanisms within the framework of continuum theory. In particular, a new approach toward developing a non-local micropolar constitutive model of granular media using micromechanics and internal variable theory is discussed. To demonstrate the predictive potential of these models, we present their application in the analysis of two fundamental problems to the mechanics of granular media: (i) formation and evolution of shear bands (the precursors of material failure), (ii) the classical Flamant problem. Finally, we briefly discuss the computational challenges in bridging the gap between micromechanical studies of granular media and the applications of continuum theory on the macro-scale via a finite element analysis of the flat punch problem. In practice, this problem is used to assess the load bearing capacity of a material and is fundamental to civil and structural engineering.     

An experimental study of a turbulent shear layer at a clean and contaminated free-surface

An experimental study was performed to measure the flow properties of a vertically-orientated shear layer in the vicinity of a free-surface. The effect of surface contamination on the near surface flow field was also determined. Digital Particle Image Velocimetry was used to measure instantaneous and averaged velocity, vorticity, and Reynolds stresses. Results show that the presence of surfactants can cause directional shifts of the shear layer, as well as an overall damping of the turbulence in the vicinity of the free-surface, except in the vicinity of a Reynolds ridge where an increase in Reynolds stress was observed.     

Noise correlations in shear flows

We consider the effects of a shear on velocity fluctuations in a flow. The shear gives rise to a transient amplification that not only influences the amplitude of perturbations but also their time correlations. We show that, in the presence of white noise, time correlations of transversal velocity components are exponential and that correlations of the longitudinal components are exponential with an algebraic prefactor. Cross correlations between transversal and downstream components are strongly asymmetric and provide a clear indication of non-normal amplification. We suggest experimental tests of our predictions. Received 26 February 2002 / Received in final form 11 March 2003 Published online 20 June 2003 RID="a" ID="a"e-mail: bruno.eckhardt@physik.uni-marburg.de RID="b" ID="b"Also at: Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore, India     

冰洲石-玻璃组合平行分束偏光镜的设计研究

为了既节省稀有昂贵的冰洲石晶体材料，又实现偏振光的大剪切差输出，采用冰洲石晶体与光学玻璃组合的方法，设计了一种新型平行分束偏光镜。该棱镜的前后半块分别为ZBaF₃玻璃和冰洲石晶体，由大折射率液态胶合剂溴代萘胶合而成。实验测试表明：该棱镜透射的2束平行光的消光比，o光可达10^－5；尽管受到光学玻璃的影响，e光的消光比仍优于10^－3；透射比均与纯冰洲石晶体材料的棱镜基本相当。理论分析表明：该棱镜自身结构带来的性能影响在一定情况下完全可以忽略，因此具有较好的应用前景。     

测定圆柱体杨氏模量的原理分析

分析了测量圆柱体弯曲形变杨氏模量的实验原理,得出了理论公式,将测量拉压形变、弯曲形变的杨氏模量以及扭转形变的剪切模量3个实验中样品形状统一成圆柱体.     

Reliability analysis of stochastic structural system considering static strength, stiffness and fatigue

Multi-failures are possible to appear in the process of using the structural system, such as dead load failure, fatigue failure and stiffness failure. The expression of residual resistance is given based on the impact of random crack propagation in- duced by the fatigue load on the critical limit stress and section modulus in this paper. The failure modes of every element of the structural system are analyzed under dead and fatigue loads, and the influence of the correlation of failure modes on reliability of the element is considered. Failure mechanism and the correlation of failure modes under dead and fatigue loads are discussed, and the method of reli- ability analysis considering static strength, fatigue and stiffness is given. A nu- merical example is analyzed, which indicates that the failure probability is different for different use life and the influence of dead and fatigue loads on reliability of the structural system is different as well. This method of reliability analysis, in the pa- per, is better than the method only considering a single factor (or static strength, or fatigue, or stiffness, etc.) in the case of practical engineering.     

Speckle interferometry methods for displacement and strain measurements using photorefractive crystal

Photorefractive crystals offer several attractive features such as high resolution and in situ processing. As the images are erasable, these crystals are suitable for read–write applications and hence find potential use in speckle photography, image processing and holography. The barium titanate (BaTiO₃) crystal as recording medium has been extensively used as a novelty filter for real-time in-plane displacement measurements employing two-beam coupling configuration. This paper presents new optical configurations in speckle shear photography to measure in-plan displacement and the strain in real time using BaTiO₃ crystal as recording medium. Speckle photography studies are made using a simple two-beam coupling configuration. In speckle shear photography, a diffused object illuminated with two parallel narrow laser beams is imaged inside the crystal, and a pump beam is added at this plane. The speckle patterns due to each beam and the pump beam produce index gratings. When the object is deformed, the speckle patterns shift consequently. We now have four speckle fields: two generated from the interaction of pump beam with the index gratings and two pertaining to deformed states directly transmitted through the crystal. Thus, the fields from respective points on the object interfere after passage through the crystal and produce the Young's fringe patterns. Due to strain, the fringes in each pattern are of different width and orientation, resulting in the generation of a Moiré pattern. The strain is obtained from the width and orientation of the fringes in the Moiré pattern. The experiments are conducted on a specimen with a notch, which is subjected to tensile loading. The in-plane displacement is measured separately in another experiment. The above studies are carried out at Nd–Yag laser.     

Selective synthesis of poly(p‐oxybenzoyl) by fractional polycondensation: Enhancement of selectivity by shearing

The influence of shear flow, especially the timing for the application of shearing, was examined to enhance the selectivity for the preparation of poly(p‐oxybenzoyl) (Pp‐OB) by using hydrodynamically induced phase separation during polymerization of 4‐(4‐acetoxybenzoyloxy)benzoic acid (p‐ABAD) and m‐acetoxybenzoic acid (m‐ABA). The polymers containing few m‐oxybenzoyl (m‐OB) moieties were obtained as precipitates even at high content of m‐OB moiety in feed (χ_f) under shear flow. The content of m‐OB moiety in the precipitates (χ_p) prepared under shearing throughout the polymerization at the shear rate (γ) of 489 s^?1 was 6.3 mol % even at χ_f of 60 mol %. Especially, the Pp‐OB was obtained as the precipitates at χ_f of less than 50 mol %. The timing of the application of the shearing influenced the selectivity significantly, and the shearing just after the precipitation of the oligomers started was quite efficient to enhance the selectivity more. The χ_p of the precipitates prepared with shearing at γ of 489 s^?1 just after the precipitation was only 3.9 mol % even at χ_f of 60 mol %. The shear flow reduced the difference in the reactivity between p‐ABAD and m‐ABA, resulting in the decrease in the selectivity with regard to the formation of p‐oxybenzoyl homo‐oligomer. However, the shear flow enhanced the difference in the miscibility between homo‐oligomers and co‐oligomers. This change in the miscibility by shear flow brought about the more rapid precipitation of homo‐oligomers, leading to the enhancement of the selectivity. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Fracture of model polyurethane elastomeric networks

Fracture properties of model elastomeric networks of polyurethane have been investigated with a double‐edge notch geometry. The networks were synthesized from monodisperse end‐functionalized polypropylene glycol precursors and a trifunctional isocyanate. All reagents were carefully purified and nearly defect‐free ideal networks were prepared at a stoichiometry very close to the theoretical one. Three networks were prepared: an unentangled network of short chains (M_n = 4 kg mol^?1), an entangled network of longer chains (M_n = 8 kg mol^?1) and a bimodal network with 8 kg mol^?1 and 1 kg mol^?1 chains. The presence of entanglements was found to increase significantly the toughness of the rubber, in particular at room temperature, relative to the bimodal networks and to the short chains network. Fracture experiments were carried out at different strain rates and temperatures and showed for all three networks a marked decrease in fracture toughness with increasing temperature and decreasing strain rate which mirrored reasonably well the rate and temperature dependence of tan δ, the dissipative factor. However the proportionality factor between tan δ, and G_IC was very material dependent and the shift factors obtained for the master curves of the viscoelastic properties could not be used to build fracture energy master curves. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2010     

Aspects of fatigue failure mechanisms in polymer fuel cell membranes

The swelling‐driven fatigue behavior of polymer fuel cell membranes during relative humidity (RH) cycling is investigated. In particular, swelling‐induced membrane stresses are obtained from a numerical model simulating fuel cell RH cycle tests, and compared to the lifetimes obtained experimentally from tests conducted in the absence of electrochemical effects. A strong correlation between the lifetimes of the membranes in the actual tests and model results is obtained. In general, higher RH (or swelling) amplitude results in larger stress amplitudes and shorter lifetime, that is, fewer cycles to failure. Tensile stresses are needed for forming local cavities in the membrane, which may eventually lead to craze formation. Cavitation is less likely to occur in compressed membrane at high humidities. The stress–lifetime plots for polymer fuel cell membranes exhibit similar features to those observed for other polymers. The crazing criterion for polymers suggests that craze initiation during RH cycling is more likely to occur in the low compression regions, such as under the channels, which is in agreement with experimental observations. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 49: 1506–1517, 2011