Network topology and the theory of rubber elasticity

The earliest investigations on rubber elasticity, commencing in the 19th century, were necessarily limited to phenomenological interpretations. The realisation that polymers consist of very long molecular chains. commencing c. 1930, gave impetus to the molecular theory of rubber elasticity (1932-). according to which the high deformability of an elastomer, and the elastic force generated by deformation, stem from the configurations accessible to long molecular chains. Theories of rubber elasticity put forward from 1934-1946 relied on the assumption that the junctions of the rubber network undergo displacements that are affine in macroscopic strain. The theory of James and Guth (1947) dispensed with this premise, and demonstrated instead that the mean positions of the junctions of a ‘phantom’ network consisting of Gaussian chains devoid of material properties are affine in the strain. The vital significance of the distinction between the actual distribution of chain vectors in a network and their distribution if the junctions would be fixed at their mean positions went unnoticed for nearly 30 years. Experimental investigations, commencing with the incisive work of Gee in 1946. revealed large departures from the relationship of stress to strain predicted by the theories cited. This discrepancy prompted extensive studies, theoretical and experimental, during succeeding years. Inquiry into the fundamentals of polymer networks, formed for example by interlinking very long polymer molecules, exposed the need to take account of network imperfections, typically consisting of chains attached at only one end to a network junction. Various means were advocated to make corrections for these imperfections. The cycle rank ζ of the network has been shown (1976) to be the fundamental measure of its connectivity, regardless of the junction functionality and pattern of imperfections. Often overlooked is the copious interpenetration of the chains comprising typical elastomeric networks. Theories that attempt to represent such networks on a lattice are incompatible with this universal feature. Moreover, the dense interpenetration of chains may limit the ability of junctions in real networks to accommodate the fluctuations envisaged in the theory of phantom networks. It was suggested in 1975 that departures from the form predicted for the elastic equation of state are due to constraints on the fluctuations of junctions whose effect diminishes with deformation and with dilation. Formulation of a self-consistent theory based on this suggestion required recognition of the non-affine connection between the chain vector distribution function and the macroscopic strain in a real network, which may partake of characteristics of a phantom network in some degree. Implementation of the idea was achieved through postulation of domains of constraint affecting the equilibrium distribution of fluctuations of network junctions from their mean positions. This led in due course to a theory that accounts for the relationship of stress to strain virtually throughout the ranges of strain accessible to measurement. The theory establishes connections between structure and elastic properties. This is achieved with utmost frugality in arbitrary parameters.     

Significance of the elastic peak stress evaluated by FE analyses at the point of singularity of sharp V-notched components

The paper presents an expression useful to estimate the notch stress intensity factor (NSIF) from finite element analyses carried out by using a mesh pattern with a constant element size. The evaluation of the NSIF from a numerical analysis of the local stress field usually requires very refined meshes and then large computational effort. The usefulness of the presented expression is that (i) only the elastic peak stress numerically evaluated at the V‐notch tip is needed and no longer the whole stress–distance set of data; (ii) the adopted meshes are rather coarse if compared to those necessary for the evaluation of the whole local stress field. The proposed expression needs the evaluation of a virtual V‐notch tip radius, i.e. the radius which would produce the same elastic peak stress than that calculated by FEM at the sharp V‐notch tip by means of a given mesh pattern. Once such a radius has been theoretically determined for a given geometry, the expression can be applied in a wide range of notch depths and opening angles.     

F-X域粘弹性波动方程保幅偏移

提出了一种利用粘弹性声波波动方程进行偏移的新方法。其基本思路是,修改成像条件,使修改后的成像方程中考虑振幅补偿,然后利用粘弹性、单程波动方程在F-X域对震源和接收点波场进行延拓,进而完成散射、透射等补偿。理论数据处理和实际地震资料处理表明,该方法理论基础可靠,处理效果明显,能较好地解决实际地质问题。     

圆杆弹性和弹—塑性扭转公式的探讨

对圆杆在线弹性阶段，弹－塑性阶段和全塑性阶段的扭转剪应力的计算公式作了分析，并推导了在材料的应力－应变关系（τ－γ关系）不服从虎克定律时，扭转真实剪应力的计算公式。文中对扭转强度计算公式的来源，物理含义及其都作了详细的说明。这对执行和理解国家ＧＢ１０１２８－８８《金属室温扭转试验方法》是有益的，而且对高校中材料力学的教学具有一定的参考价值。     

Testing viability of cross subsidy using time-variant price elasticities of industrial demand for electricity: Indian experience

Indian electric tariffs are characterized by very high rates for industrial and commercial classes to permit subsidized electric consumption by residential and agricultural customers. We investigate the viability of this policy using monthly data for 1997–2003 on electric consumption by a few large industrial customers under the aegis of a small distribution company in the state of Uttar Pradesh. For a given price/cost ratio, it can be shown that if the cross-subsidizing class’ electricity demand is sufficiently elastic, increasing the class’ rates fail to recover incremental cross-subsidy necessary to support additional revenues for subsidized classes. This suboptimality is tested by individually estimating time-variant price-elasticities of demand for these industrial customers using Box-Cox and linear regressions. We find that at least for some of these customers, cross-subsidy was suboptimal prior to as late as October 2001, when rates were changed following reforms.     

MBS树脂改性PVC的研究

研究了不同类型及用量的MBS树脂对PVC抗冲击性、光学性能、拉伸性能及加工塑化性能的改性效果以及加工条件等因素的影响。结果表明 :在低用量条件下 ,随MBS树脂含量增加 ,MBS/PVC抗冲击性能有所提高 ,光学性能略有下降。此外 ,MBS/PVC制品的拉伸性能和加工性能受MBS树脂类型及用量影响不大。     

Transient Green’s Tensor for a Layered Solid Half-Space With Different Interface Conditions

Pulsed ultrasonic techniques can be and have been used to examine the interface conditions of a bonded structure. To provide a theoretical basis for such testing techniques we model the structure as a layer on top of a half-space, both of different elastic properties, with various interface bonding conditions. The exact dynamic Green’s tensor for such a structure is explicitly derived from the three-dimensional equations of motion. The final solution is a series. Each term of the series corresponds to a successive arrival of a “generalized ray” and each is a definite line integral along a fixed path which can be easily computed numerically. Willis’ method is used in the derivation. A new scheme of automatic generation of the arrivals and ray paths using combinatorial analysis, along with the summation of the corresponding products of reflection coefficients is presented. A FORTRAN code is developed for computation of the Green’s tensor when both the source and the detector are located on the top surface. The Green’s tensor is then used to simulate displacements due to pulsed ultrasonic point sources of known time waveform. Results show that the interface bonding conditions have a great influence on the transient displacements. For example, when the interface bonding conditions vary, some of the first few head waves and regular reflected rays change polarities and amplitudes. This phenomenon can be used to infer the quality of the interface bond of materials in ultrasonic nondestructive evaluation. In addition the results are useful in the study of acoustic microscopy probes, coatings, and geo-exploration.     

Material constant sensitivity boundary integral equation for anisotropic solids

In this paper, the material constant sensitivity boundary integral equation is presented, and its numerical solution proposed, based on boundary element techniques. The formulation deals with plane problems with general rectilinear anisotropy. Expressions for the computation of sensitivities for displacements, tractions, strains and stresses are derived, both for boundary and interior points. The sensitivities can be computed with respect to the bulk material properties or to the properties of part of the domain (inclusions, coatings, etc.). To assess the accuracy of the proposed approach, the computed results are compared to analytical ones derived from exact solutions obtained by complex potential theory, when possible, or finite difference derivatives otherwise. Copyright © 2005 John Wiley & Sons, Ltd.