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.     

Longitudinal elastic waves in columns due to earthquake motion

An analysis is presented of longitudinal waves in a thin elastic column. Velocity is specified at one end, and the boundary condition at the other end is expressed in terms of a range of effective impedances of an attached structure. Propagation, reflection and interference of the waves are followed by the method of characteristics. Integration of differential equations along characteristics yields the wave-induced stress, which is then applied to problems of earthquake excitation. Numerical examples are given for recorded updown ground motion of the Kobe Earthquake.     

串联法氧化铝生产中的合流脱硅

合流脱硅是简化联合法生产流程、降低能耗的有效措施。因此。国内外业界做了大量卓有成效的工作。串联法的工艺特点，更宜于采用合流脱硅。试验结果表明，串联法采用常压合流脱硅流程可以达到所需要的硅量指数。文中还对合流脱硅的硅量指数、合流点、合流脱硅温度、赤泥种子和添加石灰乳等问题进行了讨论。     

Models to predict the deformation modulus and the coefficient of subgrade reaction for earth filling structures

Determination of deformation modulus and coefficient of subgrade reaction of soils have major importance, whether the projects are in design, and construction or compaction assessment stage of earth filling structures. Plate load test is one of the frequently used method to directly determine the parameters but the method is both costly and time consuming. For this reason, this paper is concerned with the applications of artificial neural networks (ANN) and simple-multiple regression analysis to predict deformation modulus and coefficient of subgrade reaction of compacted soils from compaction parameters (such as maximum dry density (MDD) and optimum moisture content (OMC), field dry density (FDD), and field moisture content (FMC)). Regression analysis and artificial neural network estimation indicated that there are acceptable correlations between deformation modulus and coefficient of subgrade reaction and these parameters. Artificial neural networks model exhibits higher performance than traditional statistical model for predicting deformation modulus and coefficient of subgrade reaction.     

Dynamic Response Calculation of Spatial Elastic Multibody Systems with High-Frequency Excitation

The objective of this paper is to establish a computationalscheme for dynamic response calculations of a three-dimensionalmultibody mechanical system with impulsive forces, which give rise tohigh-frequency excitations. The finite-element method is employed torepresent the local deformations of three-dimensional beam-like elasticcomponents by either a finite set of nodal coordinates or a truncatedset of modal coordinates. A reduced-order model is obtained by invokinga modal transformation. Both planar and complex modal reduction schemesare established. The developed formulation is implemented into amultibody simulation program that assembles the equations of motion andproceeds with its solution. The computational scheme permits a change inthe basis of the modal space in order to regulate the admittance ofhigher frequencies and to accommodate any change in the kinematicconfiguration. Numerical examples are presented to demonstrate theapplicability of the developed computational scheme.     

Measurement of piezoelectric modulus by pulsed excitation of piezoelectric ceramic elements

The possibility of measuring the piezoelectric modulus by exciting piezoelectric ceramic components with a radio pulse is considered. It is shown that there is a relation between the piezoelectric modulus and the rate of change of the current envelope at the beginning of the transient. Theoretical relations are derived. __________ Translated from Izmeritel’naya Tekhnika, No. 10, pp. 71–72, October, 2006.     

柔度法测量三点弯曲试样弹性模量的影响因素

根据柔度法测量金属材料裂纹长度的原理,讨论了测量三点弯曲SE(B)试样弹性模量的影响因素,并分析了主要因素的影响。在此基础上,用柔度法测量了裂纹尖端张开位移(CTOD)试验用大尺寸SE(B)试样预制疲劳裂纹的长度。经断口测量发现,用柔度法测量的两组母材与焊缝试样的原始裂纹长度具有很好的同一性,为进一步进行CTOD试验提供了保证。     

Relations between compliances of inhomogeneities having the same shape but different elastic constants

The contributions of inhomogeneities having the same shape but different elastic constants, to the overall elastic properties are interrelated. The utility of these relations lies, in particular, in the possibility to extend available results for pores or rigid inclusions to inhomogeneities of arbitrary elastic properties. The relations are exact for ellipsoids and approximate for non-ellipsoidal shapes. The constructed approximation also constitutes approximate connection between the first Eshelby’s problem (the eigenstrain problem) and the second one (the inhomogeneity problem), for non-ellipsoidal shapes. It also yields approximate formulas for the contribution of a non-ellipsoidal inhomogeneity to effective elastic properties.