A Two-Strand Ply Hanging Under Its Own Weight

We consider an idealised model for a plied structure such as may form when a straight rod or filament is subjected to a high twisting moment. Examples are found in textile yarns, interwound DNA molecules and bacterial macrofibres. Plied structures, generally composed of more than two strands, are also used widely in engineering (mooring ropes, cables in lift shafts), although here the strands are often not intrinsically straight. The ply is assumed to consist of two strands of thin circular elastic rod winding around each other while touching on a straight line of contact. Each strand is therefore constrained to lie on a cylinder. Using a variational approach we give an unconstrained Hamiltonian formulation for this problem. We also derive an exact expression for the contact force acting between the two strands. We study the symmetry-breaking effect of gravity on the ply configuration as well as on the contact force.     

Elastic-plastic deformation of sandwich rod on elastic basis

Sandwich composite material possesses advantages of both light weight and high strength. Although the mechanical behaviors of sandwich composite material with the influence of single external environment have been intensively studied, little work has been done in the study of mechanical property, in view of the nonlinear behavior of sandwich composites in the complicated external environments. In this paper, the problem about the bending of the three-layer elastic-plastic rod located on the elastic base, with a compressibly physical nonlinear core, has been studied. The mechanical response of the designed three-layer elements consisting of two bearing layers and a core has been examined. The complicated problem about curving of the three-layer rod located on the elastic base has been solved. The convergence of the proposed method of elastic solutions is examined to convince that the solution is acceptable. The calculated results indicate that the plasticity and physical nonlinearity of materials have a great influence on the deformation of the sandwich rod on the elastic basis.     

考虑纤维断裂特征的Nb3Sn股线统计拉伸强度和失效概率

Nb₃Sn 超导复合股线在强磁场工程中有着重要的应用,其拉伸强度为保证和评估其长期服役安全的一个关键参数。本文从 “剪滞”理论出发,利用基于Weibull/Possion统计理论的复合材料纤维断裂的Curtin-Zhou模型,较好地描述复合股线中Nb₃Sn超导纤维碎片化过程,建立了分析超导复合股线统计拉伸强度和失效概率的模型。计算结果表明,青铜法Nb₃Sn超导复合股线的拉伸强度随着初始损伤参数的增大而迅速减小;在4.2K服役温度下,当Weibull模量为8时,随着初始损伤参数的增加,股线的拉伸强度约从900MPa衰减至480MPa,与已有实验结果吻合良好;初始损伤参数约为1时,正规化方差最大。初始损伤和Weibull模量对Nb₃Sn复合股线统计拉伸强度和失效概率函数的分布有着显著影响。     

A Double-Strand Elastic Rod Theory

Motivated by applications in the modeling of deformations of the DNA double helix, we construct a continuum mechanics model of two elastically interacting elastic strands. The two strands are described in terms of averaged, or macroscopic, variables plus an additional small, internal or microscopic, perturbation. We call this composite structure a birod. The balance laws for the macroscopic configuration variables of the birod can be cast in the form of a classic Cosserat rod model with coupling to the internal balance laws through the constitutive relations. The internal balance laws for the microstructure variables also take a mathematical form analogous to that for a Cosserat rod, but with coupling to the macroscopic system through terms corresponding to distributed force and couple loads.     

Damage Analysis of Superconducting Composite Wire with Bridging Model

The multi-filamentary Bi_2 Sr_2 CaCu_2 O_(8+x)(Bi-2212) round wires are made of superconducting filaments, metal Ag and Ag alloy, which are typical composite structure. Since the filament is brittle, there are various defects and cracks in the Bi-2212 round wire after heat treatment. In this paper, we assume that the filaments in the wire are uniformly arranged. Adopting the bridging model which is often used in the fiber-reinforced composite, we calculate the ultimate strength of the round wire. The effects of the volume fraction, elastic modulus and interface shear strensgth are discussed in detail.     

Helical Birods: An Elastic Model of Helically Wound Double-Stranded Rods

We consider a geometrically accurate model for a helically wound rope constructed from two intertwined elastic rods. The line of contact has an arbitrary smooth shape which is obtained under the action of an arbitrary set of applied forces and moments. We discuss the general form the theory should take along with an insight into the necessary geometric or constitutive laws which must be detailed in order for the system to be complete. This includes a number of contact laws for the interaction of the two rods, in order to fit various relevant physical scenarios. This discussion also extends to the boundary and how this composite system can be acted upon by a single moment and force pair. A second strand of inquiry concerns the linear response of an initially helical rope to an arbitrary set of forces and moments. In particular we show that if the rope has the dimensions assumed of a rod in the Kirchhoff rod theory then it can be accurately treated as an isotropic inextensible elastic rod. An important consideration in this demonstration is the possible effect of varying the geometric boundary constraints; it is shown the effect of this choice becomes negligible in this limit in which the rope has dimensions similar to those of a Kirchhoff rod. Finally we derive the bending and twisting coefficients of this effective rod.     

The effect of brittle interfacial compounds on deformation and fracture of molybdenum-aluminum fiber composites

The effect of brittle intermetallic compounds at the fiber-matrix interface on the deformation characteristics of molybdenum-aluminum fiber composites was investigated. If the filament is ductile and notch-insensitive, then composite strength degradation is relatively minor and composite strength can be predicted by a modified mixture-rule which neglects the strength contribution of the brittle compound. For the case of notch-sensitive filaments, severe filament degradation occurs upon compound formation. The degradation was shown to result from cracks formed during deformation at the roots of compound nodules. The presence of 10 per cent compound by volume results in a 50 per cent decrease in tensile strength, but larger amounts of compound cause little additional strength reduction. At filament volume fractions of 25 and 34 per cent and compound volume fractions less than 10 per cent, composite fracture occurs by the statistical accumulation of fiber necks or fractures depending on the notch sensitivity of the fiber. At high fiber or compound volume fractions, composite failure occurs upon the first or the second filament fracture.     

Analytical modeling of synthetic fiber ropes. Part II: A linear elastic model for 1 + 6 fibrous structures

In part I of this study it was shown that, to model synthetic fiber ropes, two scale transition models can be used in sequence. The first model (continuum model) has been presented in the part I and the present paper examines the behavior of a fibrous structure consisting of 6 helicoidal strands around a central core (1 + 6 structure). An analytical model will be presented which enables the global elastic behavior of such a cable under tension–torsion loading to be predicted. In this model, first, the core and the strands are described as Kirchhoff–Love beams and then the traction–torsion coupling behavior is taken into account for both of them. By modeling the contact conditions between the strands and the core, with certain assumptions, it is possible to describe the behavior of the cable section as a function of the degrees of freedom of the core. The behavior of the cable can thus be deduced from the tension–torsion coupling behavior of its constituents. Tensile tests have been performed on the core, the strands and then on a full scale 205 ton failure load cable. Finally, predicted stiffness from the analytical models is compared to the test results.     

On the Bending and Stretching Elasticity of Biopolymer Filaments

Elastic filaments play an important role in the behaviour of cells and biological tissues. In this paper a two-dimensional nonlinear elastic framework, incorporating both bending and stretching, for the behaviour of biopolymer filaments treated as one-dimensional continua is developed. Explicit formulas for the extension-force relationship are obtained which include dependence on the initial end-to-end distance of the filament, unlike some existing models in the literature of, for example, the worm-like chain. The approach adopted allows treatment of both flexible and semi-flexible filaments and has the flexibility to accommodate different degrees of approximation. A key ingredient in the application of the model is inclusion of a body force term in the equilibrium equation. This is essential for finding non-trivial solutions of the governing equations and boundary conditions for filaments under tension. This highlights certain inconsistencies in the mechanics evident in the biophysics literature. Since the behaviour of individual filaments has a strong influence on the behaviour of networks of filaments the theory developed here can serve as a basis for analyzing the elasticity of networks such as actin and other filamentous biopolymer networks.     

Load absorption and interaction of two adjacent filaments in a fiber-reinforced material

This investigation is concerned with the interaction—as far as load-absorption is concerned—of a pair of identical parallel elastic filaments in a fiber-reinforced composite material. The filaments are assumed to have uniform circular cross-sections, are taken to be semi-infinite, and are supposed to be continuously bonded to an all-around infinite matrix of distinct elastic properties. At infinity the matrix is subjected to uniaxial tension parallel to the filaments. Two separate but related problems are treated. In the first both filaments extend to infinity in the same direction and their terminal cross-sections are coplanar. In the second problem the filaments extend to infinity in opposite directions and their terminal cross-sections need no longer be coplanar, the two filaments being permitted to overlap partly. An approximate scheme based in part on three-dimensional linear elasticity and developed originally by Muki and Sternberg is employed in the analysis. The problems are ultimately reduced to Fredholm integral equations which characterize the distribution of the axial filament force. The integral equations are analyzed asymptotically and numerically. Results are presented which show the variation of filament force with position and the effect on this variation of various relevant geometrical and material parameters. One result is of particular interest. In the second problem, involving the overlapping filaments, for certain cases the filament force exceeds its far-field asymptotic value for a portion of the filament length. Stated another way, this means that the filament is loaded in excess of that which one would calculate by equating axial strains.

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Zusammenfassung Die Wechselwirkung eines identischen parallelen elastischen Fadenpaares in einem faserverstärkten Verbundstoff wird in Bezug auf die Lastaufnahme untersucht. Man nimmt an, dass die Fäden einen gleichmässigen runden Querschnitt haben, halbunendlich sind, und dass sie ohne Unterbrechung an einem überall unendlichen Grundstoff eindeutiger elastischer Eigenschaften anhaften. Im Unendlichen wird der Grundstoff einem einachsigen Zug parallel zu den Fäden ausgezetzt. Es werden zwei verschiedene, aber in Verbindung stehende, Fragenstellungen behandelt. In der Ersten erstrecken sich beide Fäden unendlich lang in derselben Richtung und ihre Endquerschnitte sind koplanar. In der Zweiten erstrecken sie sich unendlich lang in entgegengesetzten Richtungen und ihre Endquerschnitte müssen nicht koplanar sein, obwohl die Fäden sich teilweise überlagern dürfen. Die Analyse wird mit einem von Muki und Sternberg entwickelten Näherungsverfahren durchgeführt, welches zum Teil auf einer dreidimensionalen linearen Elastizitätstheorie beruht. Letzten Endes nehmen diese Probleme die Form Fredholmscher Integralgleichungen an, welche die Verteilung der Fadenlängskraft kenzeichnen. Die Integralgleichungen werden asymptotisch und zahlenmässig analysiert.

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The results communicated in this paper were obtained in the course of an investigation supported in part by the Office of Naval Research under Contract N00014-67-A-0094-0020. The work was carried out during the author's tenure of a National Science Foundation Traineeship.     

Stochastic modeling of multi-filament yarns: II. Random properties over the length and size effect

The present study addresses the influence of variations in material properties along the multi-filament yarn on the overall response in the tensile test. In Part I (Chudoba, Vořechovský and Konrad, 2006), we have described the applied model and studied the influence of scatter of material characteristics varying in the cross-section with no variations along the filaments. In particular, we analyzed the influence of varying cross-sectional area, filament length and delayed activation. Inclusion of these effects has lead to a better interpretation of the experimental data, especially with respect to the gradual stiffness activation, post-peak behavior and some form of size effect. In the present paper, the length-related distributions of local stiffness and strength are included in terms of theoretical considerations and by applying the Monte Carlo type simulation of random fields. Such an approach allows us (1) to demonstrate the strong need for including length scale to random fluctuation of strength along the filaments and (2) to combine several sources of randomness in a single analysis so that their significance can be evaluated from the tensile test response.     

The Saint-Venant torsion of a circular bar consisting of a composite cylinder assemblage with cylindrically orthotropic constituents

We consider the Saint-Venant torsion of a cylindrical rod of a circular cross section which is filled up by an assemblage of composite circular cylinders. The constituent cylinders consist of a core and a coating both of which are cylindrically orthotropic with the volume fraction of the core being the same in every composite cylinder. The described microstructure is the composite cylinder assemblage of Hashin and Rosen [J. Appl. Mech. 29 (1964) 143] which is now subjected to torsion. The main results are (a) the warping function on the lateral surface of the host rod is zero, (b) an exact expression for the torsional rigidity of the host rod is derived which depends on the size distribution of the composite cylinders but not on their position and (c) there are two circumstances in which the torsional rigidity becomes size distribution independent: The first one is that in which the sizes of the composite cylinders are much smaller than the size of the host rod; the second one is that in which a certain specific relation holds between the properties of the composite cylinder and the volume fraction of the core. If the coating disappears and the core is cylindrically orthotropic, we get the configuration of a polycrystalline rod. Simple bounds for the torsional rigidity of the constructed composite rod are obtained.     

Effective pressure-sensitive elastoplastic behavior of particle-reinforced composites and porous media under isotropic loading

The composite under investigation consists of an elastoplastic matrix reinforced by elastic particles or weakened by pores. The material forming the matrix is pressure-sensitive. The Drucker–Prager yield criterion and a one-parameter non-associated flow rule are employed to formulate the yield behavior of the matrix. The objective of this work is to estimate the effective elastoplastic behavior of the composite under isotropic tensile and compressive loadings. To achieve this objective, the composite sphere assemblage model of Hashin [Z. Hashin, The elastic moduli of heterogeneous materials, ASME J. Appl. Mech. 29 (1962) 143–150] is used. Exact solutions are thus derived as estimations for the effective secant and tangent bulk moduli of the composite. The effects of the loading modes and phase properties on the effective elastoplastic behavior of the composite are analytically and numerically evaluated.     

Band-gap Properties of Elastic Sandwich Metamaterial Plates with Composite Periodic Rod Core

A novel elastic sandwich metamaterial plate with composite periodic rod core is designed,and the frequency band-gap characteristics are numerically and experime...     

The effect of pre-shear on the extensional rheology of wormlike micelle solutions

The effect of initial microstructural deformation, alignment, and morphology on the response of wormlike micelle solutions in transient uniaxial extensional flows is investigated using a pre-shear device attached to a filament stretching rheometer. In filament stretching experiments, increasing the strength and the duration of the pre-shear just before stretch is found to delay the onset of strain hardening. In these experiments, the wormlike micelle solution filaments fail through a rupture near the axial midplane. The value of the elastic tensile stress at rupture is found to decrease with increasing pre-shear rate and duration. The most dramatic effects are observed at shear rates for which shear banding has been independently observed. The reduction in the strain hardening suggests that pre-shear before filament stretching might break down the wormlike micelles reducing their size before stretch. Strain hardening is also observed in capillary breakup rheometry experiments; however, the pre-sheared wormlike micelle solutions strain harden faster, achieve larger steady-state extensional viscosities and an increase in the extensional relaxation time with increasing shear rate and duration. The difference between the response of the wormlike micelles in filament stretching and capillary breakup experiments demonstrates the sensitivity of these self-assembling micelle networks to pre-conditioning.     

钨纤维增强金属玻璃复合材料分段弹体侵彻性能研究

结合穿甲实验，基于复合材料细观有限元模拟，系统开展针对钨纤维增强金属玻璃复合材料分段弹体侵彻性能的研究，并与复合材料长杆弹进行对比分析。结果表明，相对于复合材料长杆弹显著的穿甲“自锐”行为和优异的侵彻性能，复合材料分段弹体在侵彻过程中的“自锐”特性有所减弱，且弹体结构容易发生分散，进而导致弹体侵彻能力明显降低。另外，分段数目和分段间隔等因素对复合材料分段弹体的侵彻性能具有一定影响，但总体而言，不同构型分段弹体的侵彻能力均弱于复合材料长杆弹。     

Extensional flow behavior of polymer solutions and particle suspensions in a spinning motion

Mechanical spinning of fluid filaments was used to generate an extensional flow, in which rheological measurements were obtained for a Newtonian fluid, two aqueous polymer solutions, and two fluid suspensions of rod-shaped particles. The tensile stress was determined by measuring the tensile force of the fluid filament while the kinematics were determined from photographic measurement of the filament profile and the assumption of a flat velocity profile. The measured tensile stresses for the Newtonian fluid matched predicted stresses, thereby confirming the validity of the experimental technique.The spinning behavior of each polymer solution could be correlated as stress versus extension rate. The apparent “spinning viscosity” increased with increasing rate of extension, in contrast to shear-thinning behavior in viscometric flow. For the fluid suspensions, the presence of rod-shaped particles increased the apparent viscosity far more in extensional flow than in shear. Tensile stresses calculated from a theoretical formula for suspensions proposed by Batchelor agreed rather well with experiment. Some general criteria for the interpretation of the spinning experiment are proposed, and some microrheological implications of the present findings are discussed.     

A penny-shaped crack in a filament-reinforced matrix—II. The crack problem

Using the filament model developed in the previous paper, the elastostatic interaction problem between a penny-shaped crack and a slender inclusion or filament in an elastic matrix is formulated. For a single filament as well as multiple identical filaments located symmetrically around the crack the problem is shown to reduce to a singular integral equation. The solution of the problem is obtained for various geometries and filament to-matrix stiffness ratios, and the results relating to the angular variation of the stress intensity factor and the maximum filament stress are presented.     

Homogenization method for strength and inelastic behavior of nanocrystalline materials

Homogenization techniques are used for modeling the so-called “breakdown” of the Hall–Petch law in the case of nanocrystalline (NC) materials. In this paper, the NC material is modeled as a composite material composed of two phases: the grain core (inclusion) and the grain boundaries (matrix). The deformation of the inclusion phase has a viscoplastic component that takes into account the dislocation glide mechanism as well as Coble creep. The boundary phase is modeled as an amorphous material with a perfect elastic–plastic behavior. An application of the model is developed on pure copper under tensile load. The results are compared with various experimental data.