bluuebunny/crossref_metadata_2025 huggingface dataset:
Buckling Calculations and Measurements on a Technologically Relevant Toroidal Magnet System
Authors: Geiger W. , Jungst K. P.
Published: April 2008

The coils in a toroidal magnet system may deform laterally and become mechanically unstable when a critical value of the current is exceeded as a result of magnetoelastic coupling. This instability is called magnetoelastic buckling. It was studied in the TESPE arrangement, a toroidal magnet system the design and size of which meet technical demands. A generalized theoretical model was developed for the calculation of the buckling behavior of toroidal magnet systems. It was shown by the measurements that in a torus of complex design, the lateral elastic stiffnesses of the coils may vary considerably with the current. Monitoring of the natural frequencies of the vibration modes proved to be a suitable method for the supervision of the mechanical stability during operation.
Acoustoelastic Birefringences in Plastically Deformed Solids: Part II—Experiment
Authors: Wu Tsung-Tsong , Hirao Masahiko , Pao Yih-Hsing
Published: April 2008

Ultrasonic experiments are preformed on a carbon steel specimen to determine the change of elastic wave speeds by plastic strains and residual stresses in the specimen. Under repeated uniaxial loadings, the acoustoelastic birefringence was found to be a linear function of plastic strains at various states of total unloading. In elastoplastic bendings, the acoustoelastic birefringes are dependent on the natural anisotropy, plastic strains, and residual stresses as predicted by the theory of Part I. The uniaxial residual stress and plastic strain in the beam are determined by acoustoelastic experiments.
Chaos in a Weakly Nonlinear Oscillator With Parametric and External Resonances
Authors: Yagasaki K.
Published: April 2008

This paper describes a study of the chaotic dynamics of a weakly nonlinear single degree-of-freedom system subjected to combined parametric and external excitation. We consider a case of double resonance in which primary resonances, with respect to parametric and external forces, exist simultaneously. By using the averaging method and Melnikov’s technique, it is shown that chaos may occur in certain parameter regions. These chaotic motions result from the existence of orbits homoclinic to a normally hyperbolic invariant torus which corresponds to a hyperbolic periodic orbit in the averaged system. The mechanism and structure of chaos in this situation are also described. Furthermore, the existence of steady-state chaos is demonstrated by numerical simulation.
Co-dimension Two Bifurcations in the Presence of Noise
Authors: Sri Namachchivaya N.
Published: April 2008

Some results pertaining to co-dimension two stochastic bifurcations are presented. The normal form associated with non-semi-simple double-zero eigenvalues is considered. The method of stochastic averaging applicable for singularly perturbed stochastic differential equations is used to further reduce the problem to a one dimensional diffusion process. Probability density, most probable values, stability conditions in probability, and mean exit times are obtained for the reduced system.
Statistical Theory for Predicting the Failure of Brittle Materials
Authors: She S. , Landes J. D. , Boulet J. A. M. , Stoneking J. E.
Published: April 2008

Statistical models for predicting failure probability of brittle materials are investigated. A formula is derived from a physical consideration for the fracture of microcracks in materials based on the general forms of a fracture criterion and a statistical distribution function incorporating the weakest link principle. The relationships of this model and other statistical models in the literature are discussed; they were found to be equivalent for isotropic materials in which microcracks are randomly distributed in all directions. The statistical model is also used in a failure analysis of the round-notch four-point bending specimen made of an AISI 1008 steel. The grain boundary carbide particles are considered to be microcracks in the plastic zone near the notch tip. The distribution function in the statistical theory is derived from the density and size distribution of carbide particles in the steel. The statistical theory for a triaxial stress state is used to predict the failure probability for any given load on the specimen. The failure loads (loads corresponding to 50 percent of failure probability) are calculated for the specimen at different temperatures. The results are compared with experimental data; good agreement is obtained.
The Proportional Anisotropic Elastic Invariants
Authors: Sadegh A. M. , Cowin S. C.
Published: April 2008

There are two proportional invariants for a linear isotropic material, the hydrostatic invariant, and the deviatoric invariant. The former is proportional to the trace of the tensor and the latter is proportional to the trace of the square of the associated deviatoric tensor. The hydrostatic stress and strain and the von Mises stress and strain are directly related to the hydrostatic and deviatoric proportional invariants, respectively, for an isotropic, linear elastic material. For each anisotropic linear elastic material symmetry there are up to six proportional invariants. In this paper we illustrate the six proportional invariants of an orthotropic elastic material using the elastic constants for spruce as the numerical example. The proportional elastic invariants play a role in anisotropic linear elasticity similar to the roles played by the hydrostatic stress and strain and the von Mises stress and strain in isotropic elasticity. They are the unique parameters whose contours represent both the stress and the strain distributions. They also have potential for representing failure or fracture criteria.
Prediction of Dynamic Contact Loads in Granular Assemblies
Authors: Zhu C. Y. , Shukla A. , Sadd M. H.
Published: April 2008

An experimental-numerical hybrid technique has been developed to predict the intergranular contact load transfer in granular media subjected to explosive loading. The granular media were simulated by assemblies of circular disks in contact. The peak contact load transfer coefficients (i. e., the ratio of the maximum output contact load to the input contact load as a function of the contact angles) of a given particle were obtained through controlled experimental studies. These coefficients, along with the principle of superposition, were then used to predict the peak contact loads in several regular as well as irregular assemblies of disks. The predicted results compared favorably with the experimental data for several different assemblies.
Torsion of a Rigid Smooth Elliptic Insert in an Infinite Elastic Plane
Authors: Gross Robert S. , Goree James G.
Published: April 2008

A solution is presented for the non-Hertzian contact stress problem developed during torsion of a smooth rigid elliptic insert in an infinite, linearly elastic plane. The problem is reduced to a singular integro-differential equation which is solved numerically. Results are presented for the contact zones, and for the normal and tangential stresses at the plane-insert interface. The contact region is independent of the magnitude of the applied moment, but depends strongly on the shape of the ellipse, and is weakly dependent on Poisson’s ratio of the plane. Results are also given for the reduction in torsional stiffness between a fully bonded insert and the present solution, (i.e., a completely failed bond).
The Nonlinear Elastic Behavior of Open-Cell Foams
Authors: Warren W. E. , Kraynik A. M.
Published: April 2008

A constitutive model for the nonlinear elastic behavior of isotropic low-density opencell foams with three-dimensional structure is formulated in terms of a strain energy function. The theory is based on micromechanical analysis of an idealized tetrahedral unit cell of arbitrary orientation that contains four half-struts joining at equal angles. The force-displacement relations for each strut are expressed by compliances for bending and stretching that do not depend on the magnitude of applied force. Contributions to the strain energy from large deformation effects are assumed to depend on strut reorientation and stretching, and are determined by analyzing a pin-jointed structure. The analysis is considered to be valid for finite strains below the onset of yielding associated with strut buckling.
Dynamic Stress on a Partially Bonded Fiber
Authors: Norris Andrew , Yang Yang
Published: April 2008

The dynamic stress on a partially bonded fiber is analyzed for shear wave incidence, with particular attention given to the stress intensity factor at the neck joining the fiber to the matrix. The problem is formulated in terms of the unknown stress across the neck and the remainder of the fiber-matrix interface is modeled as a curved interfacial crack. Explicit asymptotic expressions are derived for the near and farfields that are valid in the frequency range in which the recently discussed resonance phenomenon occurs (Yang and Norris, 1991). This resonance is a rattling effect that is most prominent when the neck becomes very thin, and can occur at arbitrarily small values of the dimensionless frequency ka, where a is the radius of the fiber. The asymptotic results indicate that the dynamic stress intensity factor becomes unbounded as the neck vanishes, in contrast to the prediction of a purely quasistatic analysis that the stress intensity factor vanishes in the same limit.
Interface Crack in a Three-Phase Composite Constitutive Model
Authors: Luo H. A. , Chen Y.
Published: April 2008

An arc-shaped crack in fiber-reinforced composite material is the subject of this paper. A three-phase composite cylinder is taken as the material model to take into account the effect of surrounding fibers. Using Muskhelishvili’s complex variable method, an exact elastic solution is derived based on the conventional crack opening assumption. The complex stress intensity factors for the interface crack, in the sense defined by Hutchinson, Mear, and Rice, are determined. Some numerical examples are given. It is shown that, as the volume concentration of the fiber is increased, the magnitude of the complex stress intensity factors varies considerably.
A New Approach to Microbuckling of Fibrous Composites
Authors: Lagoudas Dimitris C. , Tadjbakhsh Iradj , Fares Nabil
Published: April 2008

A new approach for the evaluation of the compressive strength of fibrous composites due to microbuckling is considered in this paper. Most of the proposed models, thus far, have tried to improve on the classical analysis by Rosen regarding both phases as separate continua with appropriate interface conditions. In this work the fibrous composite is represented by an inhomogeneous two-dimensional continuum with spatial variation in the axial Young’s modulus to account for fibers and matrix. The periodicity of the microstructure is taken into account by expanding the axial Young’s modulus in a Fourier series with wavelength the average spacing between fibers. The compressive strength is determined by examining the stability of small perturbations superimposed on a uniform applied compressive strain. It is found that the compressive strength depends on the wavelength of initial imperfections and bound estimates for minimum and maximum imperfection sizes are derived. The upper bound corresponds to perfectly aligned fibers without any imperfections and coincides with Rosen’s prediction of the compressive strength, while the lower bound corresponds to the more realistic case of imperfect systems and correlates well with experimental data.
Plate Tenting With a One-Sided Constraint
Authors: Benson Richard C.
Published: April 2008

This paper concerns the loads and deflections of a “tented” plate. A concentrated load pushes the plate transversely away from a rigid surface. Bending rigidity, inplane tension, foundation stiffness, and weight all act to draw the plate back down to the surface. The deflected region of the tent is assumed to have an ellipsoidal shape, the extent of which is a variable of the problem. Interfacial pressure between the plate and surface is redistributed, after tenting, into a concentrated load at the “tent pole” and a line load along the contour separating contact and noncontact. The problem is analyzed using energy minimization, and approximate, closed-form expressions are obtained for tent dimensions and interfacial loads. Predictions for the tentpole force are compared to experiment and found to be in good agreement.
Extension of the Upper Bound Method to Include Estimation of Stresses
Authors: Azarkhin A. , Richmond O.
Published: April 2008

The upper bound method is a convenient tool for evaluating the rate of work in processes involving predominantly plastic deformation of rigid/perfectly plastic material. Since the rate of work for an incompressible material depends only on the deviator portion of the stress, the hydrostatic portion does not enter the formulation and the stress field is not determined. Here we show that this limitation can be overcome by adding a relatively simple postprocessing procedure. We then apply this technique to examples of rigid asperities penetrating a plastic material undergoing subsurface bulk deformation and compare our results with previous approximate solutions.
Systems With Infinitesimal Mobility: Part II—Compound and Higher-Order Infinitesimal Mechanisms
Authors: Kuznetsov E. N.
Published: April 2008

Building on the analytical results presented in Part I, the issue of multiple singularity is explored. The attained understanding is applied to the analysis and synthesis of compound infinitesimal mechanisms illustrated in several examples. Employing power expansion techniques, higher-order mechanisms are investigated, revealing, in particular, the existence of even-order mechanisms and their peculiar nature. The equivalence condition is established between prestressability and kinematic immobility of underconstrained structural systems with one singularity. A previously unidentified class of systems—unprestressable infinitesimal mechanisms—is revealed. It complements the conventional source of infinitesimally mobile systems associated with a strict constrained extremum and the resulting feature of prestressability.
On Stability and Stabilization of Mechanical Structures Under Nonlinear Time-Varying Perturbations
Authors: Lin Chun-Liang , Chen Bor-Sen , Hsiao Fei-Bin
Published: April 2008

Asymptotic stability and bounded-input, bounded-output (BIBO) stability of a class of underdamped mechanical structures with nonlinear time-varying perturbations are studied. An upper norm-bound of the state transition matrix of a normal mode system is derived. We provide a sufficient condition which guarantees both asymptotic stability and BIBO stability for the perturbed system. A straightforward extension to a robust modal-space control is also briefly introduced. Finally, simple illustrative examples are presented for demonstrating the applications of our results
A Reformation of the Equations of Anisotropic Poroelasticity
Authors: Thompson M. , Willis J. R.
Published: April 2008

The constitutive equations of linear poroelasticity presented by Biot (1955) and Biot and Willis (1957) extended the description of rock behavior into the realm of saturated porous rocks. For isotropic material behavior, Rice and Cleary (1976) gave a formulation which involved material constants whose physical interpretation was particularly simple and direct; this is an aid both to their measurement and to the interpretation of predictions from the theory. This paper treats anisotropic poroelasticity in terms of material tensors with interpretations similar to those of the constants employed by Rice and Cleary. An effective stress principle is derived for such anisotropic material. The material tensors are defined, rigorously, from the stress field and pore fluid content changes produced by boundary displacements compatible with a uniform mean strain and uniform pore pressure increments. Such displacements and pore pressure increments lead to homogeneous deformation on all scales significantly larger than the length scale of microstructural inhomogeneities. This macroscopic behavior is related to the microscopic behavior of the solid skeleton. The tensors which describe the microscopic behavior of the solid skeleton would be difficult, even impossible, to measure, but their introduction allows relationships between measurable quantities to be identified. The end product of the analysis is a set of constitutive equations in which the parameters are all measurable directly from well-accepted testing procedures. Relationships exist between measurable quantities that can be used to verify that the constitutive equations described here are valid for the rock under consideration. The case of transverse isotropy is discussed explicitly for illustration.
Biaxial Loading Experiments for Determining Interfacial Fracture Toughness
Authors: Liechti K. M. , Chai Y.-S.
Published: April 2008

The paper establishes the range of in-plane fracture mode mixtures and contact zone sizes that can be obtained from an edge-cracked bimaterial strip under biaxial applied displacements. The development of a suitable loading device for and the application of crack opening interferometry to interfacial crack initiation experiments is described. The crack initiation process under bond-normal loading is examined in detail for a glass/epoxy interface in order to establish a hybrid optical interference/finite element analysis technique for extracting mixed-mode fracture parameters.
Successive Synthesis of Substructure Modes
Authors: Suarez Luis E. , Singh Mahendra P.
Published: April 2008

A mode synthesis approach is presented to calculate the eigenproperties of a structure from the eigenproperties of its substructures. The approach consists of synthesizing the substructures sequentially, one degree-of-freedom at a time. At each coupling stage, the eigenvalue is obtained as the solution of a characteristic equation, defined in closed form in terms of the eigenproperties obtained in the preceding coupling stage. The roots of the characteristic equation can be obtained by a simple Newton-Raphson root finding scheme. For each calculated eigenvalue, the eigenvector is defined by a simple closed-form expression. The eigenproperties obtained in the final coupling stage provide the desired eigenproperties of the coupled system. Thus, the approach avoids a conventional solution of the second eigenvalue problem. The approach can be implemented with the complete set or a truncated number of substructure modes; if the complete set of modes is used, the calculated eigenproperties would be exact. The approach can be used with any finite element discretization of structures. It requires only the free interface eigenproperties of the substructures. Successful application of the approach to a moderate size problem (255 degrees-of-freedom) on a microcomputer is also demonstrated.
Solutions for Non-Newtonian Flow Into Elliptical Openings
Authors: Bogobowicz A. , Rothenburg L. , Dusseault M. B.
Published: April 2008

A semi-analytical solution for plane velocity fields describing steady-state incompressible flow of nonlinearly viscous fluid into an elliptical opening is presented. The flow is driven by hydrostatic pressure applied at infinity. The solution is obtained by minimizing the rate of energy dissipation on a sufficiently flexible incompressible velocity field in elliptical coordinates. The medium is described by a power creep law and solutions are obtained for a range of exponents and ellipse eccentricites. The obtained solutions compare favorably with results of finite element analysis.
Effect of Finite Thickness Flexible Boundary Upon the Stability of a Poiseuille Flow
Authors: Pierucci Mauro , Morales Pedro G.
Published: April 2008

The stability behavior, the stress, and velocity distributions for a plane Poiseuille flow bounded by a finite thickness elastic layer is studied. The analysis is performed by utilizing the coupled relationships between the Orr-Sommerfeld stability equation for the fluid and the Navier equations for the solid. The numerical instabilities experienced in the solution of the Orr-Sommerfeld equation have been overcome with the use of Davey’s orthonormalization technique. This study focuses only on the Tollimen-Schlichting instabilities. This mode is the most unstable of the three different types of instabilities. The results show that certain combinations of parameters can lead to improved stability conditions. Under these conditions the normal and shear stress distributions may behave completely different in certain regions of the fluid.
On the Disturbance of a Thin Layer of Liquid by a Moving Obstruction
Authors: Gans Roger F. , Wang Chung-Hai
Published: April 2008

We calculate the free surface shapes upstream and downstream of an obstacle obstructing a thin liquid layer on a moving surface, taking into account gravity and surface tension. We assume low Reynolds number viscous flow, a two-dimensional layer, and small ratio of vertical to horizontal length scale. The upstream and downstream shapes are very different. The upstream liquid piles up against the obstacle to provide an overpressure sufficient to drive the Poiseuille component of the lubrication flow under the obstacle. The downstream liquid is disturbed only by surface tension.
A Central Crack in a Finite Rectangular Plate With Four Hinged Edges Under the Opening Mode
Authors: Ma S. W. , Tsuei Y. G.
Published: April 2008

By combining linearly the Fourier transform and Fourier series, the stress intensity factor of a central crack in a finite rectangular plate with four hinged edges under the opening mode is expressed as the Fredholm integral equation of the second kind. The uniform loading case is considered in detail. The numerical results include the predictions by Koiter and Fichter as limiting cases.
Flexure of a Pressurized Tube
Authors: Steigmann D. J.
Published: April 2008

In this note we study the theory of combined flexure and pressurization of an initially cylindrical elastic membrane of circular cross-section. For the case of homogeneous material and uniform pressure, we obtain first integrals of the equations of equilibrium.
Micromechanics of an Extrusion in High-Cycle Fatigue With Creep
Authors: Lin T. H. , Lin S. R. , Wu X. Q.
Published: April 2008

Extrusions and intrusions often are sites of fatigue cracks. The extent of extrusions is important in fatigue crack initiation. Metals often are subject to fatigue loadings at elevated temperatures. At temperatures below one half of the melting temperature slip is the main mechanism of inelastic deformation. In this study, an aluminum polycrystal loaded in this temperature range is considered. A most favorably oriented crystal located at a free surface of a f.c.c. polycrystal subject to creep under cyclic tension and compression of high-cycle fatigue is considered. An extrusion in this crystal is shown to be produced by a positive slip in one thin slice “P” and a negative slip in a closely located slice “Q”. An initial tensile strain εααI in the thin slice “R” sandwiched between P and Q causes a positive initial shear stress ταβI in P and a negative one in Q. It is shown that the extrusion growth causes a tensile strain in R, which can activate a second slip system giving a creep strain with a tensor component εαα. It has the same effect as the initial strain εααI in causing this difference in shear stresses in P and Q and gives much additional extrusion growth. The extent of intrusion and extrusion is important in this study of crack initiation.
Thermal Dynamic Problems of Reinforced Composite Cylinders
Authors: Birman Victor
Published: April 2008

Thermal dynamic problems of circular cylindrical composite shells reinforced in the axial and circumferential directions and subject to variations of temperature are considered. Nonlinear governing equations are formulated based on the extension of Donnell shell theory. These equations are used to determine the response of geometrically nonlinear and linear shells to a thermal loading represented by the Heaviside step function (thermal shock). The solution of the nonlinear problem obtained by the assumption that displacements are single-term functions of coordinates is discussed. The analysis of the linear problem illustrates different types of response to thermal shock. The condition of thermally-induced buckling of shells is formulated. Numerical analysis results in conclusions regarding the behavior of shells subject to thermal shock if the temperature is uniformly distributed throughout the shell and stiffeners.
Nonlinear Response of Infinitely Long Circular Cylindrical Shells to Subharmonic Radial Loads
Authors: Nayfeh Ali H. , Raouf Raouf A. , Nayfeh Jamal F.
Published: April 2008

The method of multiple scales is used to analyze the nonlinear response of infinitely long, circular cylindrical shells (thin circular rings) in the presence of a two-to-one internal (autoparametric) resonance to a subharmonic excitation of order one-half of the higher mode. Four autonomous first-order ordinary differential equations are derived for the modulation of the amplitudes and phases of the interacting modes. These modulation equations are used to determine the fixed points and their stability. The fixed points correspond to periodic oscillations of the shell, whereas the limit-cycle solutions of the modulation equations correspond to amplitude and phase-modulated oscillations of the shell. The force response curves exhibit saturation, jumps, and Hopf bifurcations. Moreover, the frequency response curves exhibit Hopf bifurcations. For certain parameters and excitation frequencies between the Hopf values, limit-cycle solutions of the modulation equations are found. As the excitation frequency changes, all limit cycles deform and lose stability through either pitchfork or cyclic-fold (saddle-node) bifurcations. Some of these saddlenode bifurcations cause a transition to chaos. The pitchfork bifurcations break the symmetry of the limit cycles.
Impulsive Motions of Elastic Pseudo-Rigid Bodies
Authors: Cohen H. , Mac Sithigh G. P.
Published: April 2008

We develop the formalism for treating impact problems in the theory of pseudorigid bodies developed by Cohen and Muncaster. Our treatment is general enough to include the effect of kinematical constraints.
Singular Fields in Plane-Strain Penetration
Authors: Durban David , Rand Omri
Published: April 2008

Local singular fields are investigated in the vicinity of the vertex of a sharp wedge that penetrates a viscous solid. Material behavior is modeled by the usual powerlaw constitutive relation. Wall friction is accounted for by imposing friction factors along the walls of the wedge. The case of a Newtonian fluid is investigated analytically, and sample numerical results are presented for nonlinear strain rate hardening. It is shown that the exponent of strain rate singularity increases as the wedge becomes sharper and smoother. Increasing the hardening parameter also results in a stronger strain rate singularity. High levels of wall friction induce an intensive shear boundary layer near the wall.
A Micromechanics Analysis of Cracks in Unidirectional Fiber Composites
Authors: Ahmad Jalees
Published: April 2008

The elastic problem of a crack normal to a bimaterial interface is addressed in the context of unidirectional fiber composites. The structure of asymptotic crack-tip stress fields is obtained numerically. The numerical results are then analyzed to formulate criteria for assessing cracking normal to the fiber, interface splitting, and fiber pull-out.
Analysis of the Fully Developed Chute Flow of Granular Materials
Authors: Ahn Hojin , Brennen Christopher E. , Sabersky Rolf H.
Published: April 2008

Existing constitutive relations and governing equations have been used to solve for fully developed chute flows of granular materials. In particular, the results of Lun et al. (1984) have been employed and the boundary value problem has been formulated with two parameters (the coefficient of restitution between particles, and the chute inclination), and three boundary values at the chute base wall, namely the values of solid fraction, granular temperature, and mean velocity at the wall. The boundary value problem has been numerically solved by the “shooting method.” The results show the significant role played by granular conduction in determining the profiles of granular temperature, solid fraction, and mean velocity in chute flows. These analytical results are also compared with experimental measurements of velocity fluctuation, solid fraction, and mean velocity made by Ahn et al. (1989), and with the computer simulations by Campbell and Brennen (1985b).
Response of a Liquid Bridge With Rotationally Excited Bottom
Authors: Bauer Helmut F.
Published: April 2008

The response of a cylindrical liquid column consisting of an incompressible and frictionless liquid has been investigated for a pitching bridge bottom. The response of the free surface and velocity distribution has been determined and numerically evaluated. In addition, the transient behavior of the column has been treated. Since for nonviscous liquid the response exhibits at the resonances singularity, a semi-empirical damping was introduced in the resonance terms. Its magnitude has to be determined by experiments.
Transient Wave Propagation in a Harmonically Heterogeneous Elastic Solid
Authors: Kim Hyun-Sil , Ginsberg Jerry H.
Published: April 2008

Transient propagation of a one-dimensional dilatational wave in a harmonically heterogeneous elastic solid is studied by several techniques. A regular perturbation analysis in terms of the characteristics of the differential equation shows that initiation of a temporally harmonic excitation that generates a signal whose wavelength is twice the periodicity of the heterogeneity leads to secularity in the first approximation. The frequency at which this situation occurs matches the frequency at which Floquet theory predicts that steady-state waves may be unstable. A finite difference algorithm based on integrating along the characteristics is developed and implemented to obtain a numerical solution. In the critical case, backscattering of the wave from the heterogeneity results in a mixture of propagating and standing wave features. However, rather than being unstable, the heterogeneity in this condition is shown to result in maximum interference with forward propagation. A comparable analysis for a step excitation on the boundary provides additional insight into the underlying propagation phenomena.
A Study of the Fiber-Matrix Interface in Composite Materials
Authors: Kim Jin O. , Bau Haim H.
Published: April 2008

A novel experimental technique for studying the characteristics of the interface between the fibers and the matrix in both undamaged and damaged fiber-reinforced composite materials is described. The experimental technique involves the transmission of stress waves in one or more fibers of the composite. The characteristics of the stress waves, such as speed, dispersion, and attenuation, are measured. These measured variables can be correlated with the characteristics of the bonding between the fiber and the matrix.
Modification of the Shear Lag Analysis for Determination of Elastic Modulus of Short-Fiber (or Whisker) Reinforced Metal Matrix Composites
Authors: Nair S. V. , Kim H. G.
Published: April 2008

A major shortcoming of the original shear lag analysis is its inability to provide sufficiently accurate strengthening predictions when the fiber aspect ratio is small. This is due to its neglect of stress transfer across fiber ends and the stress concentrations that exist in the matrix regions near fiber ends. In this paper, a straightforward, yet rigorous, modification of the original shear lag analysis is presented by taking fiber end effects into account and to result in fully closed-form solutions. It is demonstrated that the modification not only results in a correct prediction of the modulus increases in the small aspect ratio regime when compared to finite element results, but is also able to correctly predict the values of interfaciat shear stresses and local stress variations in the matrix and fiber.
Differential Hardening in Sheet Metal Under Biaxial Loading: A Theoretical Framework
Authors: Hill R. , Hutchinson J. W.
Published: April 2008

A simple constitutive framework is proposed to take account of progressive changes in a stress-based criterion of yielding as plastic deformation accumulates. The analysis is relevant to a sheet of isotropic or orthotropic material which is subsequently loaded in its plane by biaxial tensions (σ1, σ2) in arbitrary fixed ratio. Under these circumstances there is evidence that texture development causes significant changes in the shapes of successive yield loci in (σ1, σ2) space. Here such departures from geometric similarity are explicitly linked to a presumed dependence on σ1/σ2 of the exponent m in a standard power-law representation of the stress-strain characteristic under each constant value of σ1/σ2. The linkage is formulated in detail for several types of representation, and it is shown how a family of yield loci associated with any conjectural dependence m(σ1/σ2) can be generated readily by computer graphics. Some typical examples are given, in particular when m (σ1/σ2) reflects the distinctive trends reported for certain kinds of brass and aluminum sheet (e.g., Wagoner, 1980; Stout and Hecker 1983).
Simulation of Homogeneous Two-Dimensional Random Fields: Part I—AR and ARMA Models
Authors: Mignolet Marc P. , Spanos Pol D.
Published: April 2008

The determination of autoregressive (AR) and autoregressive moving average (ARMA) algorithms for simulating realizations of two-dimensional random fields with a specified (target) power spectrum is examined. The form of both of these models is justified first by considering infinite-variate vector processes of appropriate spectral matrix. Next, the AR parameters are selected to achieve the minimum of a positive integral. Then, a technique is formulated to derive an ARM A simulation algorithm from the prior AR approximation by relying on the minimization of frequency domain errors. Finally, these procedures are critically assessed and an example of application is presented.
Eigenvalue Inclusion Principles for Discrete Gyroscopic Systems
Authors: Yang B.
Published: April 2008

In his famous treatise The Theory of Sound, Rayleigh enunciated an eigenvalue inclusion principle for modified discrete nongyroscopic systems. According to this principle, the natural frequencies of a nongyroscopic system without and with modification are alternatively located along the positive real axis. Although vibration and dynamics of discrete gyroscopic systems have been extensively studied, the problem of inclusion principles for discrete gyroscopic systems has not been addressed. This paper presents several eigenvalue inclusion principles for a class of discrete gyroscopic systems. A transfer function formulation is proposed to describe modified gyroscopic systems. Six types of modifications and their effects on the system natural frequencies are studied. It is shown that the transfer function formulation provides a systematic and convenient way to handle modification problems for discrete gyroscopic systems.
The Elastic Potentials for Coplanar Interaction Between an Infinitesimal Prismatic Dislocation Loop and a Circular Crack for Transverse Isotropy
Authors: Hanson M. T.
Published: April 2008

This paper gives a closed-form evaluation in terms of elementary functions for the title problem of coplanar dislocation—crack interaction. The two cases of an external and internal crack are considered and the potential for each is found for an isotropic material. The similarity between isotropy and transverse isotropy is discussed in the beginning sections and is used to write the corresponding potential for a transversely isotropic material from the isotropic result.
A Multiaxial Stochastic Constitutive Law for Concrete: Part I—Theoretical Development
Authors: Fafitis A. , Won Y. H.
Published: April 2008

An incremental three-dimensional constitutive relation for concrete has been developed. The linear anisotropic and path-dependent behavior is modeled by updating the stiffness matrix at each load increment. The material is assumed incrementally elastic and the six elastic moduli E11, E12 .... E33 are expressed in terms of both the tangential hydrostatic and deviatoric stiffness whereas the three tangential shear moduli are expressed in terms of the deviatoric stiffness only. The hydrostatic and deviatoric stiffness are determined from uniaxial stress-strain relationships by employing the space truss concept. The unaxial stress-strain relationships are in a sense the stress-strain relationships of the members of the truss, and they were based on a rheological stochastic model developed earlier. The predictions of the model compare favorably with experimental data reported by various investigators. Complex loading paths are reproduced with acceptable accuracy as is demonstrated in the second part of this paper.
A Multiaxial Stochastic Constitutive Law for Concrete With Dilatancy: Part II—Comparison With Experimental Data
Authors: Won Y. H. , Fafitis A.
Published: April 2008

The salient features and concepts of a model developed in Part I of this paper are reviewed. The model is extended to include dilatancy and shear compaction which are determined from uniaxial stress-strain relationships. The parameters of the model are the peak stress, initial elastic modulus, and tangential Poisson’s ratio. The peak stress is assumed equal to the compressive strength of the concrete specimen, the initial elastic modulus and the Poisson’s ratio is calculated by proposed empirical formulas. Predictions of the model compare favorably with experimental data reported by various investigators. Responses of concrete specimens subjected to prescribed triaxial proportional stresses, triaxial proportional strains and stresses, hydrostatic plus stress combinations with loading paths on the deviatoric stress plane, biaxial compressive, biaxial tensile, and uniaxial tensile loadings are predicted and compared with test data. All predictions are satisfactory.
Asymmetric Shielding in Interfacial Fracture Under In-Plane Shear
Authors: Liechti K. M. , Chai Y. S.
Published: April 2008

The toughness of a glass/epoxy interface was measured over a wide range of mode mixes. A toughening effect was associated with increasing positive and negative inplane shear components. Optical interference measurements of normal crack opening displacements near the crack front and complementary finite element analyses were used to examine near-front behavior during crack initiation. Estimates of the toughening based on plastic dissipation, bulk viscoelastic dissipation, and interface asperity shielding did not fully account for the measured values. The results suggest that the inelastic behavior of the epoxy, frictional, and, perhaps, three-dimensional effects should be considered.
Target Configurations for Plate-Impact Recovery Experiments
Authors: Chang S. N. , Chung D.-T. , Li Y.-F. , Nemat-Nasser S.
Published: April 2008

Normal plate impact recovery experiments have been perfomed on thin plates of ceramics, with and without a back momentum trap, in a one-stage gas gun. The free-surface velocity of the momentum trap was measured, using a normal velocity (or displacement) interferometer. In all recovered samples, cross-shaped cracks were seen to have been formed during the impact, at impact velocities as low as 27 m/s, even though star-shaped flyer plates were used. These cracks appear to be due to in-plane tensile stresses which develop in the sample as a result of the size mismatch between the flyer plate and the specimen (the impacting area of the flyer being smaller than the impacted area of the target) and because of the free-edge effects. Finite element computations, using PRONTO-2D and DYNA-3D, based on linear elasticity, confirm this observation. Based on numerical computations, a simple configuration for plate impact experiments is proposed, which minimizes the inplane tensile stresses allowing recovery experiments at much higher velocities than possible by the star-shaped flyer plate configuration. This is confirmed by normal plate impact recovery experiments which produced no tensile cracks at velocities in a range where the star-shaped flyer invariably introduces cross-shaped cracks in the sample. The new configuration includes lateral as well as longitudinal momentum traps.
Two-Dimensional Green’s Functions for Elastic Bi-materials
Authors: Carvalho J. L. , Curran J. H.
Published: April 2008

Two-dimensional plane-strain fundamental solutions for elastic bi-materials are developed using the nuclei of strain method. The method is a reduction of the threedimensional approach previously derived by Vijayakumar and Cormack. The structure of the three-dimensional solution is preserved and the two-dimensional nuclei of strain and their corresponding vector functions are reported in this paper. Application of these solutions to the boundary element method is demonstrated via a hydraulic fracturing example.
On the Role of Elastic Constants in Multiphase Contact Problems
Authors: Neumeister J. M.
Published: April 2008

For a plane composite body consisting of an arbitrary number of different linearly elastic constituents under conditions of plane deformation or plane stress, the minimum number of required elastic constants describing the stress field is determined. For conditions in accordance with the assumptions of Michell and Dundurs, i.e., for prescribed surface tractions and no net forces on internal boundaries, the state of stress in a body involving N different phases is found to be determined by only 2N-2 combinations of the elastic constants. This result holds for conditions of complete adhesion and frictionless slip at the interfaces of the materials.
Three-Dimensional Slightly Nonplanar Cracks
Authors: Gao Huajian
Published: April 2008

Three-dimensional slightly nonplanar cracks are studied via a perturbation method valid to the first-order accuracy in the deviation of the crack shape from a perfectly planar reference crack. The Bueckner-Rice crack-face weight functions are used in the perturbation analysis to establish a relationship, within first-order accuracy, between the apparent and local stress intensity factors for the nonplanar crack. Perturbation solutions for a cosine wavy crack with arbitrary wavelengths are used to examine the effects of three T-stress components, Txx, TXZ, TZZ, on the stability of a mode 1 planar crack in the x-z plane with front lying along the z-axis. A condition for the mode 1 crack to be stable against three-dimensional wavy perturbations of wavelengths λx and λz is determined as Txx + Tzzg < 0 where g is negative, with a very small magnitude, for 0<λx/λz<1/3 and positive for 1/3<λx/λz<∞; this suggests that when Txx = 0, a compressive stress Tzz may cause crack deflection with large wavelengths parallel to the crack front and a tensile stress Tzz may cause deflection with small wavelengths parallel to the front. For comparable T-stress values, it is shown that a negative Txx always enhances the stability of a mode 1 planar crack and a negative Tzz ensures the stability of a mode 1 crack against perturbations parallel to the crack front. The shear component Txz, while not affecting the mode 1 path stability, induces a mode 3 stress intensity factor once crack deflection occurs, and thus promotes the formation of en echelon-type cracking patterns.
A New Boundary Integral Equation Formulation for Linear Elastic Solids
Authors: Wu Kuang-Chong , Chiu Yu-Tsung , Hwu Zhong-Her
Published: April 2008

A new boundary integral equation formulation is presented for two-dimensional linear elasticity problems for isotropic as well as anisotropic solids. The formulation is based on distributions of line forces and dislocations over a simply connected or multiply connected closed contour in an infinite body. Two types of boundary integral equations are derived. Both types of equations contain boundary tangential displacement gradients and tractions as unknowns. A general expression for the tangential stresses along the boundary in terms of the boundary tangential displacement gradients and tractions is given. The formulation is applied to obtain analytic solutions for half-plane problems. The formulation is also applied numerically to a test problem to demonstrate the accuracy of the formulation.
A Solution Procedure for Laplace’s Equation on Multiply Connected Circular Domains
Authors: Bird M. D. , Steele C. R.
Published: April 2008

A solution procedure is presented for the two-dimensional Laplace’s equation on circular domains with circular holes and arbitrary boundary conditions. The shape functions use the traditional trigonometric Fourier series on the boundaries with a power series decay into the domain thereby satisfying the governing equation exactly. The interaction of the boundaries is expressed simply and exactly resulting in quick processing time. The only simplification made is the use of a finite number of terms in the boundary conditions. The results are compared with a Green’s function method due to Naghdi (1991) and a Mo¨bius transformation method due to Honein et al. (1991).
On Cauchy’s Mean Rotation
Authors: Zheng Q.-S. , Hwang K. C.
Published: April 2008

In this paper, a new treatment of Cauchy’s measure of mean rotation in continuum mechanics is given, a representation theorem is proved, and the connection between Cauchy’s measure and the finite rotation tensor is established. Cauchy’s and Novozhilov’s measures of mean rotation are compared.
The Geometry of Virtual Work Dynamics in Screw Space
Authors: Peterson Steven
Published: April 2008

In this paper, screw theory is employed to develop a method for generating the dynamic equations of a system of rigid bodies. Exterior algebra is used to derive the structure of screw space from projective three space (homogeneous coordinate space). The dynamic equation formulation method is derived from the parametric form of the principle of least action, and it is shown that a set of screws exist which serves as a basis for the tangent space of the configuration manifold. Equations generated using this technique are analogs of Hamilton’s dynamical equations. The freedom screws defining the manifold’s tangent space are determined from the contact geometry of the joint using the virtual coefficient, which is developed from the principle of virtual work. This results in a method that eliminates all differentiation operations required by other virtual work techniques, producing a formulation method based solely on the geometry of the system of rigid bodies. The procedure is applied to the derivation of the dynamic equations for the first three links of the Stanford manipulator.
On the Dynamics of a Conservative Elastic Pendulum
Authors: Gans Roger F.
Published: April 2008

This paper presents a finite element model of the elastica, without dissipation, in a form realizable in the laboratory: a set of rigid links connected by torsion springs. The model is shown to reproduce the linear elastic behavior of beams. The linear beam, and most nonlinear beams are not periodic. (The linear eigenfrequencies are incommensurate.) They do exhibit a basic cyclic behavior, the beam waving back and forth with a measurable period. Extensive exploration of the behavior of a fourlink model reveals windows of periodicity—isolated points in parameter space where the motion is nearly periodic. (The basic phase plane diagrams are asymmetric, and the time evolution of the motion distributes this asymmetry symmetrically in time.) The first such window shows a period twice the basic cycle time, the next, less well observed one, four times the basic cycle time.