bluuebunny/crossref_metadata_2025 huggingface dataset:
Description of Nonproportional Cyclic Plasticity of Stainless Steel by a Two-Surface Model
Authors: Takahashi Yukio , Ogata Takashi
Published: April 2008

A simple elastic-plastic constitutive model based on the two-surface theory is developed to describe deformation behavior of austenitic stainless steels under multiaxial cyclic loading. Dependency of saturated stress range both on strain range and the proportionality of loading is considered. To establish a precise procedure for determination of material constants for nonproportional loading, the intervariable relation in the axial-torsional circular strain-path condition is studied in detail. A full procedure is then developed for determination of all material parameters. Finally, the effectiveness of the present model is demonstrated by application to axial-torsional cyclic tests for type 304 stainless steel at 550°C.
Reflection and Transmission of Rayleigh Surface Waves by a Material Interphase
Authors: Li Z. L. , Achenbach J. D.
Published: April 2008

Reflection and transmission of Rayleigh surface waves by a juncture normal to the free surface, between identical or different materials, has been investigated. The juncture, which may be an interface containing defects or a thin layer, is represented by a layer of extensional and shear springs. The mathematical statement of the problem is reduced to a system of singular integral equations for the displacements on the free surface and the tractions and the displacements across the juncture. Numerical solutions of this system have been computed by the use of the boundary element method. Expressions for the reflection and transmission coefficients have subsequently been obtained by the use of half-plane Green’s functions in conjunction with an elastodynamic representation integral. Results are presented for selected values of the elastic constants of the joined bodies and the stiffness parameters of the juncture.
Transient Analysis for Antiplane Crack Subjected to Dynamic Loadings
Authors: Ma Chien-Ching , Hou Ying-Chung
Published: April 2008

The problem considered here is the antiplane response of an elastic solid containing a half-plane crack subjected to suddenly applied concentrated point forces acting at a finite distance from the crack tip. A fundamental solution for the dynamic dislocation is obtained to construct the dynamic fracture problem containing a characteristic length. Attention is focused on the time-dependent full-field solutions of stresses and stress intensity factor. It is found that at the instant that the first shear wave reaches the crack tip, the stress intensity factor jumps from zero to the appropriate static value. The stresses will take on the appropriate static value instantaneously upon arrival of the shear wave diffracted from the crack tip, and this static value is thereafter maintained. The dynamic stress intensity factor of a kinked crack from this stationary semi-infinite crack after the arrival of shear wave is obtained in an explicit form as a function of the kinked crack velocity, the kink angle, and time. A perturbation method, using the kink angle as the perturbation parameter, is used. If the maximum energy release rate is accepted as the crack propagation criterion, then the crack will propagate straight ahead of the original crack when applying point load at the crack face.
A Modified Transfer Matrix Method for Linear Rotor-Bearing Systems
Authors: Lee An-Chen , Kang Yuan , Liu Shin-Li
Published: April 2008

The steady-state responses of linear flexible rotor-bearing systems are analyzed by the modified transfer matrix method. The transfer matrix has the advantage of solving the problems in frequency domain with fixed matrix size. This makes the method more economical in analyzing a large degree-of-freedom rotor system than many time-marching integrating methods. In this paper, the modifications of transfer matrix method include that the transfer matrix of shaft is derived from the “continuous system” concept instead of conventional “lumped system” concept, and the paper tries to extend the transfer matrix method to fit synchronous elliptical orbit and nonsynchronous multi-lobed whirling orbit. To demonstrate the applications of the method, three examples are presented; two synchronous and one nonsynchronous.
Measurements of Velocity, Velocity Fluctuation, Density, and Stresses in Chute Flows of Granular Materials
Authors: Ahn Hojin , Brennen Christopher E. , Sabersky Rolf H.
Published: April 2008

Experiments on continuous, steady flows of granular materials down an inclined channel or chute have been conducted with the objectives of understanding the characteristics of chute flows and of acquiring information on the rheological behavior of granular material flow. Two neighboring fiber-optic displacement probes provide a means to measure (1) the mean velocity by cross-correlating two signals from the probes, (2) the unsteady or random component of the particle velocity in the longitudinal direction by a procedure of identifying particles, and (3) the mean particle spacing at the boundaries by counting the frequency of passage of the particles. In addition, a strain-gauged plate built into the chute base has been employed to make direct measurement of shear stress at the base. With the help of these instruments, the vertical profiles of mean velocity, velocity fluctuation, and linear concentration were obtained at the sidewalls. Measurements of some basic flow properties such as solid fraction, velocity, shear rate, and velocity fluctuation were analyzed to understand the characteristics of the chute flow. Finally, the rheological behavior of granular materials was studied with the experimental data. In particular, the rheological models of Lun et al. (1984) for general flow and fully developed flow were compared with the present data.
Downstream Development of Viscous Fluid Wakes Behind Rod-Like Bodies
Authors: Marshall Jeffrey S.
Published: April 2008

A new theory of viscous fluid wakes behind rod-like bodies is presented and is used to study the onset and downstream development of vortex street flows. Analytical solutions are obtained for the evolution of wave number, mean centerline velocity, vortex velocity, and vortex “spacing ratio” as a function of downstream distance in a laminar vortex street. A simple criterion for the onset of oscillations in the far wake, which slightly precede vortex street initiation, is also obtained. All of these solutions account for the action of viscous diffusion in spreading the street, and they are found to compare quite well with available experimental results.
The Generalized Cell Mapping Method in Nonlinear Random Vibration Based Upon Short-Time Gaussian Approximation
Authors: Sun J. Q. , Hsu C. S.
Published: April 2008

A short-time Gaussian approximation scheme is proposed in the paper. This scheme provides a very efficient and accurate way of computing the one-step transition probability matrix of the previously developed generalized cell mapping (GCM) method in nonlinear random vibration. The GCM method based upon this scheme is applied to some very challenging nonlinear systems under external and parametric Gaussian white noise excitations in order to show its power and efficiency. Certain transient and steady-state solutions such as the first-passage time probability, steady-state mean square response, and the steady-state probability density function have been obtained. Some of the solutions are compared with either the simulation results or the available exact solutions, and are found to be very accurate. The computed steady-state mean square response values are found to be of error less than 1 percent when compared with the available exact solutions. The efficiency of the GCM method based upon the short-time Gaussian approximation is also examined. The short-time Gaussian approximation renders the overhead of computing the one-step transition probability matrix to be very small. It is found that in a comprehensive study of nonlinear stochastic systems, in which various transient and steady-state solutions are obtained in one computer program execution, the GCM method can have very large computational advantages over Monte Carlo simulation.
A Study of Belleville Spring and Diaphragm Spring in Engineering
Authors: Zhiming Ye , Kaiyuan Yeh
Published: April 2008

This paper deals with the static response of a Belleville spring and a diaphragm spring by using the finite rotation and large deflection theories of a beam and conical shell, and an experimental method as well. The authors propose new mechanical analysis mathematical models. The exact solution of a variable width cantilever beam is obtained. By using the integral equation method and the iterative method to solve the simplified equations and Reissner’s equations of finite rotation and large deflection of a conical shell, this paper has calculated a great number of numerical results. The properties of loads, strains, stresses and displacements, and the distribution rules of strains and stresses of diaphragm springs are investigated in detail by means of the experimental method. The unreasonableness of several assumptions in traditional theories and calculating method is pointed out.
Elastic Field Due to a Dynamically Transforming Spherical Inclusion
Authors: Mikata Y. , Nemat-Nasser S.
Published: April 2008

As a first step towards a systematic study of the interaction between a stress-pulse traveling in transformation toughened ceramics and possible phase transformation of zirconia particles, a dynamic inclusion problem is investigated. An exact closed-form solution is obtained for the case of a spherical inclusion. With this result, the dynamic Eshelby tensors for the inside and outside fields of the spherical inclusion are defined and determined. It is confirmed that the static Eshelby tensor is obtained as a static limit of the dynamic Eshelby tensor. It is found in the numerical results that the frequency of the dynamic inclusion has a relatively large influence on the amplitudes of the stress components inside and outside the inclusion.
Force on a Piezoelectric Screw Dislocation
Authors: Pak Y. E.
Published: April 2008

A screw dislocation in a hexagonal crystal exhibiting piezoelectric behavior is analyzed in the framework of linear elasticity theory. Considered is a straight dislocation with the Burgers vector normal to the isotropic basal plane. In addition to having a discontinuous displacement and a discontinuous electric potential across the slip plane, the dislocation is subjected to a line force and a line charge at the core. The solution is obtained in a closed form by means of a semi-inverse method. The electric enthalpy which takes the place of the internal energy is calculated for the screw dislocation considered in the analysis. The interaction energy for two different internal stress-field systems is derived to calculate the force acting on an electroelastic singularity. Both the standard method and a generalized path-independent integral is used to calculate the force on a piezoelectric screw dislocation subjected to external mechanical and electrical loads. Also calculated are the force between two parallel screw dislocations and the image force due to a free surface.
Self-Similar Solution in Problems of Hydraulic Fracturing
Authors: Huang N. C. , Szewczyk A. A. , Li Y. C.
Published: April 2008

The problem of hydraulic fracturing in geological materials is investigated based on a model of the growth of a finite crack in an infinite and linearly elastic medium induced by fluid pressure. The fluid is injected into the crack through an injection well at the center of the crack. The surface of the crack is considered to be impermeable. Flow is present in the crack as the crack propagates. In this study, the fluid is considered to be inviscid and incompressible. Assumptions of a one-dimensional flow in the fracture and a plane-strain deformation of the medium are imposed. At the crack tip, the value of stress intensity factor is considered to be constant during crack propagation. Self-similarity is found in the solution. Crack length, crack profile, fluid pressure, and other related physical characteristics are evaluated as functions of time.
Stress Intensity Factor and Energy Release Rate for Interfacial Cracks Between Dissimilar Anisotropic Materials
Authors: Wu Kuang-Chong
Published: April 2008

The framework of fracture mechanics analysis for interface cracks as outlined by Willis (1971) is recast into a form resembling the customary framework for cracks in homogeneous materials. Based on the complex-valued “stress concentration vector” introduced by Willis, a new definition of real-valued stress intensity factors is introduced. The definition is an extension to that for cracks in homogeneous materials and reduces to the one given recently by Rice for isotropic interface cracks. In terms of the new stress intensity factors, tractions ahead of the crack and the relative crack face displacements given by Willis are rewritten into real-form expressions. The energy release rate obtained by Willis is also expressed into a real form in terms of the stress intensity factors. The validity of using the stress intensity factors as parameters controlling fracture is discussed along the line advanced by Rice (1988).
A General Algorithm for Multidimensional Cauchy Principal Value Integrals in the Boundary Element Method
Authors: Guiggiani M. , Gigante A.
Published: April 2008

This paper presents a new general method for the direct evaluation of Cauchy principal value integrals in several dimensions, which is an issue of major concern in any boundary element method analysis in applied mechanics. It is shown that the original Cauchy principal value integral can be transformed into an element-by-element sum of regular integrals, each one expressed in terms of intrinsic (local) coordinates. The actual computation can be performed by standard quadrature formulae and can be easily included in any existing computer code. The numerical results demonstrate the accuracy and efficiency of the method, along with its insensitivity to the mesh pattern. This new method has full generality and, therefore, can be applied in any field of applied mechanics. Moreover, there are no restrictions on the numerical implementation, as the singular integrals may be defined on surface elements or internal cells of any order and type.
Lamb Wave Propagation in Anisotropic Laminates
Authors: Liu G. R. , Tani J. , Watanabe K. , Ohyoshi T.
Published: April 2008

The wave propagation in arbitrary anisotropic laminates is investigated on the basis of an exact theory. The dispersion relations of Lamb waves are determined for graphite/epoxy symmetric angle-ply laminates and hybrid composite ones which consist of carbon/epoxy and glass/epoxy layers. The dispersion and anisotropy of phase velocities for fundamental modes are discussed in detail. The energy distributions in the thickness direction of laminates are calculated for each kind of Lamb wave. A hybrid composite laminate is found to have better capability in absorbing impact energy by analyzing the strain energy distribution during the wave propagation. The results of the strain energy distribution are useful in determining the arrangement and the fiber orientation of the layers of hybrid composite laminates.
A Three-Dimensional Constitutive Theory for Fiber Composite Laminated Media
Authors: Christensen R. M. , Zywicz E.
Published: April 2008

A three-dimensional elastic constitutive theory is developed for application to fiber composite laminated media. The lamina level constitutive relationship is a specific subset of general, transversely isotropic media behavior. This special class of lamina behavior permits the development of an exact lamination procedure for systems assembled from a single lamina type. The three-dimensional constitutive form for the laminate is determined in terms of the subscale lamina properties and the orientations of each lamina. The extension of this specific constitutive relationship to general transversely isotropic lamina involves separation of the five lamina-scale properties into fiber-dominated versus matrix-dominated classifications and the development of a generalized averaging procedure for the matrix-dominated properties. The resulting three-dimensional constitutive/lamination theory is evaluated through comparisons between exact solutions, using data bases appropriate for graphite and glass epoxy systems in quasi-isotropic layups. The theory remains highly effective through the transition from thin laminate to thick laminate behavior and even beyond that through the transition from thick laminate behavior to fully and strongly three-dimensional elastic behavior. The generalized averaging procedure for the matrix-dominated properties produces variations in results that are the same or less than the variations in results due to the experimental uncertainty in the matrix-dominated properties themselves. The theory is fairly simple and extremely versatile in its application.
Effect of Interphases on Micro and Macromechanical Behavior of Hexagonal-Array Fiber Composites
Authors: Achenbach J. D. , Zhu H.
Published: April 2008

The effect of interphase stiffness on microstresses and macromechanical behavior has been investigated for transverse loading of an hexagonal-array unidirectional fiber composite. The interphase is modeled by a layer which resists radial extension and circumferential shear deformation. Taking advantage of the periodicity of the medium, the states of stress, and deformation in a basic cell have been analyzed numerically by the use of the boundary element method. The circumferential tensile stress along the matrix side of the interphase and the radial stress in the interphase have been analyzed for various values of the interphase parameters and the fiber volume ratio. The micromechanical results have also been used to determine the effect of interphase stiffness on the effective moduli. The calculated values have been compared with analytical results that were adjusted for interphase stiffness.
A New Method for Determination of Bending Rigidities of Thin Anisotropic Plates
Authors: Gre´diac M. , Vautrin A.
Published: April 2008

The paper presents a new method to determine the six elastic bending rigidities of thin anisotropic plates. The experimental procedure only requires one plate specimen submitted to several bending tests performed on the same testing device. The data processing is based on the principle of virtual work and it is shown that simple linear relationships between the bending rigidities, applied loads, and plate curvature can be derived using particular virtual displacement fields. The unknown plate rigidities are the solution of a set of linear equations. The numerical simulations of various relevant bending configurations of anisotropic laminated plates point out the efficiency of this new approach.
Wave Propagation in a Multilayered Laminated Cross-Ply Composite Plate
Authors: Karunasena W. , Shah A. H. , Datta S. K.
Published: April 2008

Dispersion of guided waves in a cross-ply laminated plate has been studied here using a stiffness method and an exact method. It is shown that number of laminae strongly influences the dispersion behavior. Further, it is found that when the number of laminae is sufficiently large, then the dispersion behavior can be predicted by treating the plate as homogeneous with six stiffness constants obtained by using an effective modulus method.
Unraveling Paradoxical Theories for Rigid Body Collisions
Authors: Stronge W. J.
Published: April 2008

A collision between two rigid bodies has a normal impulsive reaction at the contact point (CP). If the bodies are slightly rough and the contact points have a relative tangential velocity (slip), there is also a frictional force that opposes slip. Small initial slip can halt before contact terminates; when slip halts the frictional force changes and the collision process is separated into periods before and after halting. An energetically consistent theory for collisions with slip that halts is based on the work done by normal (nonfrictional) forces during restitution and compression phases. This theory clearly separates dissipation due to frictional forces from that due to internal irreversible deformation. With this theory, both normal and tangential components of the impulsive reaction always dissipate energy during collisions. In contrast, Newton’s impact law results in calculations of paradoxical increases in energy for collisions where slip reverses. This law relates normal components of relative velocity for the CP at separation and incidence by a constant (the coefficient of restitution e). Newton’s impact law is a kinematic definition for e that generally depends on the slip process and friction; consequently it has limited applicability.
Dynamic Response and Buckling Failure Measures for Structures With Bounded and Random Imperfections
Authors: Lindberg H. E.
Published: April 2008

Comparisons between an unknown-but-bounded imperfection model and a random imperfection model show that for simple pointwise failure measures, at least, the two models give the same expressions for their measures of response, but each measure has a distinctly different interpretation. The former gives the maximum possible response for any imperfection within a specified bound. The latter gives the standard deviation of response, which, together with the statistical distribution, can be used to specify the maximum response at a specified confidence level. However, since the statistical distributions of imperfections, and hence of the response are often unknown, confidence levels are difficult to define, especially in the tail of the distribution at high confidence levels. The unknown-but-bounded model requires less information about the imperfections to come to a well-defined bound on response. It is further shown that, while the maximum possible response might seem to be a severe failure avoidance criterion, it can be less constricting than having to impose artificially high confidence levels with poorly known statistical distributions.
An Exact Solution of Oscillatory Couette Flow in a Rotating System
Authors: Mazumder B. S.
Published: April 2008

An exact solution of oscillatory Ekman boundary layer flow bounded by two horizontal flat plates, one of which is oscillating in its own plane and other at rest, is obtained. The effect of coriolis force on the resultant velocities and shear stresses for steady and unsteady flow has been studied.
Complete Crack-Tip Shielding of the Mode III Crack in a Work-Hardening Solid
Authors: Weertman J.
Published: April 2008

The crack-tip shielding stress intensity factor L, for the mode III crack in a work-hardening solid is equal to L = - K, where K is the applied stress intensity factor. That is, the crack tip is perfectly shielded. This result is shown two ways: from the dislocation shielding and from the dislocation crack extension force.
A Continuum Damage Model for Fracture of Brittle Solids Under Dynamic Loading
Authors: Fahrenthold E. P.
Published: April 2008

A continuum damage mechanics description of elastic-brittle fracture provides an appropriate constitutive model for impact simulations involving ceramic, rock, or similar materials. For an orthotropically damaged solid, a complementary energy function may be derived from a mesomechanical description of three orthogonal arrays of coalescing cracks. Damage evolution equations suggested by dynamic fracture test measurements may be expressed in terms of tensor power functions which generalize classical one-dimensional analyses. Measured Weibull strength distributions may be employed to account for flaw size distribution effects on the damage accumulation rate. The resulting model avoids the introduction of effective stress assumptions or the use of specialized material property coefficients obtained from nonstandard mechanical tests.
A Micromechanical Damage Model for Uniaxially Reinforced Composites Weakened by Interfacial Arc Microcracks
Authors: Ju J. W.
Published: April 2008

A micromechanical anisotropic damage model is presented for uniaxially reinforced (brittle matrix) composites weakened by an ensemble of (fiber/matrix) interfacial microcracks. All microcracks are assumed to occur along the fiber/matrix interfaces, and are modeled as arc microcracks under “cleavage 1” deformation processes. Microcrack-induced strains and overall elastic-damage compliances are analytically derived based on micromechanical bimaterial (interfacial) arc-microcrack opening displacements and mesostructural probabilistic distributions. Both “stationary” and “evolutionary” damage models are given. In particular, microcrack kinetic equations are constructed based on micromechanical fracture criterion and mesostructural geometry in a representative volume element. Simple and efficient computational algorithms as well as some numerical uniaxial tension tests are also presented. Finally, it is noted that not a single arbitrary (fitted) “material constant” is employed in the present work.
Three-Dimensional Stress Fields of Elastic Interface Cracks
Authors: Nakamura T.
Published: April 2008

Various aspects of stress fields near an interface crack in three-dimensional bimaterial plates are investigated. Due to the nature of the resulting deformation field, three-dimensional effects are more critical in a bimaterial plate than in a homogeneous plate. In the close vicinity of the crack front, the stress field is characterized by the asymptotic bimaterial K-field, and its domain size is a very small fraction of a plate thickness. Unlike a homogeneous case, the asymptotic field always consists all three modes of fracture, and an interface crack must propagate under mixed-mode conditions. Furthermore, computational results have shown that the two phase angles representing the relative magnitudes of the three modes strongly depend on the bimaterial properties. It has been also observed that a significant antiplane (Mode III) deformation exists along the crack front, especially near the free surface. Since experimental investigations have shown that critical energy release rate Gc is highly dependent on the phase angles, accurate prediction of the interface fracture behavior requires not only the G distribution but also the variations of phase angles along the crack front.
Dynamic Response of an Orthotropic Half-Space With a Subsurface Crack: In-Plane Case
Authors: Karim M. R. , Kundu T.
Published: April 2008

Scattering of elastic waves by a subsurface crack in an orthotropic half-space subjected to a surface line load of arbitrary angle of inclination is studied. Green’s functions are developed and used along with the representation theorem to reduce the problem to a set of simultaneous singular integral equations in the Fourier transformed domain. Solution to these equations is then obtained by expanding the unknown crack opening displacement (COD) in terms of Chebyshev polynomials. Numerical results are given for specific examples involving orthotropic materials.
A Solution of the Mixed Boundary Value Problem for an Infinite Plate With a Hole Under Uniform Heat Flux
Authors: Hasebe Norio , Irikura Hideaki , Nakamura Takuji
Published: April 2008

A general solution of the mixed boundary value problem with displacements and external forces given on the boundary is obtained for an infinite plate with a hole subjected to uniform heat flux. Complex stress functions, a rational mapping function, and the dislocation method are used for the analysis. The stress function is obtained in a closed form and the first derivative is given by such a form that does not contain the integral term. The mapping function is represented in the form of a sum of fractional expressions. A problem is solved for a crack initiating from a point of a circular hole on which the displacement is rigidly stiffened. Stress distributions and stress intensity factors are calculated.
Boundary Conditions for Rapid Granular Flow: Flat, Frictional Walls
Authors: Jenkins J. T.
Published: April 2008

We employ Coulomb friction and both tangential and normal restitution in a model for a collision between a homogeneous sphere and a flat wall. We calculate the impulse and change in kinetic energy in typical collisions and use a particularly simple velocity distribution function to obtain the rates at which momenta and energy are supplied to the flow over a unit area of the wall. From these, we determine boundary conditions that relate the shear stress and energy flux in the flow at the wall to the normal stress, slip velocity, and fluctuation energy and to the parameters that characterize a collision.
A Viscoelastic Model for the Dynamic Behavior of Saturated Poroelastic Soils
Authors: Bardet J. P.
Published: April 2008

A viscoelastic model is proposed to describe the dynamic response of the saturated poroelastic materials that obey the Biot theory (1956). The viscoelastic model is defined from the velocity and attenuation of dilatational and distortional waves in poroelastic materials. Its material properties are defined in terms of the elastic moduli, porosity, specific gravity, degree of saturation, and permeability of the soils. The proposed model is tested by comparing its response with the one of poroelastic materials in the case of axial and lateral harmonic loadings of one-dimensional columns. The viscoelastic model is simpler to use than poroelastic materials but yields similar results for a wide range of soils and dynamic loadings.
Inertially Coupled Galloping of Iced Conductors
Authors: Yu P. , Shah A. H. , Popplewell N.
Published: April 2008

This paper is concerned with the galloping of iced conductors modeled as a two-degrees-of-freedom system. It is assumed that a realistic cross-section of a conductor has eccentricity; that is, its center of mass and elastic axis do not coincide. Bifurcation theory leads to explicit asymptotic solutions not only for the periodic solutions but also for the nonresonant, quasi-periodic motions. Critical boundaries, where bifurcations occur, are described explicitly for the first time. It is shown that an interesting mixed-mode phenomenon, which cannot happen in cocentric cases, may exist even for nonresonance.
Nonlinear Vibrations of Piecewise-Linear Systems by Incremental Harmonic Balance Method
Authors: Lau S. L. , Zhang W.-S.
Published: April 2008

The incremental harmonic balance (IHB) method is extended to analyze the periodic vibrations of systems with a general form of piecewise-linear stiffness characteristics. An explicit formulation has been worked out. This development is of significance as many structural and mechanical systems of practical interest possess a piecewise-linear stiffness. Typical examples show that the IHB method is very effective for analyzing this kind of systems under steady-state vibrations.
The Pseudo-Shakedown of Beams and Plates When Subjected to Repeated Dynamic Loads
Authors: Shen Wei Qin , Jones Norman
Published: April 2008

A conjecture is derived in this paper for the pseudo-shakedown phenomenon of beams and plates which strengthen with finite displacements when subjected to repeated dynamic transverse loads causing material plastic flow and permanent deflections. This behavior is illustrated for a fully clamped, rigid, perfectly plastic beam which is subjected to a repeatedly applied, rectangular-shaped pressure-time history at the midspan. It transpires that a curve divides the dynamic load magnitude-pulse duration time area into two regions where pseudo-shakedown may or may not occur. Another curve in the region where pseudo-shakedown does not occur identifies when the dynamic problem may be studied with a static analysis.
Stability Properties of a Viscoelastic Column Under a Periodic Force
Authors: Cederbaum G. , Mond M.
Published: April 2008

The dynamic stability of a viscoelastic column subjected to a periodic longitudinal load is investigated. The viscoelastic behavior is given in terms of the Boltzmann superposition principle which yields an integro-differential equation of motion. The stability boundaries of this equation are determined analytically by using the multiplescales method. It is shown that due to the viscoelasticity the stability regions are expanded, relative to the elastic ones, and the time for which a stable system becomes unstable is given. In addition, the stability properties of the viscoelastic column are time dependent and an initially stable system can turn unstable after a finite time, unlike columns that are described by the elastic model.
Effect of Strain Hardening and Rate Sensitivity on the Dynamic Growth of a Void in a Plastic Material
Authors: Ortiz M. , Molinari A.
Published: April 2008

The problem studied in this paper concerns the dynamic expansion of a spherical void in an unbounded solid under the action of remote hydrostatic tension. The void is assumed to remain spherical throughout the deformation and the matrix to be incompressible. The effects of inertia, strain hardening, and rate sensitivity on the short and long-term behavior of the void, as well as on its response to ramp loading, are investigated in detail.
A Complete Acoustic Microscopical Analysis of Multilayered Specimens
Authors: Kundu T.
Published: April 2008

A theoretical analysis is carried out to synthesize the V(z) curves of multilayered solids immersed in water. Solid layers attenuate ultrasound and change its phase. A liquid layer may be located in between two solid layers. The goal of this analysis is to avoid the three major simplifying assumptions of the presently available techniques, as paraxial approximation, assumption of perfect reflection and ambiguous pupil function or incident field strength variation in the illuminated region. Presently available techniques developed for conventional acoustic microscopes can avoid some but not all of these assumptions for computing the V(z) curve. In this paper, the analysis is carried out for a spherical cavity lens with a large aperture angle. The V(z) curve for a uniform glass half-space is synthesized analytically and compared with experimental results. Analytical results are also presented for chromium plated glass specimens and biological cells on uniform glass half-space. Such an exact analysis of multilayered specimens is necessary for material science research as well as cell research in biology, because advanced engineering composite materials and biological cells in culture have multiple layers.
The Influence of Thermal Deformation on the Contact Temperature of Sliding Asperities
Authors: Lu C.-J. , Bogy D. B.
Published: April 2008

The effect of thermal deformation on contact temperature is investigated by considering a spherical asperity sliding on the surface of a semi-infinite insulated solid. The usual assumption that thermal deformation does not change the contact conditions is examined. The problem is mathematically formulated using appropriate Green’s functions to derive singular integral equations for the contact pressure. The relations between the radius of contact area, indentation, surface temperature, and moving velocity are calculated. A two asperities model is used to explain the load partition due to thermal deformation.
The Elastic Field for Conical Indentation Including Sliding Friction for Transverse Isotropy
Authors: Hanson M. T.
Published: April 2008

This paper gives closed-form expressions in terms of elementary functions for the title problem of conical indentation of elastic bodies possessing transverse isotropy. Traction in the contact region is also included in the form of Coulomb friction; thus, the shear stress is taken proportional to the contact pressure. The present expressions are derived here by integration of the point force Green’s functions.
Analysis of Acoustic Pulses Reflected From Fiber-Reinforced Composite Laminates
Authors: Mal A. K. , Yin C.-C. , Bar-Cohen Y.
Published: April 2008

The time histories and spectral characteristics of acoustic pulses reflected from fiberreinforced composite laminates immersed in water are recorded in the laboratory and analyzed through a generalized ray theory and an exact theory. Calculated results for an unidirectional laminate and two angle-ply laminates are compared with measured data. It is shown that for a unidirectional laminate a finite number of mode-converted waves contribute to the overall signal reflected from a thick specimen resulting in certain irregular behavior of the reflected pulses. A phenomenological model of wave attenuation is introduced in the theoretical simulation and the damping parameters are shown to have a strong influence on the amplitude of the reflected pulses. The phase velocity of the guided waves in the laminates are shown to be nearly independent of water loading and material dissipation in a broad frequency range. Agreement between measured and calculated results is found to be excellent to very good in all cases.
A Variational Approach to Three-Dimensional Elasticity Solutions of Laminated Composite Plates
Authors: Savoia M. , Reddy J. N.
Published: April 2008

The displacements in a laminated composite are represented as products of two sets of unknown functions, one of which is only a function of the thickness coordinate and the other is a function of the in-plane coordinates (i.e., separation of variables approach), and the minimization of the total potential energy is reduced to a sequence of iterative linear problems. Analytical solutions are developed for cross-ply and angle-ply laminated composite rectangular plates. The solution for simply-supported cross-ply plates under sinusoidal transverse load reduces to that of Pagano. Numerical results for stresses and displacements for antisymmetric angle-ply laminates are presented. The three-dimensional elasticity solutions developed are important because they can be used to study the behavior of composite laminates, in addition to serving as reference for approximate solutions by numerical methods and twodimensional theories.
Exact Solutions for the Analysis of General Elastically Restrained Nonuniform Beams
Authors: Lee Sen Yung , Kuo Yee Hsiung
Published: April 2008

The exact solutions for the problems governed by a general self-adjoint fourth-order nonhomogeneous ordinary differential equation with arbitrarily polynomial varying coefficients and general elastic boundary conditions are derived in Green’s function form. To illustrate the analysis, the static deflection and dynamic analysis of a general eiastically end restrained Bernoulli-Euler beam with polynomial varying bending rigidity, applied axial and force, and elastic foundation modulus along the beam, subjected to an arbitrary transverse force are presented. The Green’s function is concisely expressed in terms of the four normalized fundamental solutions of the system and these fundamental solutions are given in power series forms. The characteristic equations for elastic stability and free vibrational analysis of the beam can be obtained by setting the denominator of the corresponding Green’s function equal to zero. Finally, examples are given to illustrate the accuracy and efficiency of the analysis.
Simulation of Homogeneous Two-Dimensional Random Fields: Part II—MA and ARMA Models
Authors: Spanos Pol D. , Mignolet Marc P.
Published: April 2008

Alternatively to the autoregressive (AR) models examined in Part I, the determination of moving average (MA) algorithms for simulating realizations of twodimensional random fields with a specified (target) power spectrum is presented. First, the mathematical form of these models is addressed by considering infinitevariate vector processes of an appropriate spectral matrix. Next, the MA parameters are determined by relying on the maximization of an energy-like quantity. Then, a technique is formulated to derive an autoregressive moving average (ARMA) simulation algorithm from a prior MA approximation by relying on the minimization of frequency domain errors. Finally, these procedures are critically assessed and an example of application is presented.
Weakly Nonlinear Instability of a Liquid Jet in a Viscous Gas
Authors: Ibrahim E. A. , Lin S. P.
Published: April 2008

The weakly nonlinear instability of a viscous liquid jet emanated into a viscous gas contained in a coaxial vertical circular pipe is investigated as an initial-value problem. The linear stability theory predicted that the jet may become unstable either due to capillary pinching or due to interfacial stress fluctuation. The results of nonlinear stability analysis shows no tendency of supercritical stability for both of the linearly unstable modes. In fact, the nonlinear growth rate of the disturbance is faster than the exponential growth rate of the linear normal mode disturbance for the same flow parameters. Moreover, the most amplified linear normal mode disturbance evolves nonlinearly into a nonsinusoidal wave of shorter wavelength. No nonlinear instability is found for the linearly stable disturbances. Thus, while the linear theory is adequate for the prediction of the onset of jet breakup, nonlinear theory is required to describe the outcome of the jet breakup.
Thermal Stresses in Nonlinearly Viscoelastic Solids
Authors: Losi Giancarlo U. , Knauss Wolfgang G.
Published: April 2008

Three different rheological models are applied to the study of transient and residual thermal stresses in amorphous polymers cooled across the glass transition. The models differ mainly in their treatments of the nonequilibrium (time-dependent) portion of the morphological changes in the polymer and their influence on the relaxation process. The interstitial volume between polymer chains (free volume) is found to play an important role in the residual stresses; they are affected by the relative time scale of thermal diffusion and thermoviscoelastic relaxation/creep. This result has implications for injection molded parts of different section dimensions and for extrusion products. This fact must also be accounted for in determining the thermomechanicalproperties in the glass transition range. The step cooling ofPVAc spheres (1 and 20 mm dia.) and a cylinder (20 mm dia.) have been considered; most of the results presented apply to the sphere(s). Residual stresses can vary by as much as 100percent depending on whether the interstitial molecular (free) volume is counted or not. It is also demonstrated that residual stresses can be higher than an elastic analysis based on the glassy properties would suggest; thus the “stressfree temperature” is found to be significantly above the glass transition.
A Direct Method for the Shakedown Analysis of Structures Under Sustained and Cyclic Loads
Authors: Jiang W. , Leckie F. A.
Published: April 2008

This paper presents a straightforward method for the direct determination of the steady solutions in shakedown analysis. The direct method was first proposed by Zarka et al. This paper simplifies this method by showing that the modified hardening parameter field can be directly found from the yield condition and the incremental residual stress. Thus, only two elastic analyses are required to obtain the shakedown solutions without the need of performing a full-scale analysis. The two-bar structure and the tube problem are solved as examples to show the feasibility and efficiency of this approach.
A Theory of Plasticity for Porous Materials and Particle-Reinforced Composites
Authors: Qiu Y. P. , Weng G. J.
Published: April 2008

An energy criterion is introduced to define the effective stress of the ductile matrix, and with which Tandon and Weng’s (1988) theory of particle-reinforced plasticity is capable of predicting the desired plastic volume expansion under a pure hydrostatic tension. This modification also makes the theory suitable for application to porous materials at high triaxiality. Despite its simplicity, it offers a reasonable range of accuracy in the fully plastic state and is also versatile enough to account for the influence of pore shape. The theory is especially accurate when the work-hardening modulus of the ductile matrix is high, consistent with the concept of a linear comparison material adopted. If the matrix is also elastically incompressible, the theory with spherical voids is found to coincide with Ponte Castaneda’s (1991) lower bound for the strain potential (or upper bound in the sense of flow stress) of the Hashin-Shtrikman (1963) type, and with any other randomly oriented spheroidal voids, it provides an overall stress-strain relation which lies below this upper-bound curve. This energy approach is finally generalized to a particle-reinforced composite where the inclusions can be elastically stiffer or softer than the matrix, and it is also demonstrated that the prediction by the new theory is always softer than Tandon and Weng’s original one.
Textural and Micromorphological Effects on the Overall Elastic Response of Macroscopically Anisotropic Composites
Authors: Marzari Nicola , Ferrari Mauro
Published: April 2008

The Mori-Tanaka elastic response of composites with inclusions exhibiting nontrivial orientation distributions is studied. The effect of texture is evaluated for various fiber and matrix materials, various inclusion geometries, and in the presence of anisotropic fibers. In particular, the effect of misalignment is studied. The polyphase extension of the Mori-Tanaka theory is employed to determine the effective response of aligned composites containing defects of different morphologies.
Green’s Functions for Axisymmetric Problems of Dissimilar Elastic Solids
Authors: Hasegawa Hisao , Lee Ven-Gen , Mura Toshio
Published: April 2008

Green’s functions are obtained for axisymmetric body force problems of dissimilar elastic solids. The Green’s functions are defined as a solution to the problem of a dissimilar elastic solid subjected to axisymmetric body forces acting along a circle in a radial, a torsional, and an axial direction. As a special case of the present results, Green’s functions are obtained for problems of an elastic half-space with the free surface or rigidly fixed surface and of a homogeneous isotropic elastic solid. An application of the Green’s functions is investigated for an eigenstrain problem.
Stress Wave Radiation From a Crack Tip During Dynamic Initiation
Authors: Prakash V. , Freund L. B. , Clifton R. J.
Published: April 2008

Plate impact experiments are conducted to study the dynamic fracture processes which occur on submicrosecond time scales. These experiments involve the plane strain loading of a plane crack by a square tensile pulse with a duration of approximately one microsecond. The crack-tip loading rates achieved are K1 ˜ 108MPams−1, which are approximately two orders of magnitude higher than those obtained in other dynamic fracture configurations. Motion of the rear surface caused by waves diffracted from the stationary crack and by waves emitted by the running crack is monitored at four points ahead of the crack tip using a laser interferometer system. The measured normal velocity of the rear surface of the specimen agrees very well with the scattered fields computed using an assumed elastic viscoplastic model, except for the appearance of a sharp spike with a duration of less than 80 nanoseconds. This spike, which is not predicted by the inverse square root singular stress fields of linear elastic fracture mechanics, is understood to be related to the onset of crack growth and coincides with the abrupt and unstable ductile growth of a microstructural void to coalescence with the main crack. The crack initiation process is modeled as the sudden formation of a very small hole at the crack tip. This admits the possibility of dynamic crack-tip stress fields with crack-tip singularities stronger (˜r−3/2) than the inverse square root singular fields of fracture mechanics. The elastodynamic radiation resulting from the formation of a traction free hole at the crack tip is applied first to the case of antiplane shear deformation and then to the corresponding plane strain problem. The radiated fields predicted by the strongly singular solutions are found to be in good agreement with the spikes observed in the experiments. The radius of the hole, which appears as a parameter in the solution for the radiated field, agrees reasonably well with the interparticle spacing.