bluuebunny/crossref_metadata_2025 huggingface dataset:
Effects of State Recovery on Creep Buckling Under Variable Loading
Authors: Robinson D. N. , Arnold S. M.
Published: April 2008

Structural alloys embody internal mechanisms that allow recovery of state with varying stress and elevated temperature; that is, they can return to a softer state following periods of hardening. Such material behavior is known to strongly influence structural response under some important thermomechanical loadings; for example, those involving thermal ratcheting. Here, we investigate the influence of dynamic and thermal recovery on the creep buckling of a column under variable loading. The column is taken as the idealized (Shanley) sandwich column. The constitutive model, unlike the commonly employed Norton creep model, incorporates a representation of both dynamic and thermal (state) recovery. The material parameters of the constitutive model are chosen to characterize NARloy-Z, a representative copper alloy used in thrust nozzle liners of reusable rocket engines. Variable loading histories include rapid cyclic unloading/reloading sequences and intermittent reductions of load for extended periods of time; these are superimposed on a constant load. The calculated results show that state recovery significantly affects creep buckling under variable loading. Failure to account for state recovery in the constitutive relations can lead to nonconservative predictions of the critical creep-buckling time.
Effects of Crack Surface Heat Conductance on Stress Intensity Factors
Authors: Kuo An-Yu
Published: April 2008

Effects of crack surface heat conductance on stress intensity factors of modes I, II, and III are investigated. The crack problem is first solved by assuming perfect (infinite) heat conductance at crack surfaces. Finite heat conductance at crack surfaces is then accounted for by imposing a set of distributed dipoles at the crack surfaces. Distribution function of the dipoles is the solution of a Fredholm integral equation. It is shown that, for cracks in a homogeneous, isotropic, linear elastic solid, the degree of thermal conductivity at crack surfaces will affect the magnitude of mode I and mode II stress intensity factors but not mode III stress intensity factor. It is also shown that, for a geometrically symmetric cracked solid, only the mode II stress intensity factor will be influenced by different crack surface heat conductance even if the thermal loading is not symmetric. More importantly, for a given material thermal conductivity (K) and crack surface heat convection coefficient (h), effects of crack surface heat conductance on stress intensity factors is found to depend upon crack size. This “size effect” implies that, for a given set of K and h, an extremely small crack can be treated as if the crack surfaces are insulated and a very long crack can be treated as if the crack surfaces are perfectly heat conductive. As an example, the problem of a finite crack in an infinite plate subjected to a constant temperature gradient at infinity is studied.
Effect of Material Properties on the Stability of Static Thermoelastic Contact
Authors: Zhang Ronggang , Barber J. R.
Published: April 2008

When heat is conducted across an interface between two different materials, the interaction between thermoelastic distortion and thermal contact resistance can cause the system to be unstable. This paper investigates the influence of material properties on the stability criterion for an interface between two half planes. It is found that most material combinations exhibit one or other of two kinds of stability behavior. In one of these, the stability criterion is closely related to that for uniqueness of the steady-state solution and instability is only possible for one direction of heat flow. In the other, instability can occur for either direction of heat flow and in one case is characterized by the oscillatory growth of a pressure perturbation.
A High-Order Mixture Homogenization of Bi-laminated Composites
Authors: Murakami H. , Toledano A.
Published: April 2008

An asymptotic mixture theory of bi-laminated composites with periodic microstructure is presented for rate-independent inelastic responses, such as elastic-plastic deformation. Key elements are the modeling capability of simulating critical interaction between adjacent layers and the inclusion of the kinetic energy of microdisplacements. A variational procedure is adopted in order to construct a mixture model, which is deterministic, instead of phenomenological. The principle of virtual work is used for total quantities to construct mixture equations of motion, while Reissner’s mixed variational principle (1984, 1986) applied to rate boundary value problems is used to yield mixture constitutive relations. In order to assess the model accuracy in the time domain, the predicted values were compared with experimental and numerically exact data. Good agreements between the predicted and experimental or numerically exact data for plastic as well as elastic waves were observed.
On the Free Vibrations of Suspended Cables with Frictional End Restraint
Authors: Irvine H. M.
Published: April 2008

Results are obtained for the free vibrations of suspended cables for which longitudinal end restraint is supplied by friction. The problem is germane to submarine telecommunication cables. It is shown that all modes of vibration are independent of any characteristic dimensionless parameters, at least insofar as the linear theory applies to flat-sag cables, and the friction capability of the soil at the mudline is low. This sets the problem apart from the traditional, firmly founded suspended cable where, for some of the important in-plane modes, there is variability in the results. The theory is of importance in determining the vortex-induced vibratory response of suspended cable spans to currents of various sorts.
Nonclassically Damped Dynamic Systems: An Iterative Approach
Authors: Udwadia Firdaus E. , Esfandiari Ramin S.
Published: April 2008

This paper presents a new, computationally efficient, iterative technique for determining the dynamic response of nonclassically damped, linear systems. Such systems often arise in structural and mechanical engineering applications. The technique proposed in this paper is heuristically motivated and iteratively obtains the solution of a coupled set of second-order differential equations in terms of the solution to an uncoupled set. Rigorous results regarding sufficient conditions for the convergence of the iterative technique have been provided. These conditions encompass a broad variety of situations which are commonly met in structural dynamics, thereby making the proposed iterative scheme widely applicable. The method also provides new physical insights concerning the decoupling procedure and shows why previous approximate approaches for uncoupling nonclassically damped systems have led to large inaccuracies. Numerical examples are presented to indicate that, even under perhaps the least ideal conditions, the technique converges rapidly to provide the exact time histories of response.
On the Use of Approximation Methods for Microcrack Shielding Problems
Authors: Cai H. , Faber K. T.
Published: April 2008

There is experimental evidence that stress-induced microcracking near a macrocrack tip enhances the fracture toughness of brittle materials. In considering the interaction of the macrocrack with multiple microcracks using a discrete model, it is essential to use approximation methods in order to keep the amount of the computation to a tractable level. However, when crack distances are small, the results of the approximation methods can be significantly different from the numerical solution based upon the exact formulation. The results obtained by these approximation methods will be compared with the numerical solution to show the applicability ranges in which the errors are acceptably small. The use of results obtained by the approximation methods outside applicability ranges in literature is shown to lead to incorrect conclusions concerning microcrack shielding.
An Interlaminar Shear Stress Continuity Theory for Both Thin and Thick Composite Laminates
Authors: Lu Xianqiang , Liu Dahsin
Published: April 2008

The interlaminar shear stress plays a very important role in the damage of composite laminates. With higher interlaminar shear stress, delamination can easily occur on the composite interface. In order to calculate the interlaminar shear stress, a laminate theory, which accounts for both the interlaminar shear stress continuity and the transverse shear deformation, was presented in this study. Verification of the theory was performed by comparing the present theory with Pagano’s elasticity analysis. It was found that the present theory was able to give excellent results for both stresses and displacements. More importantly, the interlaminar shear stress can be presented directly from the constitutive equations instead of being recovered from the equilibrium equations.
Analysis of a Crack Bridged by a Single Fiber
Authors: Meda G. , Steif P. S.
Published: April 2008

With the goal of assessing the accuracy of a widely used approximate method of analyzing bridged matrix cracks, an idealized problem representing a crack bridged by a single fiber is studied in detail. Our solution technique, which accounts for frictional slip at the fiber-matrix interface explicitly, involves the use of distributions of edge dislocations to represent the opening of the crack faces and the slip at the interface. Through this method, the solution is reduced to a set of three coupled singular integral equations which are solved numerically. The results are compared with those from the approximate method, and some sources of discrepancy between the two results are explored.
A General Algorithm for the Numerical Solution of Hypersingular Boundary Integral Equations
Authors: Guiggiani M. , Krishnasamy G. , Rudolphi T. J. , Rizzo F. J.
Published: April 2008

The limiting process that leads to the formulation of hypersingular boundary integral equations is first discussed in detail. It is shown that boundary integral equations with hypersingular kernels are perfectly meaningful even at non-smooth boundary points, and that special interpretations of the integrals involved are not necessary. Careful analysis of the limiting process has also strong relevance for the development of an appropriate numerical algorithm. In the second part, a new general method for the evaluation of hypersingular surface integrals in the boundary element method (BEM) is presented. The proposed method can be systematically applied in any BEM analysis, either with open or closed surfaces, and with curved boundary elements of any kind and order (of course, provided the density function meets necessary regularity requirements at each collocation point). The algorithm operates in the parameter plane of intrinsic coordinates and allows any hypersingular integral in the BEM to be directly transformed into a sum of a double and a one-dimensional regular integrals. Since all singular integrations are performed analytically, standard quadrature formulae can be used. For the first time, numerical results are presented for hypersingular integrals on curved (distorted) elements for three-dimensional problems.
Two-Dimensional Rigid-Body Collisions With Friction
Authors: Wang Yu , Mason Matthew T.
Published: April 2008

This paper presents an analysis of a two-dimensional rigid-body collision with dry friction. We use Routh’s graphical method to describe an impact process and to determine the frictional impulse. We classify the possible modes of impact, and derive analytical expressions for impulse, using both Poisson’s and Newton’s models of restitution. We also address a new class of impacts, tangential impact, with zero initial approach velocity. Some methods for rigid-body impact violate energy conservation principles, yielding solutions that increase system energy during an impact. To avoid such anomalies, we show that Poisson’s hypothesis should be used, rather than Newton’s law of restitution. In addition, correct identification of the contact mode of impact is essential.
The Dynamics of a Nonharmonically Excited System Having Rigid Amplitude Constraints
Authors: Tung Pi-Cheng
Published: April 2008

We consider the dynamic response of a single-degree-of-freedom system having two-sided amplitude constraints. The model consists of a piecewise-linear oscillator subjected to nonharmonic excitation. A simple impact rule employing a coefficient of restitution is used to characterize the almost instantaneous behavior of impact at the constraints. In this paper periodic and chaotic motions are found. The amplitude and stability of the periodic responses are determined and bifurcation analysis for these motions is carried out. Chaotic motions are found to exist over ranges of forcing periods.
Decay Rates for the Hollow Circular Cylinder
Authors: Stephen N. G. , Wang M. Z.
Published: April 2008

The self-equilibrated end load problem for a hollow circular cylinder is considered using the Papkovitch-Neuber solution to the elastostatic displacement equations of equilibrium; both axi- and nonaxisymmetric solutions are derived. The requirement of zero traction on the surface generators of the cylinder leads to an eigenequation whose roots determine the rate of decay with axial coordinate. The locus of the smaller roots is plotted for circumferential harmonic loadings n = 0, 1, 2, and 3, for different wall thicknesses, and supplement previously known decay rates for the solid section and the circular cylindrical shell which are the extremes of diameter ratio. The loci are of considerable intricacy, and for small wall thickness, simple shell theory and two modes of decay for the semi-infinite plate are employed to identify the various modes of decay. Whereas for the solid cylinder the characteristic decay length of Saint-Venant’sprinciple is the radius (or diameter), for the hollow cylinder it becomes possible to discriminate between “wall thickness” and “rmt” modes of decay according to the limiting behavior as the cylinder assumes shell-like proportions; the one exception is “membrane bending” for which self-equilibrating end loading does not decay as thickness tends to zero.
Propagation of Rayleigh Waves in Magneto-Elastic Media
Authors: Lee Jong S. , Its Elizabeth N.
Published: April 2008

Propagation of Rayleigh waves in a perfectly conducting elastic half-space in the presence of magnetic fields is considered for a possible application in nondestructive measurements of mechanical and/or electromagnetic parameters in electromagnetic materials. In particular, the dependence of Rayleigh wave velocity on magnetic and elastic parameters of the conducting medium in tangentially and normally oriented primary magnetic fields is investigated. Numerical results for three elastic materials with different elastic parameters are presented for a range of magnetic permeability. It is shown that the effect of magnetic fields render the medium essentially anisotropic and that the magnetic permeability of the medium and the orientation of the primary magnetic field strongly affect the Rayleigh wave velocity field.
Stress Singularities at the Interface in Bonded Dissimilar Materials Under Mechanical and Thermal Loading
Authors: Munz D. , Yang Y. Y.
Published: April 2008

Stress singularities occur at the free edge of the interface of bonded dissimilar materials. General relations for a compound with 90-degree angles of the two materials are given for the parameters which describe the stress field. Differences between mechanical and thermal loadings are discussed.
Elastodynamic Response of a Unidirectional Composite Laminate to Concentrated Surface Loads: Part II
Authors: Lih Shyh-shiuh , Mal Ajit K.
Published: April 2008

The quantitative features of the elastodynamic field produced in a unidirectional graphite/epoxy composite laminate by surface loads are studied. The material of the composite is modeled as a transversely isotropic dissipative medium with its symmetry axis parallel to the laminate surface. The surface displacement produced by a transient concentrated point load on the surface of a uniform half-space and a plate of finite thickness is calculated by means of a multiple transform technique followed by inversion through numerical integration. The two-dimensional (plane-strain) line load problems for the plate are also solved as special cases. In addition, an approximate solution based on the classical plate bending theory which includes transverse shear and rotary inertia is obtained and the range of validity of the approximate solution is determined through comparison with the exact results. The multiple transform technique is shown to be a viable alternative to finite element and other numerically intensive computational schemes for wavefield calculations in composite laminates. The mathematical formulation of the problem was described in Part I of the paper, numerical treatment and results are presented in this part.
Liapunov Stability Analysis of Elastic Shaft-Rigid Disk-Bearing Systems
Authors: Huang H.-Y. , Schlack A. L.
Published: April 2008

A general method of analysis based on Liapunov’s direct method is presented for studying the dynamic stability of elastic shaft-rigid disk-bearing systems. A model comprised of a rigid disk rigidly attached at an arbitrary location along a flexible, rotating shaft which is mounted on two eight-component end bearings is used to develop stability criteria involving system stiffness and damping parameters. It is quantitatively shown by means of graphs for typical cases how the instability regions are reduced by (a) increasing the shaft dimensionless stiffness parameters, (b) increasing the bearing direct stiffness and damping parameters, (c) decreasing the bearing cross-coupling stiffness and damping parameters, (d) decreasing the mass ratio of the disk, and (e) increasing the disk’s radius ratio. These graphs present typical examples of the types of design information available to engineers through the equations provided in this paper. These graphs also verify that a two-modal term (N = 2) expansion is normally adequate to model the system deformations since the curves are not significantly altered by adding another term (N = 3) to the expansion. The critical value of the shaft dimensionless stiffness parameters is also studied.
On the Transitivity Equations of Rigid-Body Dynamics
Authors: Papastavridis John G.
Published: April 2008

This paper presents direct derivations of the various forms of the famous transitivity equations of rigid-body kinematics from a simple and unified viewpoint. These forms are indispensable in the derivation of the Eulerian (gyro) equations of motion via the Lagrangean (analytical mechanics) method. Both true (holonomic) and quasi (nonholonomic) coordinate forms are presented. A vectorial derivation of the Eulerian equations from the Central Equation and from Hamilton’s Principle is also included in the Appendix.
Dynamic Analysis of Flexible Gear Trains/Transmissions: An Automated Approach
Authors: Amirouche F. M. L. , Shareef N. H. , Xie M.
Published: April 2008

In this paper an automated algorithmic method is presented for the dynamic analysis of geared trains/transmissions. These are treated as a system of interconnected flexible bodies. The procedure developed explains the switching of constraints with time as a result of the change in the contacting areas at the gear teeth. The elastic behavior of the system is studied through the employment of three-dimensional isoparametric elements having six degrees-of-freedom at each node. The contact between the bodies is assumed at the various nodes, which could be either a line or a plane. The kinematical expressions, together with the equations of motion using Kane’s method, strain energy concepts, are presented in a matrix form suitable for computer implementation. The constraint Jacobian matrices are generated automatically based on the contact information between the bodies. The concepts of the relative velocity at the contacting points at the tooth pairs and the subsequent use of the transmission ratios in the analysis is presented.
Variational Formulation, Discrete Conservation Laws, and Path-Domain Independent Integrals for Elasto-Viscoplasticity
Authors: Simo J. C. , Honein T.
Published: April 2008

A discrete variational formulation of plasticity and viscoplasticity is developed based on the principle of maximum plastic dissipation. It is shown that the Euler-Lagrange equations (spatial conservation laws) emanating from the proposed discrete Lagrangian yield the equilibrium equation, the strain-displacement relations, the stress-strain relations, the discrete flow rule and hardening law in the form of closest-point-projection algorithm, and the loading/unloading conditions in Kuhn-Tucker form. Lack of invariance of the discrete Lagrangian relative to the group of material translations precludes the classical Eshelby law from being a conservation law. However, a discrete inhomogeneous form of Eshelby’s conservation law is derived which leads to a path-domain independent integral that generalizes the classical J-integral to elasto-viscoplasticity. It is shown that this path-domain independent integral admits a physical interpretation analogous to Budiansky and Rice interpretation of the classical J-integral.
Lode Dependences for Isotropic Pressure-Sensitive Elastoplastic Materials
Authors: Bardet J. P.
Published: April 2008

Experimental investigations indicate that the third stress invariant; Lode angle α affects significantly the behavior of pressure sensitive materials. The present communication presents a formulation to account for α in isotropic pressure-sensitive elastoplastic materials. Seven Lode dependences are reviewed. A new one, referred to as LMN, in proposed to generalize Lade and Duncan, and Matsuoka and Nakai failure surfaces. The formulation is general enough to introduce α into the isotropic elastoplastic modes which are only developed in terms of first and second-stress invariants. As an illustration, several Lode dependences are introduced into Roscoe and Burland model. The performance of the modified model is estimated by comparing experimental and analytical results in the case of true triaxial loadings on normally consolidated clay.
Swinging Wake Mechanism for Interface Wave Generation in Explosive Welding of Metals
Authors: Gupta R. C. , Kainth G. S.
Published: April 2008

A hydrodynamic model of explosive welding is considered. A swinging wake model for explosive welding is used to explain the generation of interfacial waves and to predict wave characteristics. The two plates are considered as main fluid jets divided by stagnation streamlines into a saliant jet and a reentrant jet. The model considers that the wake swings from side to side behind an imaginary obstacle bounded by the stagnation streamlines, thereby producing a wavy interface. Prediction of degree of distortion, η, and amplitude-to-wavelength ratio h/λ, by the swinging wake model show reasonable agreement with the available experimental results. The expression for the diameter of the obstacle is developed for the general situation in explosive welding.
Three-Dimensional Effects Near a Crack Tip in a Ductile Three-Point Bend Specimen: Part I—A Numerical Investigation
Authors: Narasimhan R. , Rosakis A. J.
Published: April 2008

A simultaneous numerical and experimental investigation is undertaken to assess three-dimensional effects and HRR dominance near a crack front in a ductile 3-point bend specimen. In parallel to the three-dimensional calculations, a plane-strain and a plane-stress analysis of the same in-plane specimen geometry is performed to obtain upper and lower bounds for the three-dimensional calculation. The radial, angular, and thickness variation of the stresses and displacements are studied in great detail from contained yielding to fully plastic conditions. The results indicate that the plane-strain HRR field prevails in the interior of the specimen very near the crack front even for moderate extents of yielding. On the other hand, for distances from the crack tip exceeding about half a specimen thickness, plane-stress conditions are approached. The calculations presented here model a series of laboratory experiments involving three independent experimental techniques. Details regarding the experiments and comparisons of the experimental measurements with numerical calculations and theory are emphasized in Part II of this work.
The Initial Phase of Transient Thermal Stresses Due to General Boundary Thermal Loads in Orthotropic Hollow Cylinders
Authors: Kardomateas G. A.
Published: April 2008

The stresses and displacements in the initial phase of applying a thermal load on the bounding surfaces of an orthotropic hollow circular cylinder are obtained using the Hankel asymptotic expansions for the Bessel functions of the first and second kind. Such a load may be constant temperature, constant heat flux, zero heat flux, or heat convection to a different medium at either surface. The material properties are assumed to be independent of temperature. A constant applied temperature at the one surface and convection into a medium at a different temperature at the other surface is used to illustrate the variation of stresses with time and through the thickness in the initial transient phase.
The Rotationally Flexible Pendulum Subjected to a High Frequency Excitation
Authors: Schmidt Bertram A.
Published: April 2008

A high frequency harmonic excitation is applied to the pivot of a rotationally flexible pendulum. It is found that various equilibrium positions occur depending on the stiffness of the flexible parts.
The Effective Thermal Conductivity of a Packing of Spheres
Authors: Jagota A. , Hui C. Y.
Published: April 2008

The anisotropic effective thermal conductivity of a random packing of spheres is derived. The conductivity is closely related to the fabric tensor of the theory of granular materials. The derivation involves a mean temperature field assumption which is shown to render the model an upper bound. Closed-form expressions for the conductivity are obtained in the isotropic and axisymmetric cases.
Acoustoelastic Birefringences in Plastically Deformed Solids: Part I—Theory
Authors: Pao Yih-Hsing , Wu Tsung-Tsong , Gamer Udo
Published: April 2008

A modified theory of acoustoelasticity is proposed to include the effect of small plastic deformation on propagational speeds of elastic waves in orthotropic media. In the constitutive equation for the incremental stresses of a predeformed body, the elastic moduli are modified by elastic deformation and plastic strains. The latter is related to the texture of the material. Several formulae for the acoustoelastic birefringences (differences of two shear wave speeds polarized at perpendicular directions) are derived. They can be applied to measure residual stresses and plastic strains by ultrasonic techniques.
Rigid Punch on Stressed Orthotropic Half-Plane With Partial Slip
Authors: Bjarnehed H. L.
Published: April 2008

An orthotropic half-plane carrying a transverse uniaxial stress and loaded perpendicularly on the free edge by a rigid flat punch is considered. Governing integral equations are stated for the unknown contact stresses between the punch and the half-plane. An analytical solution for contact with complete adhesion and a numerical solution with limiting friction, according to the Coulomb friction law, are presented. Besides distributions of contact stresses the numerical results show relations between vertical load, applied uniform foundation stress, coefficient of Coulomb friction, and size of the slip region.
Bending Frequency of a Rotating Beam With an Elastically Restrained Root
Authors: Lee Sen Yung , Kuo Yee Hsiung
Published: April 2008

Upper and lower bounds of the fundamental bending frequency of a rotating uniform beam with an elastically restrained root are obtained by the Rayleigh’s and minimum principles, respectively. It is shown that the fundamental bending frequency of the rotating uniform beam with rotational flexibility only is always higher than that of the nonrotating beam. If the setting angle is not equal to zero, the fundamental bending frequency of the rotating uniform beam with translational flexibility can be less than that of the nonrotating beam, and the phenomenon of divergence instability (tension buckling due to the centrifugal force) may occur. Finally, the influence of hub radius, setting angle, rotational speed, and elastic root restraints on the fundamental bending frequency of the beam is also investigated numerically by the transfer matrix method.
An Inverse Problem Associated With Modification of Incomplete Dynamic Systems
Authors: Ram Y. M. , Braun S. G.
Published: April 2008

Given an incomplete set of natural frequencies and modes of a linear structure from a vibration test, the problem of computing the necessary changes in the structure to reach a desired spectra is considered. A criterion of optimality which gives the best approximation from a certain subspace is formulated. Then formulae for evaluating the family of all mathematical solutions are given, resulting in a class of mathematical incremental mass and stiffness matrices. Finally, we describe the problem of the realization of the mathematical solutions by constructing a model of a given type.
Dynamics of Nonholonomic Mechanical Systems Using a Natural Orthogonal Complement
Authors: Saha Subir Kumar , Angeles Jorge
Published: April 2008

The dynamics equations governing the motion of mechanical systems composed of rigid bodies coupled by holonomic and nonholonomic constraints are derived. The underlying method is based on a natural orthogonal complement of the matrix associated with the velocity constraint equations written in linear homogeneous form. The method is applied to the classical example of a rolling disk and an application to a 2-dof Automatic Guided Vehicle is outlined.
Maximum Entropy Approach for Stationary Response of Nonlinear Stochastic Oscillators
Authors: Chang R. J.
Published: April 2008

A new approach based on the maximum entropy method is developed for deriving the stationary probability density function of a stable nonlinear stochastic system. The technique is implemented by employing the density function with undetermined parameters from the entropy method and solving a set of algebraic moment equations from a nonlinear stochastic system for the unknown parameters. For a wide class of stochastic systems with given density functions, an explicit density function of the stochastic system perturbed by a nonlinear function of states and noises can be obtained. Three nonlinear oscillators are selected for illustrating the present scheme and the validity of the derived density functions is further supported by some exact solutions and Monte Carlo simulations.
A New Boundary Element Method for Three-Dimensional Coupled Problems of Consolidation and Thermoelasticity
Authors: Dargush G. F. , Banerjee P. K.
Published: April 2008

A general boundary element method (BEM) for the complete three-dimensional Biot consolidation theory is developed which operates directly in the time domain and requires only boundary discretization. Consequently, the dimensionality of the problem is reduced by one and the method becomes quite attractive for geotechnical analyses, particularly those that involve extensive or infinite domains. Furthermore, as a result of a well-known analogy fully elaborated here, the new BEM formulation is equally applicable for quasi-static thermoelasticity. Several detailed examples are presented to illustrate the accuracy and suitability of this boundary element approach for both consolidation and thermomechanical analyses.
Penetration of Strain-Hardening Targets With Rigid Spherical-Nose Rods
Authors: Forrestal M. J. , Brar N. S. , Luk V. K.
Published: April 2008

We developed engineering models that predict forces and penetration depth for long, rigid rods with spherical noses and rate-independent, strain-hardening targets. The spherical cavity expansion approximation simplified the target analysis, so we obtained closed-form penetration equations that showed the geometric and material scales. To verify our models, we conducted terminal-ballistic experiments with three projectile geometries made of maraging steel and 6061-T651 aluminum targets. The models predicted penetration depths that were in good agreement with the data for impact velocities between 0.3 and 1.0 km/s.
Micromechanically Inspired Phenomenological Damage Model
Authors: Krajcinovic Dusan , Basista Michal , Sumarac Dragoslav
Published: April 2008

The paper suggests a phenomenological damage theory for perfectly brittle response of solids. The theory is based on the micromechanics of brittle deformation processes. The inelastic change of the compliance is identified as the flux and a properly averaged energy release rate as the affinity. The paper identifies conditions under which the damage potential exists. The proposed model is illustrated on the examples of plain concrete specimens subjected to uniaxial tension and compression.
A Global Damage Theory and the Hyperbolicity of the Wave Problem
Authors: Valanis K. C.
Published: April 2008

It is well known that wave equation in materials that suffer damage in the course of deformation loses it hyperbolicity when the damage process is described by a continuum damage theory of the local type. Here we develop a global (nonlocal) damage theory by (a) introducing a damage coordinate which is a spatial functional of the strain field in the material domain and (b) stipulating that the rate of evolution of damage is with respect to the damage coordinate. We then derive the axial wave equation for a thin rod and thereby demonstrate that, while the rod experiences softening, the wave speed is given in terms of the secant modulus and the wave equation retains its hyperbolicity. Various other phenomena, such as the onset of inhomogeneous damage in the presence of homogeneous deformation and the tendency of axial specimens under tension to fracture invariably at the center, are also explained.
Nonproportional Multiaxial Cyclic Loading: Experiments and Constitute Modeling
Authors: Xia Z. , Ellyin F.
Published: April 2008

Biaxial tension compression, deformation controlled, out-of-phase cyclic tests were conducted on thin-walled circular cylindrical specimens of a low alloy carbon steel. The influence of strain amplitude and phase angle (a measure of nonproportionality of strain path) on the stress-strain loops have been studied. Material aniostropy and additional cyclic hardening due to the plastic deformation and nonproportional path are clearly observed. A constitutive model is presented which describes the material behavior under complex loading histories including cyclic deformation. The predictions of the model are compared to the experimental results, and the agreement is found to be fairly good.
Dynamic Cylindrical Cavity Expansion of Compressible Strain-Hardening Materials
Authors: Luk V. K. , Amos D. E.
Published: April 2008

We developed models for the dynamic expansion of cylindrical cavities from zero initial radii for compressible, elastic-plastic, rate-independent materials with powerlaw strain-hardening. Results from cavity-expansion models were used to derive perforation models to predict residual velocities and ballistic limits for rigid, conicalnose projectiles perforating strain-hardening target plates. We compared the numerical results from models for incompressible and compressible materials to show the effect of compressibility. To verify the models, we also compared the model predictions of residual velocities and ballistic limits with the data from terminal-ballistic experiments with tungsten projectiles impacting 5083-H131 aluminum armor plates at normal incidence. Very good agreement was obtained for impact velocities between 200 and 1,200 m/s and 12.7, 50.8, and 76.2-mm thick targets.
Stress Analysis of Multilayered Anisotropic Elastic Media
Authors: Choi Hyung Jip , Thangjitham S.
Published: April 2008

The stress analysis of multilayered anisotropic media subjected to applied surface tractions is performed within the framework of linear plane elasticity. The solutions are obtained based on the Fourier transform technique together with the aid of the stiffness matrix approach. A general solution procedure is introduced such that it can be uniformly applied to media with transversely isotropic, orthotropic, and monoclinic layers. As an illustrative example, responses of the semi-infinite media composed of unidirectional and angle-ply layers to a given surface traction are presented.
Elastic Moduli of Thickly Coated Particle and Fiber-Reinforced Composites
Authors: Qiu Y. P. , Weng G. J.
Published: April 2008

Based on the models of Hashin (1962) and Hashin and Rosen (1964), the effective elastic moduli of thickly coated particle and fiber-reinforced composites are derived. The microgeometry of the composite is that of a progressively filled composite sphere or cylinder element model. The exact solutions of the effective bulk modulus κ of the particle-reinforced composite and those of the plain-strain bulk modulus κ23, axial shear modulus μ12, longitudinal Young’s modulus E11, major Poisson ratio ν12, of the fiber-reinforced one are derived by the replacement method. The bounds for the effective shear modulus μ and the effective transverse shear modulus μ23 of these two kinds of composite, respectively, are solved with the aid of Christensen and Lo’s (1979) formulations. By considering the six possible geometrical arrangements of the three constituent phases, the values of κ, and of κ23, μ12, E11, and ν12 are found to always lie within the Hashin-Shtrikman (1963) bounds, and the Hashin (1965), Hill (1964), and Walpole (1969) bounds, respectively, but unlike the two-phase composites, none coincides with their bounds. The bounds of μ and μ23 derived here are consistently tighter than their bounds but, as for the two-phase composites, one of the bounds sometimes may fall slightly below or above theirs and therefore it is suggested that these two sets of bounds be used in combination, always choosing the higher for the lower bound and the lower for the upper one.
The Crack Problem in Bonded Nonhomogeneous Materials
Authors: Erdogan F. , Kaya A. C. , Joseph P. F.
Published: April 2008

In this paper the plane elasticity problem for two bonded half-planes containing a crack perpendicular to the interface is considered. The primary objective of the paper is to study the effect of very steep variations in the material properties near the diffusion plane on the singular behavior of the stresses and stress intensity factors. The two materials are, thus, assumed to have the shear moduli μ0 and μ0exp(βx), x = 0 being the diffusion plane. Of particular interest is the examination of the nature of stress singularity near a crack tip terminating at the interface where the shear modulus has a discontinuous derivative. The results show that, unlike the crack problem in piecewise homogeneous materials for which the singularity is of the form r−α, 0<α<1, in this problem the stresses have a standard square root singularity regardless of the location of the crack tip. The nonhomogeneity constant β has, however, considerable influence on the stress intensity factors.
The Spherical Inclusion With Imperfect Interface
Authors: Hashin Z.
Published: April 2008

A rigorous solution of the spherical inclusion problem with remote uniform strain or stress and imperfect elastic spring-type interface conditions is presented. In the case of thin elastic interphase, the interface spring constants are expressed in terms of interphase elastic properties and thickness. The state of strain/stress in the inclusion is nonhomogeneous for imperfect interface conditions in contrast to the homogeneous state for perfect interface condition. Numerical results are given to demonstrate the significance of imperfect interface effects.
A Consistent Implicit Formulation for Nonlinear Finite Element Modeling With Contact and Friction: Part I—Theory
Authors: Saran M. J. , Wagoner R. H.
Published: April 2008

A formulation for finite element simulation of highly nonlinear problems including friction and contact with arbitrarily shaped rigid surfaces is proposed (CFS approach), prompted by difficulties in robust and accurate simulations of industrial forming processes. Nonlinearities are caused by large strains, plastic flow, and complex boundary conditions with frictional contact. In Part I the theoretical basis is described and the appropriate numerical algorithm is derived. The complete set of the governing relations, comprising equilibrium and interfacial equations, is appropriately linearized; resulting in a consistent tangent operator of the Newton-Raphson algorithm. In Part II, as a numerical verification, plane-strain sheet-forming processes are analyzed using a rigid-viscoplastic material model. Results are presented and discussed for test problems and for complex simulation of reverse drawing by concave tools.
A Consistent Implicit Formulation for Nonlinear Finite Element Modeling With Contact and Friction: Part II—Numerical Verification and Results
Authors: Saran M. J. , Wagoner R. H.
Published: April 2008

Using the method derived in Part I, plane-strain sheet-forming processes are analyzed and discussed. Stretch and deep draw forming by cylindrical and flat-bottom punches are presented and compared to closed-form solutions and existing numerical results. The performance of the new algorithm is successfully tested on a complex set of concave, irregular tools by simulating redrawing and reverse drawing with two-sided draw-in and various drawbead forces. The results demonstrate good robustness, accuracy, and efficiency even in the presence of large relative movements between contact surfaces. A quadratic rate of asymptotic convergence is documented for the consistent algorithm and comparison is made to the “linearized” theory which exhibits only linear rate of convergence and reduced numerical stability.
Stability and Bifurcation Analysis of Oscillators With Piecewise-Linear Characteristics: A General Approach
Authors: Kim Y. B. , Noah S. T.
Published: April 2008

A general approach is developed for determining the periodic solutions and their stability of nonlinear oscillators with piecewise-smooth characteristics. A modified harmonic balance/Fourier transform procedure is devised for the analysis. The procedure avoids certain numerical differentiation employed previously in determining the periodic solutions, therefore enhancing the reliability and efficiency of the method. Stability of the solutions is determined via perturbations of their state variables. The method is applied to a forced oscillator interacting with a stop of finite stiffness. Flip and fold bifurcations are found to occur. This led to the identification of parameter ranges in which chaotic response occurred.
On the Interaction and Reflection of Shocks in Hyperelastic Strings
Authors: Wegner J. L. , Jiang L. , Haddow J. B.
Published: April 2008

Governing equations for finite amplitude wave propagation in stretched hyperelastic strings are given in recent papers, (Beatty and Haddow, 1985), along with similarity solutions for symmetrically plucked and impacted strings. The similarity solutions are valid until the first reflections at the fixed ends and in this paper we consider symmetrically plucked Mooney-Rivlin strings and investigate the response after reflections. The method of characteristics is applied to extend the results of the similarity solutions and to obtain solutions for the interaction of a reflected longitudinal shock and incident transverse shock and the reflection of an incident transverse shock. A deformed shape, which is not intuitively obvious, is predicted by the solution of the interaction problem and is confirmed by an experimental study. A finite difference scheme is used to obtain numerical solutions, which are valid after multiple wave interactions and reflections occur. Solutions obtained by the method of characteristics are used as a partial check on the numerical results.
Chaotic Motions of a Constrained Pipe Conveying Fluid: Comparison Between Simulation, Analysis, and Experiment
Authors: Paidoussis M. P. , Li G. X. , Rand R. H.
Published: April 2008

A refined analytical model is presented for the dynamics of a cantilevered pipe conveying fluid and constrained by motion limiting restraints. Calculations with the discretized form of this model with a progressively increasing number of degrees of freedom, N, show that convergence is achieved with N = 4 or 5, which agrees with previously performed fractal dimension calculations of experimental data. Theory shows that, beyond the Hopf bifurcation, as the flow is increased, a pitchfork bifurcation is followed by a cascade of period doubling bifurcations leading to chaos, which is in qualitative agreement with observation. The numerically computed theoretical critical flow velocities are in excellent quantitative agreement (5–10 percent) with experimental values for the thresholds of the Hopf and period doubling bifurcations and for the onset of chaos. An approximation for the critical flow velocity for the loss of stability of the post-Hopf limit cycle is also obtained by using center manifold concepts and normal form techniques for a simplified version of the analytical model; it is found that the values obtained in this manner are approximately within 10 percent of those computed numerically.
Centrifugal Convection due to Mass Transfer Near a Rotating Disk at High Schmidt Number
Authors: Toren M. , Ungarish M. , Pinchuk G. , Solan A.
Published: April 2008

The centrifugally-driven flow due to a density gradient between the surface of an infinite disk and the ambient fluid in a rotating system with mass transfer is studied for the case of high Schmidt number. Under certain assumptions the velocity and density fields exhibit a similarity like the classical von Karman disk flow, and the governing equations reduce to a nonlinear system of ordinary differential equations. These equations are solved by boundary layer technique or numerically, for high Schmidt number σ = v/D and finite or small density difference ερ = (ρd - ρ∞)/ρ∞. In the latter case it is shown that the major scaling parameter is the product σερ. For σρ ≫ 1 the flow field consists of a constant density (ρ∞), linear Ekman layer driven by a buoyancy sublayer of relative thickness (σερ)-1/4 in which ρ varies from ρd to ρ∞. The representative Rossby number of the buoyancy driven flow is (σερ)-1/2. The general case ερ = O(1), σ ≫ 1 shows similar trends, i.e., a σ-1/4 sublayer. The case of simultaneous driving by density difference and angular velocity difference εv = (Ωd - Ω∞)/Ω∞ is also discussed.
Singularities in p-Type Finite Element Computations: Numerical Experiments on the Locality of Pollution Effects
Authors: Becker G. , Carnevali P. , Chayapathy B. , Imaino W. , Morris R. B. , Tsuji Y. , Yendler B.
Published: April 2008

Using a recently developed code for three-dimensional p-type finite element computations in elasticity, we have studied, with a series of numerical experiments, the behavior of the solution in the presence of singularities. Worst-cast theoretical estimates predict a global pollution of the solution, unless optimally graded meshes are used. On the other hand, we observe that except in an immediate neighborhood of a singularity, and even using uniform meshes, the quality of the solution is not degraded to any practically relevant extent. This has important practical consequences because it allows modelers to introduce artifical singularities for the purpose of simplifying models. The size of the area around a singularity where the solution is appreciably degraded can be estimated in terms of the minimum effective wavelength of the basis functions used; the latter, in turn, can be related to the element size and the polynomial order used.
An Integral Formulation for Dynamic Poroelasticity
Authors: Dominguez Jose´
Published: April 2008

A boundary integral equation formulation for dynamic poroelasticity in the frequency domain is presented. The formulation is accomplished using the solid displacements and the fluid stress as independent variables. The integral representation of the fluid stress is obtained using a fundamental solution corresponding to a combination of body forces applied in the solid and in the fluid.