bluuebunny/crossref_metadata_2025 huggingface dataset:
Steady Sliding of Two Elastic Half-Spaces With Friction Reduction due to Interface Stick-Slip
Authors: Adams G. G.
Published: February 2008

The sliding of two perfectly flat elastic half-spaces with a constant interfacial coefficient of friction is investigated. Previous work has demonstrated that this configuration is dynamically unstable due to the destabilization of frictional slip waves. It was speculated that this dynamic instability could lead to stick-slip motion at the sliding interface. It is shown here that stick-slip motion at the interface can exist with a speed-independent interface coefficient of friction. Steady motion persists sufficiently far from the interface and thus gives the impression of uniform sliding. This type of stick-slip motion is due to interfacial slip waves and allows the bodies to slide with an apparent coefficient of friction which is less than the interface coefficient of friction. Furthermore it is shown that the apparent friction coefficient decreases with increasing speed even if the interface friction coefficient is speed-independent. Finally, it is shown that the presence of slip waves may make it possible for two frictional bodies to slide without a resisting shear stress and without any interface separation. No distinction is made between static and kinetic friction.
Dynamic Response Control of Thin-Walled Beams to Blast Pulses Using Structural Tailoring and Piezoelectric Actuation
Authors: Librescu L. , Na Sungsoo
Published: February 2008

An integrated dual approach aimed at controlling the dynamic response of anisotropic cantilevered thin-walled beams to blast and sonic-boom loading is presented. The approach is based upon the simultaneous implementation of structural tailoring and adaptive materials technology. Whereas structural tailoring uses the anisotropy properties of advanced composite materials, the adaptive materials technology exploits the converse effect of piezoactuators bonded or embedded into the host structure. A combined dynamic control law relating the piezoelectrically bending moment induced at the beam tip with the various kinematic response quantities is implemented and its effects upon the closed-loop dynamic response characteristics are investigated. The obtained results reveal the powerful role played by abovementioned integrated control methodology towards enhancing the dynamic response of thin-walled beam cantilevers to transient loading.
A Nonspectral Stability Criterion for Linear Conservative Gyroscopic Systems
Authors: Bulatovic R. M.
Published: February 2008

Using a Lyapunov-type approach, a simple sufficient stability condition for linear conservative gyroscopic systems with negative definite stiffness matrix is derived. The condition is nonspectral; it involves only the definiteness of certain combinations of the system’s coefficient matrices.
Contact Problems of Two Dissimilar Anisotropic Elastic Bodies
Authors: Hwu Chyanbin , Fan C. W.
Published: February 2008

In this paper, a two-dimensional contact problem of two dissimilar anisotropic elastic bodies is studied. The shapes of the boundaries of these two elastic bodies have been assumed to be approximately straight, but the contact region is not necessary to be small and the contact surface can be nonsmooth. Base upon these assumptions, three different boundary conditions are considered and solved. They are: the contact in the presence of friction, the contact in the absence of friction, and the contact in complete adhesion. By applying the Stroh’s formalism for anisotropic elasticity and the method of analytical continuation for complex function manipulation, general solutions satisfying these different boundary conditions are obtained in analytical forms. When one of the elastic bodies is rigid and the boundary shape of the other elastic body is considered to be fiat, the reduced solutions can be proved to be identical to those presented in the literature for the problems of rigid punches indenting into (or sliding along) the anisotropic elastic halfplane. For the purpose of illustration, examples are also given when the shapes of the boundaries of the elastic bodies are approximated by the parabolic curves.
Plasticity of Particle-Reinforced Composites With a Ductile Interphase
Authors: Ding K. , Weng G. J.
Published: February 2008

A homogenization theory is developed to determine the overall elastoplastic behavior of a particle-reinforced composite with a ductile interphase. Unlike most existing homogenization theories which are primarily concerned with the ordinary two-phase composites, the present one is confronted with two ductile phases, with one enclosing the other. The theory is developed with the aid of a linear comparison composite using a field-fluctuation method to calculate an energy-based effective stress of the ductile phases. In order to examine its accuracy, an exact elastic-plastic analysis under dilatational loading is also developed, and it was found that, despite its simplicity, the theory could provide plausible estimates for the overall behavior of the three-phase composite. The theory is applicable to a composite system regardless whether the interphase is more ductile or stiffer than the matrix, and when the interphase is more ductile, it is shown that even the presence of a thin layer can have a very significant effect on the plasticity of the overall composite.
Effects of Thermomechanical Coupling and Relaxation Times on Wave Spectrum in Dynamic Theory of Generalized Thermoelasticity
Authors: Suh C. S. , Burger C. P.
Published: February 2008

A spectral study is performed to gain insight into the effects of relaxation times and thermomechanical coupling on dynamic thermoe Iastic responses in generalized thermoelasticity. The hyperbolic thermoelastic theories of Lord and Schulman (LS) and Green and Lindsay (GL) are selected for the study. A generalized characteristic equation is derived to investigate dispersion behavior of thermoelastic waves as functions of thermomechanical coupling and relaxation time constants. Thermomechanical coupling is found to impose a significant influence on phase velocities. The GL model implicitly indicates that the order of magnitude of the thermomechanical relaxation time can never be greater than that of thermal relaxation time.
The Reflection of Guided Waves From Circumferential Notches in Pipes
Authors: Alleyne D. N. , Lowe M. J. S. , Cawley P.
Published: February 2008

The reflection of the L(0, 2), axially symmetric guided elastic wave from notches in pipes is examined, using laboratory experiments and finite element simulations. The results show that the reflection coefficient of this mode is very close to a linear function of the circumferential extent of the notch, and is a stronger function of the through thickness depth of the notch. The motivation for the work was the development of a technique for inspecting chemical plant pipework, but the study addresses the nature of the reflection function and has general applicability.
The Mode Conversion of a Guided Wave by a Part-Circumferential Notch in a Pipe
Authors: Lowe M. J. S. , Alleyne D. N. , Cawley P.
Published: February 2008

A study of the reflection of mode-converted guided waves from notches in pipes has been carried out. Measurements were made on a 76-mm bore diameter (nominal 3-inch), 5.5-mm wall thickness pipe with circumferentially oriented through-thickness notches of various lengths. In parallel, a finite element model was used to simulate the experiments. The axially symmetric L(0, 2) mode was incident on the notches and the L(0, 2), F(1, 3), and F(2, 3) modes were received in reflection. The results showed excellent agreement between the measurements and the predictions for all three modes. They also showed that the F(1, 3) mode reflects as strongly as the L(0, 2) mode when the notch length is short. Finally, it has been shown that a very simple analysis based on an assumed crack-opening profile may be used to make accurate predictions of the mode conversion.
Experimental Study of a Symmetrical Piecewise Base-Excited Oscillator
Authors: Wiercigroch M. , Sin V. W. T.
Published: February 2008

This paper presents an experimental study on a base-excited piecewise linear oscillator with symmetrical flexible constrains of high stiffness ratio (above 20). The details of the adopted design of the oscillator, the experimental setup, and calibration procedure are briefly discussed. The regions of chaotic motion predicted theoretically were confirmed by the experimental results arranged into bifurcation diagrams. Clearance, stiffness ratio, amplitude, and frequency of the external force were used as branching parameters. The discussion of the system dynamics is based on bifurcation diagrams and Lissajous curves. The investigated system tends to be periodic for large clearances and chaotic for small ones. This picture is reversed for the amplitude of the forcing changes, where periodic motion occurred for small values and chaos dominated for larger forcing. The same behavior is observed for increasing frequency ratio where, for values below the natural frequency, the most interesting dynamics occurs. For the investigated parameter values, the stiffness ratio variation produces only periodic motion.
Transient Response of a Composite Plate With Delamination
Authors: Zhu J. , Shah A. H. , Datta S. K.
Published: February 2008

Transient response of a composite plate with a near-surface delamination has been studied in this paper. A new technique developed by the authors to evaluate the Cauchy Principal Value integrals and the weakly singular integrals involved in the boundary integral equations has been employed and modifided to treat the corner points on the boundary. The time harmonic Green’s functions appearing in the boundary integral equation are evaluated by combining a stiffness method and the modal summation technique. To circumvent the difficulties associated with the evaluation of hypersingular integrals for cracks, the multidomain technique is employed. The accuracy and efficiency of the method are checked by comparing the displacements in a uniaxial graphite-epoxy plate containing a delamination with results obtained by a hybrid method. It is shown that the presence of the delamination significantly alters the surface response spectra of the plate. Results are presented in both time and frequency domains. The results show that the technique would be useful for ultrasonic nondestructive evaluation of defects in composite and anisotropic plates, and for studying dynamic response of such plates to impact.
The Effect of Dynamic Surface Tension on the Oscillation of Slender Elliptical Newtonian Jets
Authors: Bechtel S. E. , Forest M. G. , Youssef N. T. , Zhou H.
Published: February 2008

We investigate free-surface oscillating jets with elliptical cross section, focusing on behavior associated with decaying surface tension. Previous one-dimensional equations for an oscillating jet are extended to allow variable surface tension on short space and time scales relevant for surfactant mixtures. We presume the decay of surface tension as a function of surface age, and derive the resulting jet behavior. Three plausible forms of decay are studied: an exponential decay, a diffusion model derived in Brazee et al. (1994), and an algebraic form due to Hua and Rosen (1991). Our simulations suggest both experimental regimes, and measurable jet features in these regimes, which may be exploited in an inverse formulation to deduce the unknown rapid surface tension decay of a given surfactant mixture. In particular, we establish numerical relationships between the amplitude and the wavelength of either a sustained far-field oscillation or oscillation at a fixed downstream location and the entire history of surface tension decay. These numerical relationships are ideal for the inverse formulation, in that the complete surface tension evolution may be deduced solely from far-field or downstream jet measurements, away from the confined part of the jet where the surface tension is rapidly changing.
Static Analysis of Reissner-Mindlin Plates by Differential Quadrature Element Method
Authors: Liu F.-L. , Liew K. M.
Published: February 2008

In this paper, a new numerical method, the differential quadrature element method has been developed for two-dimensional analysis of bending problems of Reissner-Mindlin plates. The basic idea of the differential quadrature element method is to divide the whole variable domain into several subdomains (elements) and to apply the differential quadrature method for each element. The detailed formulations for the differential quadrature element method and compatibility conditions between elements are presented. The convergent characteristics and accuracy of the differential quadrature element method are carefully investigated for the solution of the two-dimensional bending problems of Reissner-Mindlin plates. Finally, the differential quadrature element method is applied to analyze several bending problems of two-dimensional Reissner-Mindlin plates with different discontinuities including the discontinuous loading conditions, the mixed boundaries, and the plates with cutout. The accuracy and applicability of this method have been examined by comparing the differential quadrature element method solutions with the existing solutions obtained by other numerical methods and the finite element method solutions generated using ANSYS 5.3.
Conservation Principles for Systems With a Varying Number of Degrees-of-Freedom
Authors: Djerassi S.
Published: February 2008

This paper is the third in a trilogy dealing with simple, nonholonomic systems which, while in motion, change their number of degrees-of-freedom (defined as the number of independent generalized speeds required to describe the motion in question). The first of the trilogy introduced the theory underlying the dynamical equations of motion of such systems. The second dealt with the evaluation of noncontributing forces and of noncontributing impulses during such motion. This paper deals with the linear momentum, angular momentum, and mechanical energy of these systems. Specifically, expressions for changes in these quantities during imposition and removal of constraints are formulated in terms of the associated changes in the generalized speeds.
Resonant Layers in Nonlinear Dynamics
Authors: Han R. P. S. , Luo A. C. J.
Published: February 2008

A new method based on an incremental energy approach and the standard mapping technique is proposed for the study of resonant layers in nonlinear dynamics. To demonstrate the procedure, the method is applied to four types of Duffing oscillators. The appearance, disappearance and accumulated disappearance strengths of the resonant layers for each type of oscillator are derived. A quantitative check of the appearance strength is performed by computing its value using three independent methods: Chirikov overlap criterion, renormalization group technique, and numerical simulations. It is also observed that for the case of the twin-well Duffing oscillator, its perturbed left and right wells are asymmetric.
Thermodynamical Modeling of Boundary Layer Flow With Suction and Injection
Authors: Chandrasekar M.
Published: February 2008

The variational principle developed by Gyarmati embodying the principles of non-equilibrium thermodynamics is employed to investigate the laminar boundary layer effect on wedge flows with suction and injection. The velocity function is assumed as a simple third-degree polynomial and the variational principle is formulated. The hydrodynamical boundary layer thickness is derived as the Euler-Lagrange equation of the variational principle. The velocity profiles and skin friction values were computed for various values of suction and injection parameter and wedge angle parameter. The comparison of the present solution with an available exact solution establishes the fact that the accuracy is remarkable.
A Simplified Method for Calculating the Crack-Tip Field of Functionally Graded Materials Using the Domain Integral
Authors: Gu P. , Dao M. , Asaro R. J.
Published: February 2008

A finite element based method is proposed for calculating stress intensity factors of functionally graded materials (FGMs). We show that the standard domain integral is sufficiently accurate when applied to FGMs; the nonhomogeneous term in the domain integral for nonhomogeneous materials is very small compared to the first term (the standard domain integral). In order to obtain it, the domain integral is evaluated around the crack tip using sufficiently fine mesh. We have estimated the error in neglecting the second term in terms of the radius of the domain for the domain integration, the material properties and their gradients. The advantage of the proposed method is that, besides its accuracy, it does not require the input of material gradients, derivatives of material properties; and existing finite element codes can be used for FGMs without much additional work. The numerical examples show that it is accurate and efficient. Also, a discussion on the fracture of the FGM interlayer structure is given.
Recovery Experiments for Adiabatic Shear Localization: A Novel Experimental Technique
Authors: Chichili D. R. , Ramesh K. T.
Published: February 2008

A novel experimental technique has been developed that allows the recovery of specimens within which an adiabatic shear band has been grown as the result of a single torsional pulse. The technique uses a new device called the compression-torsion Kolsky bar; this is an adaptation of the classical torsional Kolsky bar in which both compression and torsion are stored in the clamped length. Recovery of the specimen is obtained by causing the transmitted compression pulse to reflect from the free end of the output bar as a tensile pulse which then causes failure of the specimen/output-bar interface. All further pulses then cause no more than rigid motions of the specimen. Thus the specimen is recovered after it has been loaded by a single torsional pulse; microscopic examination of the recovered specimen now allows the rigorous determination of the evolution of microstructure and the identification of deformation mechanisms that are active under the dynamic shear loading. As an example of the utility of this recovery technique, its application to the study of adiabatic shear localization in alpha-titanium is presented. The technique allows a systematic study of the microscopic mechanisms that drive the initiation and growth of adiabatic shear bands by recovering samples within which shear bands have been grown under controlled conditions; further characterization through sectioning, followed by optical, scanning, and transmission electron microscopy is then possible. The technique also allows one to study the influence of the shape and size of geometric defects (for example, notch tip radius and notch depth) on the initiation of adiabatic shearing failures. The effect of normal stresses on the susceptibility of a material to shear localization can also be investigated.
A Micro/Macroscopic Analysis for Cyclic Plasticity of Dual-Phase Materials
Authors: Fan J.
Published: February 2008

In this paper, a methodology is developed to simulate cyclic micro/macroscopic responses of dual-phase materials based on an extension of the self-consistent scheme. This extension is significant because it makes the self-consistent scheme capable of determining overall responses of materials as well as local stress evolution in microstructure. Results show satisfactory agreement between the cyclic responses up to 50 cycles predicted by the present methodology and the experimental data of Bower (1989). The heterogeneous feature of distributions of cyclic stress, strain and energy in microstructure, as well as the essential role of the strong-energy-absorption-capability of the thin layers on the material behavior, and the high strength of the thin-layer microstructure are exploited. The possible impact of this work on issues such as ratchetting of the dual-phase material and the ductile and fatigue behavior of its hard phase, as well as the significance on plasticity modeling of constituents and effective homogeneous inclusions are also mentioned.
Anomalous Frictional Behavior in Collisions of Thin Disks
Authors: Calsamiglia J. , Kennedy S. W. , Chatterjee A. , Ruina A. , Jenkins J. T.
Published: February 2008

We report on two-dimensional collision experiments with nine thin Delrin disks with variable axisymmetric mass distributions. The disks floated on an air table, and collided at speeds of about 0.5 to 1.0 m/s with a flat-walled stationary thick steel plate clamped to the table. The collision angle was varied. The observed normal restitution was roughly independent of angle, consistent with other studies. The frictional interaction differed from that reported for spheres and thick disks, and from predictions of most standard rigid-body collision models. For “sliding” two-dimensional collisions, most authors assume the ratio of tangential to normal impulse equals μ (friction coefficient). The observed impulse ratio was appreciably lower: roughly 0.5 μ slightly into the sliding regime, approaching μ only for nearly grazing collisions. Separate experiments were conducted to estimate μ check its invariance with force magnitude; and check that the anomalies observed are not strongly dependent on velocity magnitude. We speculate that these slightly anomalous findings are related to the two-dimensional deformation fields in thin disks, and with the disks being only “impulse-response” rigid and not “force-response” rigid.
On a Spring-Network Model and Effective Elastic Moduli of Granular Materials
Authors: Alzebdeh K. , Ostoja-Starzewaski M.
Published: February 2008

Two challenges in mechanics of granular media are taken up in this paper: (i) development of adequate numerical discrete element models of topologically disordered granular assemblies, and (ii) calculation of macroscopic elastic moduli of such materials using effective medium theories. Consideration of the first one leads to an adaptation of a spring-network (Kirkwood) model of solid-state physics to disordered systems, which is developed in the context of planar Delaunay networks. The model employs two linear springs: a normal one along an edge connecting two neighboring vertices (grain centers) which accounts for normal interactions between the grains, as well as an angular one which accounts for angle changes between two edges incident onto the same vertex; edges remain straight and grain rotations do not appear. This model is then used to predict elastic moduli of two-phase granular materials—random mixtures of soft and stiff grains —for high coordination numbers. It is found here that an effective Poisson’s ratio, νeff, of such a mixture is a convex function of the volume fraction, so that νeff may become negative when the individual Poisson’s ratios of both phases are both positive. Additionally, the usefulness of three effective medium theories—perfect disks, symmetric ellipses, and asymmetric ellipses—is tested.
Green’s Function for a Heat Source in an Infinite Region With an Arbitrary Shaped Hole
Authors: Yoshikawa K. , Hasebe N.
Published: February 2008

In two-dimensional thermoelasticity, Green’s functions of the external force boundary value problem are derived for an infinite plane with an arbitrary shaped hole under adiabatic and isothermal boundary conditions subjected to heat sources in two cases as follows. One is the case of a heat source and a heat sink arbitrarily located within the plane, the other is the case of a heat source arbitrarily located within the plane and a heat sink at infinity. Complex stress functions, temperature function, a rational mapping function, and the thermal dislocation method are used for the analysis. In analytical examples, distributions of temperature, heat flux, and stresses are shown for an infinite plane with a rectangular hole under adiabatic and isothermal boundary conditions.
Lyapunov Exponents and Stochastic Stability of Quasi-Integrable-Hamiltonian Systems
Authors: Zhu W. Q. , Huang Z. L.
Published: February 2008

The averaged equations of integrable and nonresonant Hamiltonian systems of multi-degree-of-freedom subject to light damping and real noise excitations of small intensities are first derived. Then, the expression for the largest Lyapunov exponent of the square root of the Hamiltonian is formulated by generalizing the well-known procedure due to Khasminskii to the averaged equations, from which the stochastic stability and bifurcation phenomena of the original systems can be determined approximately. Linear and nonlinear stochastic systems of two degrees-of-freedom are investigated to illustrate the application of the proposed combination approach of the stochastic averaging method for quasi-integrable Hamiltonian systems and Khasminskii’s procedure.
On Dynamic Cycle Collapse of Circular Plates
Authors: Chinh P. D.
Published: February 2008

The upper bound kinematic method, which is based on a reduced kinematic formulation and involves construction of fictitious elastic moment fields and potential incremental collapse mechanisms, is used to evaluate the dynamic cycle collapse loads for a symmetrically loaded circular plate. The respective nonshakedown curves are constructed, A point load effect is discussed.
Vibration Control of a Rotating Shaft: An Analytical Solution
Authors: Yang S. M. , Sheu G. J.
Published: February 2008

It has been shown that a rotating shaft in the Rayleigh beam model has only a finite number of whirl speeds and vibration modes when the rotating speed is higher than half of the whirl speed. The system’s unbalanced response can therefore be written analytically by the vibration modes and the generalized coordinates. This paper presents an analytical controller design of optimal sensor/actuator location and feedback gain for minimizing the steady-state unbalanced response. Because all of the critical speeds and vibration modes are included in the controller design, there will be no residual mode, hence no spillover. An example is used to illustrate that the controller design in collocated or noncollocated configuration not only guarantees the closed-loop stability but also effectively suppresses the unbalanced response.
A Theory of Continuum Damage Mechanics for Anisotropic Solids
Authors: Lee U.
Published: February 2008

This paper develops a fracture mechanics based continuum damage theory for initially anisotropic solids by extending the author’s previous damage theory for isotropic solids. The concepts of strain energy equivalence principle (SEEP) and equivalent line-crack modeling are used to develop the effective continuum elastic properties of a damaged solid in terms of the undamaged anisotropic elastic properties and a scalar damage variable.
Comments on Stability Properties of Conservative Gyroscopic Systems
Authors: Lancaster P. , Kliem W.
Published: February 2008

A conjecture of Renshaw and Mote concerning gyroscopic systems with parameters predicts the eigenvalue locus in the neighborhood of a double-zero eigenvalue. In the present paper, this conjecture is reformulated in the language of generalized eigenvectors, angular splitting, and analytic behavior of eigenvalues. Two counter-examples for systems of dimension two show that the conjecture is not generally true. Finally, splitting or analytic behavior of eigenvalues is characterized in terms of expansion of the eigenvalues in fractional powers of the parameter.
A Simplified Variation of Parameters Approach to Euler’s Equations
Authors: Richardson D. L. , Mitchell J. W.
Published: February 2008

A normalized form of Euler’s equations is rewritten in a variation of parameters approach using amplitudes and angular displacement as parameters. This new form is compact and yields a more accurate numerically integrated solution over longer simulation times than does a conventional integration of the Euler equations.
On the St. Venant Problems for Inhomogeneous Circular Bars
Authors: Rooney F. , Ferrari M.
Published: February 2008

The classical St. Venant problems, i.e., simple tension, pure bending, and flexure by a transverse force, are considered for circular bars with elastic moduli that vary as a function of the radial coordinate. The problems are reduced to second-order ordinary differential equations, which are solved for a particular choice of elastic moduli. The special case of a bar with a constant shear modulus and the Poisson’s ratio varying is also considered and for this situation the problems are solved completely. The solutions are then used to obtain homogeneous effective moduli for inhomogeneous cylinders. Material inhomogeneities associated with spatially variable distributions of the reinforcing phase in a composite are considered. It is demonstrated that uniform distribution of the reinforcement leads to a minimum of the Young’s modulus in the class of spatial variations in the concentration considered.
Double Curvature Bending of Variable-Arc-Length Elasticas
Authors: Chucheepsakul S. , Wang C. M. , He X. Q. , Monprapussorn T.
Published: February 2008

This paper deals with the double curvature bending of variable arc-length elasticas under two applied moments at fixed support locations. One end of the elastica is held while the other end portion of the elastica may slide freely on a frictionless support at a prescribed distance from the held end. Thus, the variable deformed length of the elastica between the end support and the frictionless support depends on the relative magnitude of the applied moments. To solve this difficult and highly nonlinear problem, two approaches have been used. In the first approach, the elliptic integrals are formulated based on the governing nonlinear equation of the problem. The pertinent equations obtained from applying the boundary conditions are then solved iteratively for solution. In the second approach, the shooting-optimization method is employed in which the set of governing differential equations is numerically integrated using the Runge-Kutta algorithm and the error norm of the terminal boundary conditions is minimized using a direct optimization technique. Both methods furnish almost the same stable and unstable equilibrium solutions. An interesting feature of this kind of bending problem is that the elastica can form a single loop or snap-back bending for some cases of the unstable equilibrium configuration.
Plastic Yielding as a Phase Transition
Authors: Ortiz M.
Published: February 2008

A statistical mechanical theory of forest hardening is developed in which yielding arises as a phase transition. For simplicity, we consider the case of a single dislocation loop moving on a slip plane through randomly distributed forest dislocations, which we treat as point obstacles. The occurrence of slip at the sites occupied by these obstacles is assumed to require the expenditure of a certain amount of work commensurate with the strength of the obstacle. The case of obstacles of infinite strength is treated in detail. We show that the behavior of the dislocation loop as it sweeps the slip plane under the action of a resolved shear stress is identical to that of a lattice gas, or, equivalently, to that of the two-dimensional spin-1/2 Ising model. In particular, there exists a critical temperature Tc below which the system exhibits a yield point, i.e., the slip strain increases sharply when the applied resolved shear stress attains a critical value. Above the critical temperature the yield point disappears and the slip strain depends continuously on the applied stress. The critical exponents, which describe the behavior of the system near the critical temperature, coincide with those of the two-dimensional spin-1/2 Ising model.
Dynamic Buckling and Post-buckling of Imperfect Orthotropic Cylindrical Shells Under Mechanical and Thermal Loads, Based on the Three-Dimensional Theory of Elasticity
Authors: Shariyat M. , Eslami M. R.
Published: February 2008

The three-dimensional theory of elasticity in curvilinear coordinates is employed to investigate the dynamic buckling of an imperfect orthotropic circular cylindrical shell under mechanical and thermal loads. Accurate form of the strain expressions of imperfect cylindrical shells is established through employing the general Green's strain tensor for large deformations and the equations of motion are derived in terms of the second Piola-Kirchhoff stress tensor. Then, the governing equations are properly formulated and solved by means of an efficient and relatively accurate solution procedure proposed to solve the highly nonlinear equations resulting from the above analysis. The proposed formulation is very general as it can include the influence of the initial imperfections, temperature distribution, and temperature dependency of the mechanical properties of materials, effect of various end conditions, possibility of large-deformation occurrence and application of any combination of mechanical and thermal loadings. No simplifications are done when solving the resulting equations. Furthermore, in contrast to the displacement-based layer-wise theories and the three-dimensional approaches proposed so far, the stress, force and moment boundary conditions as well as the displacement type ones, can be incorporated accurately in these formulations. Finally, a few examples of mechanical and thermal buckling of some orthotropic cylindrical shells are considered and results of the present three-dimensional elasticity approach are compared with the buckling loads predicated by the Donnell's equations, some single-layer theories, some available results of the layer-wise theory and the recently published three-dimensional approaches and the accuracy of the later methods are discussed based on the exact method presented in this paper.
Analysis of the Driving Forces for Multiple Cracks in an Infinite Nonhomogeneous Plate, Part I: Theoretical Analysis
Authors: Shbeeb N. I. , Binienda W. K. , Kreider K. L.
Published: February 2008

A general methodology is constructed for the fundamental solution of an arbitrarily oriented crack embedded in an infinite nonhomogeneous plate in which the shear modulus varies exponentially with one coordinate. The stress is evaluated as a summation of two states of stresses; one is associated with a local coordinate system in an infinite plate, while the other is associated with the boundaries of a finite plate defined in a structural coordinate system. The fundamental solution is used to generate stress intensity factors and strain energy release rates for fully interactive multiple crack problems. Part I of this paper focuses on the analytical development of the solution. In Part II, the numerical technique used in solving singular integral equations obtained in Part I is presented, along with a parametric study.
Analysis of the Driving Forces for Multiple Cracks in an Infinite Nonhomogeneous Plate, Part II: Numerical Solutions
Authors: Shbeeb N. I. , Binienda W. K. , Kreider K. L.
Published: February 2008

In Part 1 of this work, an analytical model was developed for the fundamental solution for a crack embedded in an infinite nonhomogeneous plate. This fundamental solution is used here to generate the stress intensity factors and strain energy release rates for fully interactive multiple crack problems. Also, a numerical technique used in solving the singular integral equation in Part I is presented, along with a parametric study. The parametric study addresses the influence of crack distance, relative angular orientation, and the coefficient of nonhomogeneity on the crack driving forces. The strain energy release rate is recommended for use as a crack propagation criterion because it depends on the local material properties as well as all the remaining parameters contained in the stress intensity factors.
Macrocrack-Microcrack Interaction in Piezoelectric Materials, Part I: Basic Formulations and J-Analysis
Authors: Chen Y.-H. , Han J.-J.
Published: February 2008

The macrocrack-microcrack interaction problem in transversely isotropic piezoelectric materials is studied. The microcracks near a macrocrack tip in the process zone are assumed to be parallel to the latter, while the poling direction of the piezoelectric materials is assumed to be perpendicular to the cracks. Three kinds of elementary solutions with different crack configurations and under different loading conditions are given, from which the interaction problem is reduced to a system of Fredholm integral equations by using the pseudo-traction electric displacement method (abbreviated PTED). After the equations are solved numerically, the traditional mode I and mode II stress intensity factors and the electric displacement intensity factor are evaluated. In order to confirm the proposed method as well as the numerical results, a consistency check is proposed which is based on the J-integral analysis and provides a powerful tool to examine the numerical results. Thus, any mistakes are avoided since they would certainly lead to unsatisfied numerical results contrary to the check. It is concluded also that the disturbance of the near-tip electric field provides another source of shielding.
Penetration of Rigid Projectiles Through Quasi-Brittle Materials
Authors: Mastilovic S. , Krajcinovic D.
Published: February 2008

The objective of this study is to formulate a simple, rational model for estimates of the penetration depth of rigid long rods through materials susceptible to microcracking. The proposed is based on the target resistance estimated using the particle dynamic simulations. All material parameters of the model can be identified and measured in laboratory. The accuracy of this simple model is found to be satisfactory.
Prediction of Plastic Wrinkling Using the Energy Method
Authors: Cao J.
Published: February 2008

The prediction and prevention of wrinkling during a sheet metal forming process have been challenging issues on the design of part shape, die geometry, and processing parameters. In an effort to provide a reliable and efficient tool to assess the onset of wrinkling, analytical models for flange wrinkling and straight side-wall wrinkling are presented here. Using a combination of energy conservation and plastic bending theory, the critical buckling wavelength and stress are calculated as functions of the boundary conditions (displacement constraint and binder pressure). Comparisons between the numerical and experimental results are given for both cases and excellent agreement is obtained.
Dynamic Response of Complex Structural Intersections Using Hybrid Methods
Authors: Halliday P. J. , Grosh K.
Published: February 2008

A novel application of Lagrange multipliers to couple domains modeled independently with linear elastodynamic and reduced-order theories is presented herein. This method is developed from a variational formulation of the continuous problem and is easily implemented within a finite element code. Applications include, but are not limited to, modeling of inhomogeneities such as joints, cracks, holes, and welds within a frame-like structure. Results from this method compare well with a full elastodynamic discretization and existing methods for modeling such problems.
Effective Elastic Stiffnesses of an Anisotropic Medium Permeated by Tilted Cracks
Authors: Barret C. , Baste S.
Published: February 2008

This paper is concerned with the relationship between the effective stiffness tensor and the intensity of damage in individual modes for an anisotropic material with tilted cracks. The predictions are compared favorably with the experimentally measured load-induced changes of the 13 stiffnesses of a two-dimensional C/C-SiC ceramic matrix composite subjected to an off-axis solicitation. By taking into account the thickness of the cracks, it is possible to understand the change of the elastic anisotropy of the material and of its inelastic strain.
Approximate Analysis of a Shear Band in a Thermoviscoplastic Material
Authors: Kim H.-G. , Im S.
Published: February 2008

Shear localization is systematically examined with the aid of an approximate model for the three stages of deformation in the formation and development of a shear band, which comprise: the growth of inhomogeneous deformation, the stress collapse, and the post-collapse state. A basic model of one-dimensional simple shear deformation for a thermoviscoplastic material is employed with a linear thermal softening in the absence of strain hardening. The evolution of plastic strain rate at the center of the shear band is explicitly obtained, and an approximate scaling law for the critical strain, at which the stress collapse begins, is proposed in terms of material parameters and boundary velocity. All state variables including stress, plastic strain rate, and temperature after the stress collapse are evaluated, and the overshoot of the plastic strain rate during stress collapse is explained in terms of a nondimensional parameter and elastic unloading. Finally, numerical experiments confirm the analytical results.
A Discrete Model of an Extensible String in Three-Dimensional Space
Authors: Nishinari K.
Published: February 2008

In this paper, a discrete model of an extensible string in three-dimensional space is presented. The model contains the bending and twisting of a string, and becomes the special Cosserat string in the continuous limit. We also present a new method of analyzing a string in space by the soliton theory, which can reduce the basic equations to a simpler tractable form. Some exact solutions are obtained by the soliton theory. The discrete basic equations are also shown to be suitable for numerical simulations of string dynamics.
Anisotropic Effective Moduli of Cracked Short-Fiber Reinforced Composites
Authors: Feltman R. S. , Santare M. H.
Published: February 2008

A model is presented to analyze the effect of fiber fracture on the anisotropic elastic properties of short-fiber reinforced composite materials. The effective moduli of the material are modeled using a self-consistent scheme which includes the calculated energy dissipated through the opening of a crack in an arbitrarily oriented elliptical inclusion. The model is an extension of previous works which have modeled isotropic properties of short-fiber reinforced composites with fiber breakage and anisotropic properties of monolithic materials with microcracks. Two-dimensional planar composite systems are considered. The model allows for the calculation of moduli under varying degrees of fiber alignment and damage orientation. In the results, both aligned fiber systems and randomly oriented fiber systems with damage-induced anisotropy are examined.
Nonlinear Analysis of Particle Cavitation and Matrix Yielding Under Equitriaxial Stress
Authors: Biwa S.
Published: February 2008

Cavitation of a rubber particle is a possible microscopic mechanism for toughness improvement of polymer materials, as it reduces the stress triaxiality and promotes shear yielding in the matrix. This phenomenon is presently studied theoretically by examining the radial deformation of a particle-matrix composite sphere. The rubber particle is modeled as a nonlinear elastic sphere and the surrounding matrix as a concentric elastoplastic shell. Two possible modes of deformation are identified: One represents the pure expansion of the particle and the other corresponds to particle cavitation. The analysis accounts for finite bulk stiffness of the particle and possibility of plastic yielding in the matrix. Based on the analytical expressions for the finite deformation and the stress fields derived, numerical solutions are demonstrated to illustrate the effect of cavitation to suppress the increase of triaxial stress and enhance the plastic yielding in the matrix.
Dynamic Analysis of Systems With Varying Constraints
Authors: Djerassi S.
Published: February 2008

This paper deals with constrained dynamical systems which are subject, during motion, to the replacement of one set of constraints with another. The theory of imposition and removal of constraints is used to formulate equations governing motions of such systems. To this end, the terms minimally constrained state (MCS), phase of motion, transition, and transition conditions are introduced. These terms are used to denote, respectively, state of a system subject only to constraints which are not removed throughout the motion, period of time during which an MCS system is subject to one set of constraints, event characterized by the instantaneous removal of one set of constraints and the imposition of another, and conditions, satisfaction of which initiate a transition. The indicated formulation enables the simulation of motions of the systems in question, including the evaluation of changes in the motion variables associated with the transitions. The formulation is particularly efficient in that the impulses arising during the transitions are automatically eliminated. The formulation is used to simulate motions of a number of systems, including a legged machine.
Magnetohydrodynamic Squeeze Film Characteristics Between Parallel Circular Plates Containing a Single Central Air Bubble in the Inertial Flow Regime
Authors: Usha R. , Vimala P.
Published: February 2008

In this paper, the magnetic effects on the Newtonian squeeze film between two circular parallel plates, containing a single central air bubble of cylindrical shape are theoretically investigated. A uniform magnetic field is applied perpendicular to the circular plates, which are in sinusoidal relative motion, and fluid film inertia effects are included in the analysis. Assuming an ideal gas under isothermal condition for an air bubble, a nonlinear differential equation for the bubble radius is obtained by approximating the momentum equation governing the magnetohydrodynamic squeeze film by the mean value averaged across the film thickness. Approximate analytical solutions for the air bubble radius, pressure distribution, and squeeze film force are determined by a perturbation method for small amplitude of sinusoidal motion and are compared with the numerical solution obtained by solving the nonlinear differential equation. The combined effects of air bubble, fluid film inertia, and magnetic field on the squeeze film force are analyzed.
Generation (or Degeneration) of a Separation Bubble in a Liquid-Filled Cylinder Through Spin-Up (or Spin-Down) Process
Authors: Bhattacharyya S. , Pal A.
Published: February 2008

The present study deals with the spin-up and spin-down of viscous incompressible fluid confined in a cylindrical enclosure. The spin-up (or spin-down) is developed by increasing (or decreasing) abruptly the angular velocity of the upper endwall where initial steady flow is either due to uniform rotation of the lower endwall or due to rotation of both end walls in the same direction with small rotation ratio of the top-bottom endwalls. We have seen numerically that through spin-up, an on-axis separatiorbubble can be generated (vortex breakdown) in a flow when the Reynolds number is much lower than the critical value of the Reynolds number (Re)c for the onset of vortex breakdown. At the ultimate steady state the separation bubble appears and a waviness in the stream surfaces in the vicinity of the lower endwall is found. The spin-down process acts in the opposite way. We found that for the flow with Reynolds number above the critical value (Re)c, the vortex breakdown can be prevented through spin-down and the ultimate steady-state flow is also free from it.
An Approximate Analytic Solution of the One-Dimensional Foil Bearing Problem
Authors: Renshaw A. A.
Published: February 2008

Approximate solutions are found to the one-dimensional steady-state foil bearing problem in which a longitudinally translating, flexible tensioned sheet of material rides on a thin film of entrained air as it wraps around a fixed cylinder. The approximate solutions use the first few terms of a scaled, exponential power series and minimize the squared residual in the governing differential equation. The solutions are simple, compare well with more exact solutions, and provide excellent starting points for more sophisticated, iterative solution algorithms.