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RESEARCH PAPERS

J. Appl. Mech. 1992;59(1):1-6. doi:10.1115/1.2899429.

Improved rigorous bounds on the effective elastic moduli of a transversely isotropic fiber-reinforced material composed of aligned, infinitely long, equisized, circular cylinders distributed throughout a matrix are evaluated for cylinder volume fractions up to 70 percent. The bounds are generally shown to provide significant improvement over the Hill-Hashin bounds which incorporate only volume-fraction information. For cases in which the cylinders are stiffer than the matrix, the improved lower bounds provide relatively accurate estimates of the elastic moduli, even when the upper bound diverges from it (i.e., when the cylinders are substantially stiffer than the matrix). This last statement is supported by accurate, recently obtained Monte Carlo computer-simulation data of the true effective axial shear modulus.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1992;59(1):7-15. doi:10.1115/1.2899468.

The present investigation is concerned with the behavior of an elastic, oblate, torquefree gyro model. The model has been devised such that it represents accurately arbitrarily large attitudes and arbitrarily large deformations. All simplifying assumptions are incorporated into the model before the theory is applied. The subsequent theoretical development is consequently exact; i.e., the expressions for inertia moments, angular moments, kinetic and elastic energies are all exact. Also, the mass center of the model gyro does not shift within the gyro. Equations remain tractable and the practicing engineer can readily get a feel for the phenomena uncovered. The model is composed of a rigid massless rod connected elastically to a rigid massive disk. At the tip of each rod there is a point mass. The nonlinear equations of quasistatic motion are derived using Euler’s law, and a floating coordinate frame. Following the analysis, various numerical examples are investigated and the results are plotted. The total mechanical energy of the system is determined, and the condition for existence of an energy trap state (minimum energy state at an attitude other than zero) is obtained. When trapped, the gyro is in effect rigid, has a stable attitude, and rotates around the principal axis of maximum inertia, which in turn is collinear with the space-fixed angular momentum vector.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1992;59(1):16-19. doi:10.1115/1.2899424.

The dynamic stability of a viscoelastic column subjected to a periodic longitudinal load is investigated. The viscoelastic behavior is given in terms of the Boltzmann superposition principle which yields an integro-differential equation of motion. The stability boundaries of this equation are determined analytically by using the multiplescales method. It is shown that due to the viscoelasticity the stability regions are expanded, relative to the elastic ones, and the time for which a stable system becomes unstable is given. In addition, the stability properties of the viscoelastic column are time dependent and an initially stable system can turn unstable after a finite time, unlike columns that are described by the elastic model.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1992;59(1):20-26. doi:10.1115/1.2899431.

The problem of a thick-walled cylindrical tube subjected to internal pressure is investigated within the framework of continuum plasticity. Material behavior is modeled by a finite strain elastoplastic flow theory based on the Tresca yield function. The deformation pattern is restricted by the plane-strain condition but arbitrary hardening and elastic compressibility are accounted for. A general solution is given in terms of quadratures. The analysis also includes treatment of a second plastic phase, characterized by corner relations, that may develop at the inner boundary. It is shown that the interface between the two plastic regions moves initially outwards and then, beyond a certain strain level, it moves back inwards. Some useful and simple results are given for thin-walled tubes of hardening materials and for thick-walled elastic/perfectly plastic tubes.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1992;59(1):27-32. doi:10.1115/1.2899460.

A model is developed to predict the steady-state creep behavior of misaligned short-fiber-reinforced ceramic matrix composites. The approach is based on an advanced shear-lag model and uses the multiaxial creep law for the fibers and matrix. The analysis incorporates some unique characteristics of ceramic matrix composites, such as the fiber/matrix interface sliding effect, shear and axial loads carried by the matrix, and the fact that both the fibers and matrix creep at elevated temperatures. Several parameters are varied to determine their effect on the creep behavior.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1992;59(1):33-38. doi:10.1115/1.2899461.

The paper is concerned with the dynamic response of impulsively loaded rigid-perfectly plastic structures. By combining the mode approximation technique with the upper and the lower bound theorems, we have derived a set of sequential inequalities on the final displacement of the structure. This can be applied to give a reasonable explanation for the criterion of choosing an optimal mode proposed by Symonds (1980). In addition, an approximate expression of the final displacement of the structure is suggested in cases where the “mode approximation” apparently works poorly. Finally, the suggested expression is also illustrated by examples.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1992;59(1):39-47. doi:10.1115/1.2899462.

A simple and accurate method for estimating the three-dimensional effective moduli of symmetric and orthotropic laminated composites is presented. The method is based on obtaining the exact displacement field of three boundary value problems of laminated composites using the Airy stress function solution technique. The effective moduli are estimated by matching the boundary displacements of the equivalent homogeneous system with those of the laminated system. Among the estimated effective moduli, those associated with the interlaminar direction are of special interest. It is found that the effective interlaminar normal stiffness in extensional deformation is independent of laminae stacking sequence which is consistent with the finding of Pagano (1974). However, the laminate interlaminar shear stiffness is dependent on stacking sequence, and it is shown that the rule of mixtures can not predict the interlaminar shear stiffness accurately.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1992;59(1):48-53. doi:10.1115/1.2899463.

The problem studied in this paper concerns the dynamic expansion of a spherical void in an unbounded solid under the action of remote hydrostatic tension. The void is assumed to remain spherical throughout the deformation and the matrix to be incompressible. The effects of inertia, strain hardening, and rate sensitivity on the short and long-term behavior of the void, as well as on its response to ramp loading, are investigated in detail.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1992;59(1):54-60. doi:10.1115/1.2899464.

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

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1992;59(1):61-68. doi:10.1115/1.2899465.

Very high stresses develop near the intersection of a planar interfacial crack with the free surface of joined materials with large mismatch of elastic moduli. The socalled corner singularity is more singular than the 1/distance singularity of the interior fields. The eigenvalues corresponding to the most singular state, and for which the strain energy of a finite cone is bounded, are in general complex. For a wide selection of material pairs, our calculations show that the eigenvalue of the dominant singularity, 0(r−s ) , is real and s increases from 0.5 to about 0.75 as the moduli mismatch increases. Values of s are reported for a broad range of material combinations. A class of anisotropic materials and bicrystals is also investigated.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1992;59(1):69-76. doi:10.1115/1.2899466.

Our earlier technique for a semi-infinite strip (Kim and Steele, 1990) is extended to study general end problems and corner singularities for semi-infinite and finite solid cylinders with free walls. For handling general end conditions, we expand the displacement and stress in term of the Dini series which are the solutions of the cylinders with mixed wall conditions. The relation between the harmonic coefficients of the end displacement and stress is then formed, which we call the end stiffness matrix. One advantage of the end stiffness matrix approach is that the procedure for finite cylinders can be easily built up from that of semi-infinite cylinders. For some end conditions which may yield singular stresses, the nature of the singularity is investigated by the asymptotic analysis of the Dini series coefficients of the stresses. The problems studied by Benthem and Minderhoud (1972) and Robert and Keer (1987) are solved with the present approach.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1992;59(1):77-83. doi:10.1115/1.2899467.

A problem of two bonded, dissimilar half-planes containing an elliptical hole on the interface is solved. The external load is uniform tension parallel to the interface. A rational mapping function and complex stress functions are used and an analytical solution is obtained. Stress distributions are shown. Stress concentration factors are also obtained for arbitrary lengths of debonding and for several material constants. In addition, an approximate expression of the stress concentration factor is given for elliptical holes and the accuracy is investigated.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1992;59(1):84-91. doi:10.1115/1.2899469.

Recent experiments by Wang (1990) on copper bicrystals with a [110] symmetric tilt of 38.9 degrees have shown that the mode of fracture of these bicrystals, i.e., whether fracture is of a ductile or brittle nature, depends on the direction of cracking. An analysis of this effect within the framework of continuum crystal plasticity is presented. The formulation accounts for finite deformations and finite lattice rotations, as well as for the full three-dimensional collection of slip systems in FCC crystals. Our results indicate that, whereas the level of stress ahead of the crack tip is similar for the ductile and brittle cracking directions, the sizes of the plastic regions differ significantly in the two cases.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1992;59(1):92-94. doi:10.1115/1.2899470.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1992;59(1):95-101. doi:10.1115/1.2899471.

In some polymers, stress-induced changes in molecular mobility give rise to a strain-softening effect. The influence of this effect on the stress and deformation fields near a crack tip are examined using the finite element method. A phenomenological nonlinearly viscoelastic constitutive model (based on the concept of free volume) is used in the calculations. When a load is suddenly applied to a cracked specimen, the instantaneous response of the material is linearly elastic. However, strain-induced softening in the crack-tip region leads to a relaxation in the stress and time variation of the region over which the singular field prevails. For realistic material parameters, this region may become extremely small. In addition, a zone of strain-softened material emanantes from the crack tip and extends along the crack line. This process zone can promote conditions which are favorable for the nucleation and growth of microvoids and the formation of crazes.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1992;59(1):102-108. doi:10.1115/1.2899414.

The reflection and transmission of a plane wave by a distribution of cavities in the interface of two solids of different mechanical properties are investigated. For the calculation of the reflection and transmission coefficients by a distribution of cavities, six auxiliary wave states are used in conjunction with the reciprocal identity. Specific results are presented for scattering by a doubly periodic array of cavities in the interface of solids of different elastic moduli and mass densities. For a typical cell, the boundary integral equations for scattering by a cavity at the interface of two solids are derived on the basis of continuity of displacements and tractions across the interface and by taking advantage of the geometrical periodicity. Solutions to the system of singular integral equations have been obtained by the boundary element method. Numerical results are presented as functions of the frequency for two angles of incidence.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1992;59(1):109-119. doi:10.1115/1.2899415.

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

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1992;59(1):120-127. doi:10.1115/1.2899416.

We employ Coulomb friction and both tangential and normal restitution in a model for a collision between a homogeneous sphere and a flat wall. We calculate the impulse and change in kinetic energy in typical collisions and use a particularly simple velocity distribution function to obtain the rates at which momenta and energy are supplied to the flow over a unit area of the wall. From these, we determine boundary conditions that relate the shear stress and energy flux in the flow at the wall to the normal stress, slip velocity, and fluctuation energy and to the parameters that characterize a collision.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1992;59(1):128-135. doi:10.1115/1.2899417.

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

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1992;59(1):136-139. doi:10.1115/1.2899418.

This paper considers some of the theoretical aspects of the formulation of frequency-dependent structural matrices. Two types of mass matrices are examined, the consistent mass matrix found by integrating frequency-dependent shape functions, and the mixed mass matrix found by integrating a frequency-dependent shape function against a static shape function. The coefficients in the power series expansion for the consistent mass matrix are found to be determinable from those in the expansion for the mixed mass matrix by multiplication by the appropriate constant. Both of the mass matrices are related in a similar manner to the coefficients in the frequency-dependent stiffness matrix expansion. A formulation is derived which allows one to calculate, using a shape function truncated at a given order, the mass matrix expansion truncated at twice that order. That is the terms for either of the two mass matrix expansions of order 2n are shown to be expressible using shape functions terms of order n . Finally, the terms in the matrix expansions are given by formulas which depend only on the values of the shape function terms at the boundary.

Topics: Functions , Shapes , Stiffness
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1992;59(1):140-145. doi:10.1115/1.2899419.

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

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1992;59(1):146-152. doi:10.1115/1.2899420.

An analytical model is developed to study the extension-bending-torsion coupling behavior of an initially twisted elastic beam with an irregular cross-section. The determination of the complete displacement field requires solving a coupled two dimensional boundary value problem in a curvilinear coordinate system for the local deformations in the section plane and warping out of the section plane. The principle of minimum potential energy is applied to a discretized representation of the cross-section (Ritz method) to calculate solutions to this problem. Numerical results illustrate the pronounced effects pretwist, initial twist axis location, and in-plane deformation have on the behavior of solid and single and multi-celled sections, including airfoil sections.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1992;59(1):153-160. doi:10.1115/1.2899421.

The incremental harmonic balance (IHB) method is extended to analyze the periodic vibrations of systems with a general form of piecewise-linear stiffness characteristics. An explicit formulation has been worked out. This development is of significance as many structural and mechanical systems of practical interest possess a piecewise-linear stiffness. Typical examples show that the IHB method is very effective for analyzing this kind of systems under steady-state vibrations.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1992;59(1):161-167. doi:10.1115/1.2899422.

A straight beam with fixed ends, forced with two frequencies is considered. By using Galerkin’s method, the equation of motion of the beam is reduced to a finite degree-of-freedom system. The resulting equation is transformed into a multi-frequency system and the averaging method is applied. It is shown, by using Melnikov’s method, that there exist transverse homoclinic orbits in the averaged system associated with the first-mode equation. This implies that chaotic motions may occur in the single-mode equation. Furthermore, the effect of higher modes and the implications of this result for the full beam motions are described.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1992;59(1):168-175. doi:10.1115/1.2899423.

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

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1992;59(1):176-181. doi:10.1115/1.2899425.

Some linear vibrating systems give rise to differential equations of the form Iẍ(t) + Bẋ(t) + C x(t) = 0 , where B and C are square matrices. Stability criteria involving only the matrix coefficients I, B, C , and a single parameter are obtained for some special cases. Thus, if B* = B> 0, C* = C> 0 and B>kI + k −1 C , then the system will be overdamped (and hence stable). Gyroscopic systems also have the above form where B is real and skew symmetric. The case where C >0 is well understood and for the case −C >0 we show the condition B abs >kI −k −1 C for some k >0 will ensure stability. In fact, this condition can be generalized to systems with B* = B, C> 0.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1992;59(1):182-190. doi:10.1115/1.2899426.

A Boundary Element Method (BEM) formulation for the determination of design sensitivities of temperature distributions to various shape and process parameters in steady-state convection-diffusion problems is presented in this paper. The present formulation is valid for constant or piecewise-constant convective velocities. This approach is based on direct differentiation (DDA) of the relevant BEM formulation of the problem. It retains the advantages of the BEM regarding accuracy and efficiency while avoiding strongly singular kernels. The BEM formulation is also observed to avoid any false diffusion. This approach provides a new avenue toward efficient optimization of steady-state convection-diffusion problems and may be easily adapted to investigate the thermal aspects of various machining processes.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1992;59(1):191-195. doi:10.1115/1.2899427.

The response of a cylindrical liquid column consisting of an incompressible and frictionless liquid has been investigated for a pitching bridge bottom. The response of the free surface and velocity distribution has been determined and numerically evaluated. In addition, the transient behavior of the column has been treated. Since for nonviscous liquid the response exhibits at the resonances singularity, a semi-empirical damping was introduced in the resonance terms. Its magnitude has to be determined by experiments.

Topics: Resonance , Damping
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1992;59(1):196-205. doi:10.1115/1.2899428.

This paper describes the observed dynamical behavior of a cantilevered pipe conveying fluid, an autonomous nonconservative (circulatory) dynamical system, limit-cycle motions of which, upon loss of stability via a Hopf bifurcation, interact with nonlinear motion-limiting constraints. This system was found to become chaotic at sufficiently high flow rates. Motions of the system, sensed by an optical tracking system, were analyzed by Fast Fourier Transform, autocorrelation, Poincaré map, and delay embedding techniques, and the fractal dimension of the system, d c , was calculated. Values of d c = 1.03, 1.53, and 3.20 were obtained in the period-1, “fuzzy” period-2 and chaotic regimes of oscillation of the system. Based on these calculations, a four-dimensional analytical model was constructed, which was found to capture the essential dynamical features of observed behavior quite well.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1992;59(1):206-210. doi:10.1115/1.2899430.

A symmetry reduction using a one-parameter spiral group is performed on a Reynolds equation in order to analyze this equation arising in the study of film lubrication. Approximate solutions are found for the time-independent case-both numerically and by the method of perturbation. Solutions to the time-dependent equation are found by using the invariance in the time and angular variables only. These solutions, called semi-invariant solutions, are determined through separation of variables.

Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

J. Appl. Mech. 1992;59(1):211-214. doi:10.1115/1.2899432.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1992;59(1):214-215. doi:10.1115/1.2899433.
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1992;59(1):215-217. doi:10.1115/1.2899434.

The plane elasticity problem of an internal stress source located near a lamellar inhomogeneity is considered. It is assumed that the lamella-matrix interface does not transmit tangential displacements or shear tractions (slipping interface). The elastic field is given in terms of the source bulk field and one parameter formed from the elastic constants. The image force on an edge dislocation near the lamella is calculated and discussed. A dislocation stable-equilibrium position exists in a domain of elastic constants and Burgers vector directions. This result is characteristic of the interaction with a slipping lamellar inhomogeneity having finite thickness.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1992;59(1):217-219. doi:10.1115/1.2899435.

Relaxation testing is an important alternative for investigating the creep properties of a material. A solution for the strain-hardening form of the power law is derived and compared to its time-hardening counterpart.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1992;59(1):220-221. doi:10.1115/1.2899436.
Abstract
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1992;59(1):224-225. doi:10.1115/1.2899438.
Abstract
Topics: Stress
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1992;59(1):225-228. doi:10.1115/1.2899439.
Abstract
Topics: Force , Torque , Stability
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1992;59(1):228-230. doi:10.1115/1.2899440.

A recent study suggested that the use of numerical integration methods would generally lead to the erroneous prediction of chaotic behavior for an unforced Duffing’s oscillator. It is shown herein that appropriate implementations of such methods lead to accurate, nonchaotic computations of the associated response.

Topics: Computation
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1992;59(1):233-234. doi:10.1115/1.2899442.
Abstract
Topics: Pendulums
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1992;59(1):234-235. doi:10.1115/1.2899443.

Transverse, axisymmetric vibrations of a rotating disk of uniform strength is studied. Closed-form solution for the equation of transverse motion is obtained in terms of confluent hypergeometric functions.

Commentary by Dr. Valentin Fuster

DISCUSSIONS

Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster

BOOK REVIEWS

J. Appl. Mech. 1992;59(1):245. doi:10.1115/1.2899458.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1992;59(1):245-246. doi:10.1115/1.2899459.
FREE TO VIEW
Abstract
Topics: Plasticity
Commentary by Dr. Valentin Fuster

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