bluuebunny/crossref_metadata_2025 huggingface dataset:
End Effects in Laminated Anisotropic Beams—Part II
Authors: Ackermann J. A. , Kozik T. J.
Published: February 2008

An analytical method of examining the stress field near the edge of a simply supported, laminated beam was developed in Part I of this paper. The result was a system of second-order, ordinary, linear, nonhomogeneous differential equations. A numerical and analytical technique for solving these equations is presented in this paper. The method is a versatile stress analysis procedure which can accommodate any combination of material lay-up and can simulate any prescribed distribution of normal load on the upper and lower surfaces. The reactions at the ends of the beam may be distributed over the surface edges in a fashion most accurately characterizing the physical supports. An all-steel lay-up is examined as a basis for comparison with Bernoulli-Euler and Timoshenko theory; and a two-layered steel/aluminum beam is examined to simply demonstrate the method’s capability of determining the interlaminar transverse shear and normal stresses.
Full-Fuel-Cycle Modeling for Alternative Transportation Fuels
Authors: Bell S. R. , Gupta M. , Greening L. A.
Published: February 2008

Utilization of alternative fuels in the transportation sector has been identified as a potential method for mitigation of petroleum-based energy dependence and pollutant emissions from mobile sources. Traditionally, vehicle tailpipe emissions have served as sole data when evaluating environmental impact. However, considerable differences in extraction and processing requirements for alternative fuels makes evident the need to consider the complete fuel production and use cycle for each fuel scenario. The work presented here provides a case study applied to the southeastern region of the United States for conventional gasoline, reformulated gasoline, natural gas, and methanol vehicle fueling. Results of the study demonstrate the significance of the nonvehicle processes, such as fuel refining, in terms of energy expenditure and emissions production. Unique to this work is the application of the MOBILE5 mobile emissions model in the full-fuel-cycle analysis. Estimates of direct and indirect green-house gas production are also presented and discussed using the full-cycle-analysis method.
An Operation Support System of Large City Gas Networks Based on Fluid Transient Model
Authors: Kiuchi T. , Izumi H. , Huke T.
Published: February 2008

This paper describes the essential features and experience of applying a fluid transient model to the operation support system of large city gas pipeline networks. The system, operating in the second largest city, Osaka, in Japan since 1992, includes the functions of a real-time leak detection and localization, a fast predictive computation of the pressure and flow distributions in networks, and an interactive training simulator using a transient model connected with SCADA training system. To achieve fast forecasting calculation in real-time manner, the combined method of a fully implicit transient calculation for high pressure transmission networks and a steady-state calculation for middle pressure distribution networks is developed. The actual performance of real-time leak detection and the accuracy of the forecasting model are discussed.
A Biomass Combustion-Gasification Model: Validation and Sensitivity Analysis
Authors: Bettagli N. , Desideri U. , Fiaschi D.
Published: February 2008

The aim of the present paper is to study the gasification and combustion of biomass and waste materials. A model for the analysis of the chemical kinetics of gasification and combustion processes was developed with the main objective of calculating the gas composition at different operating conditions. The model was validated with experimental data for sawdust gasification. After having set the main kinetic parameters, the model was tested with other types of biomass, whose syngas composition is known. A sensitivity analysis was also performed to evaluate the influence of the main parameters, such as temperature, pressure, and air-fuel ratio on the composition of the exit gas. Both oxygen and air (i.e., a mixture of oxygen and nitrogen) gasification processes were simulated.
Effects of Condenser Air Flow Blockage on Vapor-Compression Refrigerator Performance
Authors: Bultman D. H. , Burmeister L. C. , Bortone V.
Published: February 2008

The performance of a nominally 10.5-kW (3-ton) vapor-compression refrigeration system was numerically simulated for air flow rates across the condenser heat exchanger between 60 and 150 percent of the standard value. The results can be used for estimating the energy and cost savings achievable by restoring standard air flow rates across partially blocked condensers of vapor-compression refrigeration systems. The system coefficient of performance was predicted to decrease by 7.6 percent from its value of 2.912 at standard air flow when air flow across the condenser decreased by 40 percent. The associated pressure rise across the compressor increased by 19 percent above its standard value of 1151 kPa, suggesting that reduced compressor life might be the major economic consequence of condenser air flow blockage.
Numerical Study on Flows of Red Blood Cells With Liposome-Encapsulated Hemoglobin at Microvascular Bifurcation
Authors: Hyakutake Toru , Tominaga Shouko , Matsumoto Takeshi , Yanase Shinichiro
Published: February 2008

Flow analysis at microvascular bifurcation after partial replacement of red blood cell (RBC) with liposome-encapsulated hemoglobin (LEH) was performed using the lattice Boltzmann method. A two-dimensional symmetric Y bifurcation model with a parent vessel diameter of 20μm and daughter branch diameters of 20μm was considered, and the distributions of the RBC, LEH, and oxygen fluxes were calculated. When only RBCs flow into the daughter branches with unevenly distributed flows, plasma separation occurred and the RBC flow to the lower-flow branch was disproportionately decreased. On the other hand, when half of RBC are replaced by LEH, the biasing of RBC flow was enhanced whereas LEH flowed favorably into the lower-flow branch, because many LEH within the parent vessel are suspended in the plasma layer, where no RBCs exist. Consequently, the branched oxygen fluxes became nearly proportional to flows. These results indicate that LEH facilitates oxygen supply to branches that are inaccessible to RBCs.
Study of the Influence of Fibrous Pericellular Matrix in the Cortical Interstitial Fluid Movement With Hydroelectrochemical Effects
Authors: Lemaire Thibault , Naïli Salah , Rémond Agnès
Published: February 2008

Fluid flow within cortical bone tissue is modeled through an upscaling approach of a local description of the fluid movement. At the pore scale, the coupled phenomena (Poiseuille effect, osmosis, and electro-osmosis) governing the interstitial fluid movement are considered. Thus, actions of electro-osmotic and osmotic motions, in addition to the classical Poiseuille flow, are studied at the canaliculus scale by deriving a coupled Darcy law. The addition of a Brinkman-like term in this macroscopic result helps us to take into account the influence of the pericellular matrix on the coupled transport phenomena. At the canaliculus scale, the general trends that can be drawn from this study are as follows: (i) The presence of the fibrous matrix tends to reduce the fluid flow considerably; (ii) the role of osmotic and electro-osmotic effects is no longer negligible for dense fibrous media.
Determination of Homeostatic Elastic Moduli in Two Layers of the Esophagus
Authors: Gregersen Hans , Liao Donghua , Fung Yuan Cheng
Published: February 2008

The function of the esophagus is mechanical. To understand the function, it is necessary to know how the stress and strain in the esophagus can be computed, and how to determine the stress-strain relationship of the wall materials. The present article is devoted to the issue of determining the incremental elastic moduli in the layers of the esophagus under homeostatic conditions. The esophagus is treated as a two-layered structure consisting of an inner collagen-rich submucosa layer and an outer muscle layer. We adopt a theory based on small perturbation experiments at homeostatic conditions for determination of incremental moduli in circumferential, axial, and cross directions in the two layers. The experiments are inflation, axial stretching, circumferential bending, and axial bending. The analysis takes advantage of knowing the esophageal zero-stress state (an open sector with an opening angle of 59.4±13.2deg). The neutral axis was located 27%±1.9%away from the mucosal surface. It is demonstrated that under homeostatic conditions, the incremental moduli are layer and direction dependent. The incremental modulus is the highest in the axial direction. Furthermore, the axial moduli for the two layers are similar, whereas in the circumferential direction, the incremental modulus is a factor of 6 higher in the mucosa-submucosa layer compared to the muscle layer. Hence, the esophagus has to be treated as a composite, anisotropic body. With this additional information, we can then look forward to a vision of truly understanding the mechanical events of the esophagus.
Mechanical Characterization of Electrospun Polycaprolactone (PCL): A Potential Scaffold for Tissue Engineering
Authors: Duling Ryan R. , Dupaix Rebecca B. , Katsube Noriko , Lannutti John
Published: February 2008

This paper investigates the mechanical behavior of electrospun polycaprolactone (PCL) under tensile loading. PCL in bulk form degrades slowly and is biocompatible, two properties that make it a viable option for tissue engineering applications in biomedicine. Of particular interest is the use of electrospun PCL tubes as scaffolds for tissue engineered blood vessel implants. Stress relaxation and tensile tests have been conducted with specimens at room temperature (21°C) and 37°C. Additionally, to probe the effects of moisture on mechanical behavior, specimens were tested either dry (in air) or submerged in water. In general, the electrospun PCL was found to exhibit rate dependence, as well as some dependence on the test temperature and on whether the sample was wet or dry. Two different models were investigated to describe the experimentally observed material behavior. The models used were Fung’s theory of quasilinear viscoelasticity (QLV) and the eight-chain model developed for rubber elastomers by Arruda and Boyce (1993, “A Three-Dimensional Constitutive Model for the Large Stretch Behavior of Rubber Elastic Materials,” J. Mech. Phys. Solids, 41(2), pp. 389–412). The implementation and fitting results, as well as the advantages and disadvantages of each model, are presented. In general, it was found that the QLV theory provided a better fit.
Effects of Oral Airway Geometry Characteristics on the Diffusional Deposition of Inhaled Nanoparticles
Authors: Xi Jinxiang , Longest P. Worth
Published: February 2008

The deposition of ultrafine aerosols in the respiratory tract presents a significant health risk due to the increased cellular-level response that these particles may invoke. However, the effects of geometric simplifications on local and regional nanoparticle depositions remain unknown for the oral airway and throughout the respiratory tract. The objective of this study is to assess the effects of geometric simplifications on diffusional transport and deposition characteristics of inhaled ultrafine aerosols in models of the extrathoracic oral airway. A realistic model of the oral airway with the nasopharynx (NP) included has been constructed based on computed tomography scans of a healthy adult in conjunction with measurements reported in the literature. Three other geometries with descending degrees of physical realism were then constructed with successive geometric simplifications of the realistic model. A validated low Reynolds number k-ω turbulence model was employed to simulate laminar, transitional, and fully turbulent flow regimes for the transport of 1–200 nm particles. Results of this study indicate that the geometric simplifications considered did not significantly affect the total deposition efficiency or maximum local deposition enhancement of nanoparticles. However, particle transport dynamics and the underlying flow characteristics such as separation, turbulence intensity, and secondary motions did show an observable sensitivity to the geometric complexity. The orientation of the upper trachea was shown to be a major factor determining local deposition downstream of the glottis and should be retained in future models of the respiratory tract. In contrast, retaining the NP produced negligible variations in airway dynamics and could be excluded for predominantly oral breathing conditions. Results of this study corroborate the use of existing diffusion correlations based on a circular oral airway model. In comparison to previous studies, an improved correlation for the deposition of nanoparticles was developed based on a wider range of particle sizes and flow rates, which captures the dependence of the Sherwood number on both Reynolds and Schmidt numbers.
Stress Transmission in Polycrystals With Frictionless Grain Boundaries
Authors: Rodin G. J.
Published: February 2008

A simple method of analysis of stress transmission in polycrystals with frictionless grain boundaries is presented. This method applies to a large class of two-dimensional and three-dimensional polycrystals which can be modeled as either periodic or disordered arrays of polyhedra. Calculations are performed for the periodic arrays of rhombic dodecahedra and truncated octahedra, and for arrays generated by the Voronoy tessellation of disordered point lattices. Results of these calculations show that normal stresses transmitted by frictionless grain boundaries are significantly different from applied stresses. In particular, it is predicted that, in disordered polycrystals subjected to uniaxial compression, 45 percent of grain boundaries are in tension and the maximum tensile stress is one half of the applied stress.
Finite Element Analysis of Repeated Indentation of an Elastic-Plastic Layered Medium by a Rigid Sphere, Part II: Subsurface Results
Authors: Kral E. R. , Komvopoulos K. , Bogy D. B.
Published: February 2008

Finite element solutions are presented for the subsurface stress and deformation fields in a layered elastic-plastic half-space subjected to repeated frictionless indentation by a rigid sphere. A perfectly adhering layer is modeled using two different thicknesses and elastic modulus and yield stress two and four times greater than those of the substrate. The significance of strain hardening during plastic deformation is investigated by assuming elastic-perfectly plastic and isotropically strain-hardening constitutive laws for both the layer and substrate materials. At least three load-unload cycles are applied to a peak load of 300 times the load necessary to initiate yielding in a homogeneous half-space with substrate properties. The effects of the layer thickness and material properties of the layer and substrate on the loaded and residual stresses are interpreted, and the consequences for subsurface crack initiation are discussed. The maximum principal and interfacial shear stresses are given as a function of a nondimensional strain parameter. The effect of subsequent load cycles on the loaded, residual, and maximum tensile and interfacial shear stresses and the protection provided by the harder and stiffer layer are analyzed. Reyielding during unloading and the possibility of elastic shakedown are discussed, and the accumulation of plastic strain in the yielding regions is tracked through subsequent load cycles.
A Study of Saint-Venant’s Principle for Composite Materials by Means of Internal Stress Fields
Authors: Arimitsu Yutaka , Nishioka Kazumi , Senda Toyomitsu
Published: February 2008

It is well known that end effects in a composite material do not always decay as they do in a homogeneous and isotropic material, but there is no unified explanation for this difference. We note that the stress field in a composite material can be resolved into two kinds: one is the stress distribution in an isotropic and homogeneous reference system where Saint-Venant’s principle is satisfied and the other is the internal stress field induced by the incompatibility. Considering that the incompatibility is proportional to the difference between the elastic compliances of the components or to the deviation from isotropy, we propose, based on an argument concerning the dislocations associated with the incompatibility, a reason why end effects may survive to a long distance in a composite material.
Load Buckling of a Layer Bonded to a Half-Space With an Interface Crack
Authors: Wang Wen-Xue , Takao Yoshihiro
Published: February 2008

An analytical solution is presented for local buckling of a model of delaminated composites, that is, a layer bonded to a half-space with an interface crack. The layered system is subjected to compressive load parallel to the free surface. Basic stability equations derived from the mathematical theory of elasticity are employed to study this local buckling behavior. They are different from the conventional buckling equations used in most previous studies and based on the classical structural mechanics of beams and plates. A system of homogeneous Cauchy-type singular integral equations of the second kind is formulated by means of the Fourier integral transform and is solved numerically by utilizing Gauss-Chebyshev integral formulae. Numerical results for the buckling load and shape are presented for various delamination geometries and material properties of both the layer and half-space.
Elastic Analyses of Planar Cracks of Arbitrary Shape
Authors: Guo Quanxin , Wang Jian-Juei , Clifton R. J. , Mertaugh L. J.
Published: February 2008

A numerical method is presented for planar cracks of arbitrary shape. The fundamental solution for a dislocation segment is obtained from the point force solution and used to derive three coupled surface integral equations in which the crack-face tractions are expressed in terms of the gradients of the relative crack-surface displacements. Because the singularity of the kernel in the integral equations is one order less for fundamental solutions based on dislocation segments than for those based on dislocation loops or the body force method, no special numerical techniques are required. Most of the integrations over elements are evaluated analytically. The integral equations are solved numerically by covering the crack surface with triangular elements, and taking the relative displacements to vary linearly over the elements. The mesh is generated by optimizing the local aspect ratio, which is related to the difference in the principal stretches of the mapping of a square reference mesh onto the fracture surface. This mesh generator allows cracks of a wide variety of shapes to be analyzed with good accuracy. Comparison with known solutions indicate that accurate numerical solutions are obtained with a relatively coarse mesh.
An Axisymmetric Crack in Bonded Materials With a Nonhomogeneous Interfacial Zone Under Torsion
Authors: Ozturk M. , Erdogan F.
Published: February 2008

In this study the mode III axisymmetric crack problem for two dissimilar homogeneous materials bonded through a thin layer of nonhomogeneous interfacial region is considered. The shear modulus of the interfacial layer is assumed to be μ2(z) = μ1 exp (αz). It is also assumed that μ3 = μ1 exp (αh), h being the thickness of the layer and μ1 and μ3 the shear moduli of the adherents. The main results of the study are the stress intensity factors, the strain energy release rates and, to a limited extent, the crack-opening displacements obtained as functions of the two primary variables h/a and μ3/μ1 under various loading conditions, where a is the radius of the crack. Some results are also presented for a penny-shaped crack in an unbounded nonhomogeneous medium.
Comparison of Experimental and Simulated Grain Flows
Authors: Drake T. G. , Walton O. R.
Published: February 2008

Fully three-dimensional computer simulations of identical spheres flowing in an inclined glass-walled channel only slightly wider than a particle diameter successfully reproduce profiles of mean velocity, bulk density, and particle rotations as well as profiles of fluctuating quantities measured from high-speed motion pictures of physical experiments. All simulation parameters are measured experimentally. Both full simulations of the geometry of the physical experiments and simulations using periodic boundary conditions in the downchute direction are used to gather micromechanical information. For these collision-dominated flows, quantitative predictions of the simulations are relatively insensitive to details of the particle-interaction model and particularly the particle stiffness, but are relatively sensitive to extraneous fluid drag forces and the chute geometry.
A Three-Dimensional Unit Cell Model With Application Toward Particulate Composites
Authors: Wienecke H. A. , Brockenbrough J. R. , Romanko A. D.
Published: February 2008

A formulation of a fully three-dimensional unit cell model is presented for uniform general deformation at a point in a composite material. The unit cell model is constructed as a finite element discretization of the unit cube. General displacement periodicity boundary conditions are prescribed such that the cell may be considered as a representative volume element of material. As a particular application of the model, the problem of determining the least anisotropic periodic model of a particulate composite is considered, and comparisons are made with bounds for elastic two-phase composites possessing cubic symmetry.
Mode Localization Phenomena in Nearly Periodic Systems
Authors: Cai C. W. , Cheung Y. K. , Chan H. C.
Published: February 2008

The normal mode localization in nearly periodic systems with one-degree-of-freedom subsystems and a single subsystem departing from the regularity in one, two, and three dimensions has been studied. The closed-frequency equations may be derived by using the U-transformation technique. It is shown that in one- and two-dimensional problems any amount of simple disorder (for stiffness or mass), however small, is sufficient to localize one mode and in three-dimensional systems, a finite threshold of disorder is needed in order to localize one mode. These conclusions are in agreement with those predicted by Hodges.
Scattering of Longitudinal Elastic Waves From an Anisotropic Spherical Shell
Authors: Mittleman J. , Roberts R. , Thompson R. B.
Published: February 2008

An exact solution for scattering of ultrasound from a spherically orthotropic shell is presented. The shell is assumed to be embedded in an isotropic elastic medium, and the core surrounded by the shell is also assumed to be isotropic. The shell itself is assumed to be “spherically orthotropic,” with five independent elastic constants (the spherical analog of a transversely isotropic material in Cartesian coordinates). Field equations for this material are presented, and these equations are shown to be separable. Working with the displacement vector, we find that the radius dependent part of the solution satisfies coupled second-order ordinary differential equations. This system of equations is solved using the method of Frobenius, and results in four independent series determined by material properties to within a multiplicative constant. Use of boundary conditions expressed in terms of stresses and displacements at the inner and outer shell radii completes the solution. Numerical results for a range of shell elastic constants show that this solution matches known analytic results in the special case of isotropy and matches previously developed finite difference results for anisotropic elastic constants. The effect of shell anisotropy on far-field scattering amplitude is explored for an incident plane longitudinal wave.
Free Vibration Studies on Stress-Free Three-Dimensional Elastic Solids
Authors: Liew K. M. , Hung K. C. , Lim M. K.
Published: February 2008

A comprehensive investigation on free vibration of three-dimensional elastic solids of rectangular planform is reported. The continuum is considered to be free from normal and in-plane stresses on the facets. Functions representing the spatial displacement fields of the continuum in a complete Cartesian coordinate system are expressed in terms of sets of orthogonal polynomial functions in the x, y, and z directions. The energy functional derived based on the three-dimensional elasticity theory is minimized to arrive at the governing eigenvalue equation. In this paper, the vibration of stress-free elastic solids in the forms of short columns, thick plates, and solid cubes are studied. Frequency parameters and the first known three-dimensional deformed mode shapes have been generated for these stress-free elastic solids.
Elastic Compression of a Fiber Network
Authors: Toll S. , Manson J.-A. E.
Published: February 2008

A constitutive equation for a planar fiber network under transverse compression is derived allowing for an in-plane fiber orientation distribution. The fibers are assumed to be well dispersed in space and to have a large aspect ratio and uniform diameter. A compression experiment, performed on a glass-fiber network obtained by ashing a commercial composite preform, is accurately described by the theory.
Amplitude Bounds of Linear Free Vibrations
Authors: Schiehlen W. , Hu Bin
Published: February 2008

Linear free vibrations are completely characterized by their eigen-frequencies and eigenmodes. However, in engineering applications the amplitudes of a vibrating system have to be bounded, too. The information on the amplitudes of linear vibrations is available from the general solution for each set of initial conditions, which usually are unknown vector quantities. The initial energy is a scalar quantity which is used to identify the amplitude bounds of arbitrarily damped linear vibrating systems.
Symmetries of the Amplitude Equations of an Inextensional Beam With Internal Resonance
Authors: Feng Z. C. , Leal L. G.
Published: February 2008

We study the symmetries admitted by the amplitude equations governing the nonlinear nonplanar parametric responses of an inextensional beam (Nayfeh and Pai, 1989). As a result of these symmetries, the differential equations can be integrated in two limiting cases.
Stress Concentration Equations for Straight-Shank and Countersunk Holes in Plates
Authors: Shivakumar K. N. , Newman J. C.
Published: February 2008

Stress concentration equations for straight shank and countersunk holes in a large plate subjected to various loading conditions encountered in service were developed from three-dimensional finite element solutions. For straight shank holes, three types of loading: remote tension, remote bending, and pin loading were considered; and for the countersunk hole only remote tension and bending loads were considered. The equations are within one percent of the finite element results and are valid for isotropic materials with Poisson’s ratio of 0.3.
Existence of Stoneley Waves at an Unbonded Interface Between Two Micropolar Elastic Half-Spaces
Authors: Tajuddin M.
Published: February 2008

Following Eringen’s theory, the question whether a Stoneley mode can exist at an unbonded interface between two micropolar elastic half-spaces is examined analytically. Explicit conditions for its existence are derived when the two half-spaces are incompressible or Poisson solids whose material properties are close to each other.
A Theoretical Investigation of the Effect of Structural Stiffness in Underwater Shock Wave Loading Using the Plane Wave Approximation
Authors: Dawson R. L. , Sullivan G. M.
Published: February 2008

The equations of motion for an explosively loaded infinite plate with stiffness are derived. The structural response of this plate is compared to that of an explosively loaded infinite plate without stiffness. The effect of stiffness on water cavitation and plate displacement is determined.
The Influence of Transient Flexural Waves on Dynamic Strains in Cylinders
Authors: Simkins T. E.
Published: February 2008

The displacement response of a semi-infinite, thin-walled cylinder to a pressure moving at a constant velocity has been solved by Sing-chih Tang in closed form except for an integral term which Tang was forced to evaluate numerically. In this paper, an asymptotic evaluation of this integral is given which adds considerably to the physical interpretation of the solution. In brief, the asymptotic evaluation represents the long-term propagation of transients in the cylinder and their interaction with the steady-state solution.
Three-Dimensional Analysis of Cracking in a Multilayered Composite
Authors: Kuo C. H. , Keer L. M.
Published: February 2008

The three-dimensional problem of a multilayered composite containing an arbitrarily oriented crack is considered in this paper. The crack problem is analyzed by the equivalent body force method, which reduces the problem to a set of singular integral equations. To compute the kernels of the integral equations, the stiffness matrix for the layered medium is formulated in the Hankel transformed domain. The transformed components of the Green’s functions and derivatives are determined by solving the stiffness matrix equations, and the kernels are evaluated by performing the inverse Hankel transform. The crack-opening displacements and the three modes of the stress intensity factor at the crack front are obtained by numerically solving the integral equations. Examples are given for a penny-shaped crack in a bimaterial and a three-material system, and for a semicircular crack in a single layer adhered to an elastic half-space.
The Singular Stress Field of a Crack Terminating at a Frictional Interface Between Two Materials
Authors: Wijeyewickrema A. C. , Dundurs J. , Keer L. M.
Published: February 2008

The problem of a crack terminating at an interface between two materials which is governed by Coulomb’s law of friction is studied using Mellin integral transforms. Depending on the relative slip directions of the two wedges that are created by the crack, both the case of the two wedges moving in opposite directions and that of the two wedges moving in the same direction are treated. The characteristic equations which yield the order of the crack-tip singularity are obtained in terms of the Dundurs constants, the inclination of the crack and the coefficient of friction. For the special case when the crack is perpendicular to the interface and the two wedges slip in opposite directions, it is shown that the problem decouples into mode I (symmetric) and mode II (antisymmetric) cracks, and numerical results are presented for this case.
Dislocation Inside, Outside, or on the Interface of an Anisotropic Elliptical Inclusion
Authors: Yen Wen J. , Hwu Chyanbin , Liang Yin Ko
Published: February 2008

The plane elasticity problem of dislocation inside, outside, or on the interface of an anisotropic elliptical inclusion in an unbounded anisotropic matrix is considered. A general solution for the stresses and deformations in the entire domain is obtained by applying the Stroh’s formalism and the method of analytical continuation. Since the general solutions have not been found in the literature, in order to verify the present solution, comparison is made with some special cases of which the analytical solutions exist, which shows that our results are exact and universal.
SH-Waves in a Medium Containing a Disordered Periodic Array of Cracks
Authors: Mikata Y.
Published: February 2008

Reflection and transmission of an SH-wave by a disordered periodic array of coplanar cracks is investigated, and subsequently its application to the dispersion and attenuation of an SH-wave in a disorderedly cracked medium is also treated. This is a stochastic boundary value problem. The formulation largely follows Mikata and Achenbach (1988b). The problem is formulated for an averaged scattered field, and the governing singular integral equation is derived for a conditionally averaged crack-opening displacement using a quasi-crystalline-like approximation. Unlike our previous study (Mikata and Achenbach, 1988b) where a point scatterer approximation was used for the regular part of the integral kernel, however, no further approximation is introduced. The singular integral equation is solved by an eigenfunction expansion involving Chebyschev polynomials. Numerical results are presented for the averaged reflection and transmission coefficients of zeroth order as a function of the wave number for normal incidence, a completely disordered crack spacing, and various values of the ratio of crack length and average crack spacing. Numerical results are also presented for the dispersion and attenuation of an SH-wave in a disorderedly cracked medium.
Initial Post-buckling Behavior of Thick Rings Under Uniform External Hydrostatic Pressure
Authors: Fu Lei , Waas A. M.
Published: February 2008

The initial post-buckling behavior of thick rings under external uniform hydrostatic pressure is investigated. In the analysis, no assumptions are placed upon the relative magnitudes of the elongations and rotations, and the ring is assumed to be elastic and extensional. The importance of including certain nonlinear terms in the initial post-buckling stability analysis and the effects of nonzero shearing strains on the buckling load and the initial post-buckling stability are examined. It is shown that the classical Kirchhoff assumptions, when employed for a ring lead to nonvanishing through thickness strains, εzz and εzθ, with the latter being proportional to the through thickness coordinate z. An approximate first order shear deformation analysis and a two-dimensional elasticity analysis (without beam-type kinematical assumptions) of the initial post-buckling behavior of thick rings are presented and the thickness effects on the buckling load and the initial post-buckling behavior are examined. The formulation for the composite ring was reduced to that of an isotropic ring and the results thus obtained were compared with published one-dimensional results in the literature. It is found from both the shear deformation and the two-dimensional analysis that the initial post-buckling behavior of the isotropic ring and the composite rings studied are stable. The influence of thickness on the degree of stability in the immediate post-buckling response is characterized.
Rayleigh-Taylor Instability of a Cylindrical Interface Between Two Inviscid Fluids
Authors: Li Rui-Qing , Harris R.
Published: February 2008

A theoretical analysis for the instability of a fluid film around a cylinder in an immiscible fluid is presented. A general dispersion equation, relating wave number to growth rate, is derived with consideration of the effects of the cylindrical interface and a finite film thickness. Application of the dispersion equation to the breakup of a liquid film around a cylindrical body in still air leads to a prediction of the dominant wavelength by λ=2π2/(1/R2+ρ1g/q), where R is the radius of the cylinder, ρ1 is the density of the liquid, g is the acceleration due to gravity, σ is the surface tension. Experiments showed good agreement with the present analysis. The dominant wavelength decreases with a decrease in the radius of the cylindrical body. A previous report on the breakup of a liquid film around a horizontal cylindrical body is shown to be in error.
Adhesive Contact Between the Surface Wave and a Rigid Strip
Authors: Zharii O. Y.
Published: February 2008

A problem of adhesive contact between the running surface wave and a rigid strip is investigated. The mixed boundary-value problem of elastodynamics is reduced to a singular integral equation for a complex combination of stresses and an exact closed-form solution of it has been derived. Analysis of variation of contact area dimensions, stress distribution and rotor velocity on the frequency of excitation displayed significant differences between the results corresponding to conditions of adhesion and slipping in contact area. The origin of these differences is discussed.
The Problem of Several Indentors Moving on a Viscoelastic Half-Plane
Authors: Fan H. Z. , Graham G. A. C. , Golden J. M.
Published: February 2008

The problem of several indentors moving on a viscoelastic half-plane is considered in the noninertial approximation. The solution of this mixed boundary value problem is formulated in terms of a coupled system of integral equations in space and time. These are solved numerically in the steady-state limit for the case of two indentors. The phenomena of hysteretic friction and interaction between the two indentors are explored.
Stability of Fiber Networks Under Biaxial Stretching
Authors: Liu Xiaoping , James R. D.
Published: February 2008

This paper is concerned with the constitutive behavior of a particular orthogonal fiber network under biaxial dead loading. We also describe a new kind of biaxial, dead-loading machine which is applicable to anisotropic materials. The machine does not require that the loads are exerted along symmetry axes of the material. A specimen of the cloth was loaded by different loading paths to the same equibiaxial dead-load, and two different final deformations were observed. A related observation was reported by Treloar for rubber in 1948. In order to understand this instability, we experimentally determined the energy function for the cloth. The energy function is then used in a variational calculation to explain this instability.
Critical Angles in Bending of Rotationally Inhomogeneous Elastic Wedges
Authors: Belov A. Yu , Kirchner H. O. K.
Published: February 2008

An anisotropic rotationally inhomogeneous wedge bent by either a concentrated couple applied at the tip (Carothers problem) or uniform surface loadings (Levy problem) is considered. The existence criteria for homogeneous solutions describing stresses and strains in both problems are established. In the Levy problem there are two types of critical wedge angles, at which homogeneous solutions break down and become infinite. The first type critical wedge angles of Levy’s problem are shown to be critical also for Carothers’problem whatever the rotational inhomogeneity. Particular solutions to both problems are obtained at the critical wedge angle. The form of these solutions is established to depend on two factors: the multiplicity degree of roots of some eigenvalue equation and the number of independent eigenvectors of some real matrix. It is shown also that the eigenvalue equation does not provide an alternative way to calculate the critical angles and in the first-order perturbation theory results in just the same equations for the critical angles.
Elastothermodynamic Damping of Fiber-Reinforced Metal-Matrix Composites
Authors: Milligan K. B. , Kinra V. K.
Published: February 2008

Recently, taking the second law of thermodynamics as a starting point, a theoretical framework for an exact calculation of the elastothermodynamic damping in metal-matrix composites has been presented by the authors (Kinra and Milligan, 1994; Milligan and Kinra, 1993). Using this work as a foundation, we solve two canonical boundary value problems concerning elastothermodynamic damping in continuous-fiber-reinforced metal-matrix composites: (1) a fiber in an infinite matrix, and (2) using the general methodology given by Bishop and Kinra (1993), a fiber in a finite matrix. In both cases the solutions were obtained for the following loading conditions: (1) uniform radial stress and (2) uniform axial strain.
Damage Deactivation
Authors: Hansen N. R. , Schreyer H. L.
Published: February 2008

A phenomenological algorithm, motivated by the “mode I” microcrack opening and closing mechanism, is developed for the deactivation and reactivation of the damage effects as modeled by certain continuum damage mechanics theories. One-dimensional formulations with and without coupled plasticity are used to elucidate concepts associated with damage deactivation and to suggest multidimensional deactivation formulations applicable to continuum damage theories that employ a second-order tensor as the damage measure. Strain-based projection operators are used to deactivate the damage effects in the damage tensor. Motivated by observations from one-dimensional coupled formulations, both the total and elastic strains must be compressive for the damage to be rendered inactive. By introducing smooth functions to represent the transition from the active to the inactive state, discontinuities in the response are avoided. To illustrate the aspects associated with deactivation, a consistent set of examples using a strain-controlled one-cycle uniaxial stress loading is given for each formulation.
Bending of Superelastic Wires, Part II: Application to Three-Point Bending
Authors: Berg B. T.
Published: February 2008

The constitutive relationship between applied pure bending moment and the resulting curvature of a few superelastic alloy wires is applied to the three-point bending problem. Three-point bending experiments on hard and soft loading machines are described. The relationship between the applied deflection and the resulting force in three-point bending is calculated from a nonlinear Euler-Bernoulli rod theory. A numerical procedure used to solve the three-point bending problem for both loading and unloading is briefly described and numerical results are compared with experiment.
V(z) Curve Synthesis Using Two Ultrasonic Transducers
Authors: Awal M. A. , Kundu T.
Published: February 2008

Traditionally V(z) curves are generated by acoustic microscopes. However, because of the high costs of the commercially available acoustic microscopes, their use is rather limited. In this paper it is shown how V(z) curves, which contain quantitative information about the material under inspection, can be generated using two ultrasonic transducers instead of an acoustic microscope. A theoretical analysis is given to synthesize V(z) curves of orthotropic plates by this technique. A basic mechanics problem of the reflection of plane waves by an orthotropic plate immersed in a fluid is solved for this purpose. Theoretically synthesized V(z) values are compared with experimental results.
Fractal Dimensions in Elastic-Plastic Beam Dynamics
Authors: Symonds P. S. , Lee J.-Y.
Published: February 2008

Calculations of two types of fractal dimension are reported, regarding the elastic-plastic response of a two-degree-of-freedom beam model to short pulse loading. The first is Mandelbrot’s (1982) self-similarity dimension, expressing independence of scale of a figure showing the final displacement as function of the force in the pulse loading; these calculations were made with light damping. These results are equivalent to a microscopic examination in which the magnification is increased by factors of 102; 104; and 106. It is found that the proportion and distribution of negative final displacements remain nearly constant, independent of magnification. This illustrates the essentially unlimited sensitivity to the load parameter, and implies that the final displacement in this range of parameters is unpredictable. The second fractal number is the correlation dimension of Grassberger and Procaccia (1983), derived from plots of Poincare intersection points of solution trajectories computed for the undamped model. This fractional number for strongly chaotic cases underlies the random and discontinuous selection by the solution trajectory of the potential well leading to the final rest state, in the case of the lightly damped model.
Divergence Instability of a Spinning Disk With Axial Spindle Displacement in Contact With Evenly Spaced Stationary Springs
Authors: Chen Jen-San , Wong Cheng-Chou
Published: February 2008

The titled problem is studied numerically by finite element calculation and analytically by three-mode eigenfunction expansion. It is found that divergence instability of the coupled system is induced only when two times the number of nodal diameters 2n is equal to a multiple of the number of stationary springs N, but n itself is not a multiple of N.
Time Frequency Analysis of Dispersive Waves by Means of Wavelet Transform
Authors: Kishimoto Kikuo , Inoue Hirotsugu , Hamada Makoto , Shibuya Toshikazu
Published: February 2008

A new approach is presented for investigating the dispersive character of structural waves. The wavelet transform is applied to the time-frequency analysis of dispersive waves. The flexural wave induced in a beam by lateral impact is considered. It is shown that the wavelet transform using the Gabor wavelet effectively decomposes the strain response into its time-frequency components. In addition, the peaks of the time-frequency distribution indicate the arrival times of waves. By utilizing this fact, the dispersion relation of the group velocity can be accurately identified for a wide range of frequencies.
A Circular Inclusion With Imperfect Interface: Eshelby’s Tensor and Related Problems
Authors: Gao Zhanjun
Published: February 2008

Eshelby’s tensor for an ellipsoidal inclusion with perfect bonding at interface has proven to have a far-reaching influence on the subsequent development of micromechanics of solids. However, the condition of perfect interface is often inadequate in describing the physical nature of the interface for many materials in various loading situations. In this paper, Airy stress functions are used to derive Eshelby’s tensor for a circular inclusion with imperfect interface. The interface is modeled as a spring layer with vanishing thickness. The normal and tangential displacement discontinuities at the interface are proportional to the normal and shear stresses at the interface. Unlike the case of the perfectly bonded inclusion, the Eshelby’s tensor is, in general, not constant for an inclusion with the spring layer interface. The normal stresses are dependent on the shear eigenstrain. A closed-form solution for a circular inclusion with imperfect interface under general two-dimensional eigenstrain and uniform tension is obtained. The possible normal displacement overlapping at the interface is discussed. The conditions for nonoverlapping are established.
Self-Excited Oscillations of Two Elastic Half-Spaces Sliding With a Constant Coefficient of Friction
Authors: Adams G. G.
Published: February 2008

Two flat isotropic elastic half-spaces, of different material properties, are pressed together and slide against each other with a constant coefficient of friction. Although a nominally steady-state solution exists, an analysis of the dynamic problem demonstrates that the steady solution can be dynamically unstable. Eigenvalues with positive real parts give rise to self-excited motion which occurs for a wide range of material pairs, coefficients of friction, and sliding velocities (including very low speeds). These self-excited oscillations are generally confined to the region near the interface and can lead either to regions of loss of contact or to areas of stick slip. The mechanism responsible for the instability is essentially one of destabilization of interfacial (slip) waves. It is expected that these vibrations might play an important role in the behavior of sliding members with dry friction.
Propagation of Boundary Disturbances in an Axially Moving Strip in Contact With Rigid and Flexible Constraints
Authors: Zhu W. D. , Mote C. D.
Published: February 2008

The exact expression describing the contact force between an axially moving flexible strip and a one-sided constraint is derived using the Green’s function formulation. Discontinuity of the initial velocity at a boundary of the strip due to a disturbance, causes discontinuity in the contact force history at any constraint that is not modeled by a single spring element. The discontinuities in the contact force occur at the instants when those propagating wavefronts in the strip with nonvanishing slope interact with the constraint. A model of a magnetic tape-recording head system is analyzed. Tape-head contact loss is predicted, depending on the amplitude and frequency of a disturbance, the head location, and the preload of the tape against the head.