Showing papers in "Journal of Applied Mechanics in 2004"

Herringbone Buckling Patterns of Compressed Thin Films on Compliant Substrates

Abstract: A thin metal film vapor depositied on thick elastomer substrate develops an equi-biaxial compressive stress state when the system is cooled due to the large thermal expansion mismatch between the elastomer and the metal At a critical stress, the film undergoes buckling into a family of modes with short wavelengths characteristic of a thin plate on a compliant elastic foundation As the system is further cooled, a highly ordered herringbone pattern has been observed to develop Here it is shown that the herringbone mode constitutes a minimum energy configuration among a limited set of competing modes

The Resistance of Clamped Sandwich Beams to Shock Loading

Abstract: A systematic design procedure has been developed for analyzing the blast resistance of clamped sandwich beams. The structural response of the sandwich beam is split into three sequential steps: stage I is the one-dimensional fluid-structure interaction problem during the blast loading event, and results in a uniform velocity of the outer face sheet; during stage II the core crushes and the velocities of the faces and core become equalized by momentum sharing; stage III is the retardation phase over which the beam is brought to rest by plastic bending and stretching. The third-stage analytical procedure is used to obtain the dynamic response of a clamped sandwich beam to an imposed impulse. Performance charts for a wide range of sandwich core topologies are constructed for both air and water blast, with the monolithic beam taken as the reference case. These performance charts are used to determine the optimal geometry to maximize blast resistance for a given mass of sandwich beam. For the case of water blast, an order of magnitude improvement in blast resistance is achieved by employing sandwich construction, with the diamond-celled core providing the best blast performance. However, in air blast, sandwich construction gives only a moderate gain in blast resistance compared to monolithic construction.

Size-Dependent Eshelby’s Tensor for Embedded Nano-Inclusions Incorporating Surface/Interface Energies

Abstract: The classical formulation of Eshelby (Proc. Royal Society, A241, p. 376, 1957) for embedded inclusions is revisited and modified by incorporating the previously excluded surface/interface Stresses, tension and energies. The latter effects come into prominence at inclusion sizes in the nanometer range. Unlike the classical result, our modified formulation renders the elastic state of an embedded inclusion size-dependent making possible the extension of Eshelby's original formalism to nano-inclusions. We present closed-form expressions of the modified Eshelby's tensor for spherical and cylindrical inclusions. Eshelby original conjecture that only inclusions of the ellipsoid family admit uniform elastic state under uniform stress-free transformation strains must be modified in the context of coupled surface/interface-bulk elasticity. We reach an interesting conclusion in that only inclusions with a constant curvature admit a uniform elastic stale, thus restrict-ing this remarkable property only to spherical and cylindrical inclusions. As an immediate consequence of the derivation of modified size-dependent Eshelby tensor for nano-inclusions, we also formulate the overall size-dependent bulk modulus of a composite containing such inclusions. Further applications are illustrated for size-dependent stress concentrations on voids and opto-electronic properties of embedded quantum dots.

Parameter Analysis of the Differential Model of Hysteresis

Abstract: The extended Bouc-Wen differential model is one of the most widely accepted phenomenological models of hysteresis in mechanics. It is routinely used in the characterization of nonlinear damping and in system identification. In this paper, the differential model of hysteresis is carefully re-examined and two significant issues are uncovered. First, it is found that the unspecified parameters of the model are functionally redundant. One of the parameters can be eliminated through suitable transformations in the parameter space. Second, local and global sensitivity analyses are conducted to assess the relative sensitivity of each model parameter. Through extensive Monte Carlo simulations, it is found that some parameters of the hysteretic model are rather insensitive. If the values of these insensitive parameters are fixed, a greatly simplified model is obtained.

On the Acoustic Nonlinearity of Solid-Solid Contact With Pressure-Dependent Interface Stiffness

Abstract: Nonlinear interaction between elastic wave and contact interface, known to result in the so-called contact acoustic nonlinearity, is examined in a one-dimensional theoretical framework. The present analysis is based on a nonlinear interface stiffness model where the stiffness property of the contact interface is described as a function of the nominal contact pressure. The transmission/reflection coefficients for a normally incident harmonic wave, and the amplitudes of second harmonics as well as DC components arising at the contact interface are derived in terms of the interface stiffness properties and other relevant acoustic parameters. Implications of power-law relations between the linear interface stiffness and the contact pressure are examined in detail regarding the linear and nonlinear acoustic responses of the contact interface. Also, a plausible range of the relevant power-law exponent is provided from considerations based on the rough-surface contact mechanics. The analysis clarifies the qualitative contact-pressure dependence of various nonlinearity parameters based on different definitions, A particular power law is identified from existing experimental data for aluminum-aluminum contact, for which some explicit nonlinear characteristics are demonstrated. The theoretical contact-pressure dependence of the second harmonic generation at the contact interface is found to be in qualitative agreement with previous measurements.

Dynamic Response of a Clamped Circular Sandwich Plate Subject to Shock Loading

Abstract: An analytical model is developed for the deformation response of clamped circular sandwich plates subjected to shock loading in air and in water. The deformation history is divided into three sequential stages and analytical expressions are derived for the deflection, degree of core compression, and for the overall structural response time. An explicit finite element method is employed to assess the accuracy of the analytical formulas for the simplified case where the effects of fluid-structure interaction are neglected. The sandwich panel response has only a low sensitivity to the magnitude of the core compressive strength and to the degree of strain hardening in the face-sheets. The finite element results confirm the accuracy of the analytical predictions for the rigid ideally plastic sandwich plates. The analytical formulas are employed to determine optimal geometries of the sandwich plates that maximize the shock resistance of the plates for a given mass. The optimization reveals that sandwich plates have a superior shock resistance relative to monolithic plates of the same mass. @DOI: 10.1115/1.1778416#

Frictional collapse of granular assemblies

Abstract: The frictional collapse of an assembly of equisized spheres is studied by a discrete element model. The macroscopic constitutive response is determined as a function of the level of Coulomb friction between particles. It is found that the level of Coulomb friction has a strong effect upon the relative proportion of sliding and rolling between particles, and consequently upon the. macroscopic strength of the granular assembly. The discrete element predictions are shown to be in good agreement with experimental results obtained from triaxial tests on an aggregate of steel spheres. It is demonstrated that the shape of the collapse surface can be adequately represented by the Lade-Duncan continuum model.

Elasticity Solutions Versus Asymptotic Sectional Analysis of Homogeneous, Isotropic, Prismatic Beams

Abstract: The original three-dimensional elasticity problem of isotropic prismatic beams has been solved analytically by the variational asymptotic method (VAM). The resulting classical model (Eiiler-Bernoulli-like) is the same as the superposition of elasticity solutions of extension, Saint-Venant torsion, and pure bending in two orthogonal directions. The resulting refined model (Timoshenko-like) is the same as the superposition of elasticity solutions of extension, Saint-Venant torsion, and both bending and transverse shear in two orthogonal directions. The fact that the VAM can reproduce results from the theory of elasticity proves that two-dimensioned finite-element-based cross-sectional analyses using the VAM, such as the variational asymptotic beam sectional analysis (VABS), have a solid mathematical foundation. One is thus able to reproduce numerically with VABS the same results for this problem as one obtains from three-dimensional elasticity, but with orders of magnitude less computational cost relative to three-dimensional finite elements.

Impermeable Crack and Permeable Crack Assumptions, Which One is More Realistic?

Abstract: This paper investigates the applicability and effect of the crack-free electrical boundary conditions in piezoelectric fracture. By treating flaws in a medium as notches with a finite width, the results from different electrical boundary condition assumptions on the crack faces are compared. It is found that the electrically impermeable boundary is a reasonable one for engineering problems. Unless the flaw interior is filled with conductive media, the permeable crack assumption may not be directly applied to the fracture of piezoelectric materials in engineering applications.

Applicability and Limitations of Simplified Elastic Shell Equations for Carbon Nanotubes

Abstract: This paper examines applicability and limitations of simplified models of elastic cylindrical shells for carbon nanotubes. The simplified models examined here include Donnell equations and simplified Flugge equations characterized by an uncoupled single equation for radial deflection. These simplified elastic shell equations are used to study static buckling and free vibration of carbon nanotubes, with detailed comparison to exact Flugge equations of cylindrical shells. It is shown that all three elastic shell models are in excellent agreement (with relative errors less than 5%) with recent molecular dynamics simulations for radial breathing vibration modes of carbon nanotubes, while reasonable agreements for various buckling problems have been reported previously for Donnell equations. For general cases of buckling and vibration, the results show that the simplified Flugge model, which retains mathematical simplicity of Donnell model, is consistently in better agreement with exact Flugge equations than Donnell model, and has a significantly enlarged range of applicability for carbon nanotubes. In particular, the simplified Flugge model is applicable for carbon nanotubes (with relative errors around 10% or less) in almost all cases of physical interest, including some important cases in which Donnell model results in much larger errors. These results are significant for further application of elastic shell models to carbon nanotubes because simplified shell models, characterized by a single uncoupled equation for radial deflection, are particularly useful for multiwall carbon nanotubes of large number of layers.@DOI: 10.1115/1.1778415#

Thermal Post-Buckling of Laminated Plates Comprising Functionally Graded Materials With Temperature-Dependent Properties

Abstract: This paper presents thermal buckling and post-buckling analyses for moderately thick laminated rectangular plates that contain functionally graded materials (FGMs) and subjected to a uniform temperature change. The theoretical formulation employs the first-order shear deformation theory and accounts for the effect of temperature-dependent thermoelastic properties of the constituent materials and initial geometric imperfection. The principle of minimum total potential energy, the differential quadrature method, and iterative algorithms are used to obtain critical buckling temperatures and the post-buckling temperature-deflection curves. The results are presented for both symmetrically and unsymmetrically laminated plates with ceramic/metal functionally graded layers, showing the effects of temperature-dependent properties, layup scheme, material composition, initial imperfection, geometric parameters, and boundary conditions on buckling temperature and thermal post-buckling behavior.

Measurement and Simulation of the Performance of a Lightweight Metallic Sandwich Structure With a Tetrahedral Truss Core

Abstract: Metallic sandwich panels with tetrahedral truss cores have been fabricated and their structural performance evaluated. A fabrication technique involving deformation-shaping and brazing has been used. The responses of the structure in core shear and panel bending have been measured. The results demonstrate robust behavior beyond the limit load. A finite element simulation of the core shear response duplicates the features found experimentally. When combined with the constitutive properties of the face sheet material, these shear characteristics have been shown to predict, with good fidelity, the limit load for panels in bending. @DOI: 10.1115/1.1757487#

Development of a Finite Element Cable Model for Use in Low-Tension Dynamics Simulation

Abstract: To accurately simulate the motion of slack marine cables, it is necessary to capture the effects of the cable's bending and torsional stiffness. In this paper, a computationally efficient and novel third-order finite element is presented that provides a representation of both the bending and torsional effects and accelerates the convergence of the model at relatively large element sizes. Using a weighted residual approach, the discretized motion equations for the new cubic element are developed. Applying inter-element constraint equations, we demonstrate how an assembly of these novel elemental equations can be significantly reduced to pretreat the growth of the system equations normallly associated with such higher order elements and allow for faster evaluation of the cable dynamics in either taut or low-tension situations.

Experimental Investigation on the Plasticity of Hexagonal Aluminum Honeycomb Under Multiaxial Loading

Abstract: A new custom-built universal biaxial testing device (UBTD) is introduced and successfully used to investigate the response of aluminum honeycomb under various combinations of large shear and compressive strains in its tubular direction. At the macroscopic level, different characteristic regimes are identified in the measured shear and normal stress-strain curves: elastic I, elastic II, nucleation, softening, and crushing. The first elastic regime shows a conventional linear elastic response, whereas the second elastic regime is nonlinear due to the generation of elastic buckles in the honeycomb microstructure. Nucleation is the point at which the cellular structure loses its load carrying capacity as a result of plastic collapse. It precedes a rapid drop of stress levels in the softening regime as pronounced plastic collapse bands emerge in the microstructure. Formation and growth of plastic folds dominate the microstructural response in the crushing phase. The mechanical features of this phase are long stress plateaus for both the corresponding shear and compressive stress-strain curses. Based on these observations, honeycomb plasticity is established by making analogies of plastic hinge lines and folding systems in the cellular microstructure with dislocations and slip line systems in a solid lattice, respectively. The initial yield surface is found to take the form of an ellipse in stress space, while the crushing behavior is described by a linear envelope along with a nonassociated flow rule based on total strain increments.

Characterization of Plastic Deformation Induced by Microscale Laser Shock Peening

Abstract: Electron backscatter diffraction (EBSD) is used to investigate crystal lattice rotation caused by plastic deformation during high-strain rate laser shock peening in single crystal aluminum and copper sample on (I 10) and (001) surfaces New experimental methodologies are employed which enable measurement of the in-plane lattice rotation under approximate plane-strain conditions Crystal lattice rotation on and below the microscale laser shock peened sample surface was measured and compared with the simulation result obtained from FEM analysis, which account for single crystal plasticity The lattice rotation measurements directly complement measurements of residual strain/stress with X-ray micro-diffraction using synchrotron light source and it also gives an indication of the extent of the plastic deformation induced by the microscale laser shock peening

Elastoplastic Modeling of Metal Matrix Composites Containing Randomly Located and Oriented Spheroidal Particles

Abstract: Micromechanics-based effective elastic and plastic formulations of metal matrix composites (MMCs) containing randomly located and randomly oriented particles are developed. The averaging process over all orientations upon three elastic governing equations for aligned particle-reinforced MMCs is performed to obtain the explicit formulation of effective elastic stiffness of MMCs with randomly oriented particles. The effects of volume fraction of particles and particle shape on the overall elastic constants are studied. Comparisons with the Hashin-Shtrikman bounds and Ponte Castaneda-Willis bounds show that the present effective elastic formulation does not violate the variational bounds. Good agreement with experimental elastic stiffness data is also illustrated. Furthermore, the orientational averaging procedure is employed to derive the overall elastoplastic yield function for the MMCs. Elastoplastic constitutive relations for the composites are constructed on the basis of the derived composite yield function. The stress-strain responses of MMCs under the axisymmetric loading are also investigated in detail. Finally, elastoplastic comparisons with the experimental data for SiCp/Al composites are performed to illustrate the capability of the proposed formulation.

A definition of particle rolling in a granular assembly in terms of particle translations and rotations

Abstract: The paper presents a definition of particle rolling for the interactions of two and three-dimensional particles of arbitrary shape, in case of infinitesimal particle translations and rotations. The definition is based on a purely kinematical analysis, and it is shown to satisfy the objectivity condition.

Coupled Belt-Pulley Vibration in Serpentine Drives With Belt Bending Stiffness

Abstract: A method is developed to evaluate the natural frequencies and vibration modes of serpentine belt drives where the belt is modeled as a moving beam with bending stiffness. Inclusion of bending stiffness leads to belt-pulley coupling not captured in moving string models. New dynamic characteristics of the system induced by belt bending stiffness are investigated. The belt-pulley coupling is studied through the evolution of the vibration modes. When the belt-pulley coupling is strong, the dynamic behavior of the system is quite different from that of the string model where there is no such coupling. The effects of major design variables on the system are discussed. The spatial discretization can be used to solve other hybrid continuous/discrete eigenvalue problems.

A Coupled Zig-Zag Third-Order Theory for Piezoelectric Hybrid Cross-Ply Plates

Abstract: A new zig-zag coupled theory is developed for hybrid cross-ply plates with some piezoelectric layers using third-order zig-zag approximation for the inplane displacements and sublayer wise piecewise linear approximation for the electric potential. The theory considers all electric field components and can model open and closed-circuit boundary conditions. The deflection field accounts for the transverse normal strain due to the piezoelectric d 33 coefficient. The displacement field is expressed in terms of five displacement variables (which are the same as in FSDT) and electric potential variables by satisfying exactly the conditions of zero shear stresses at the top and bottom, and their continuity at layer interfaces. The governing equations are derived from the principle of virtual work. Comparison of the Navier solutions for the simply-supported plates with the analytical three-dimensional piezoelasticity solutions establishes that the present efficient zig-zag theory is quite accurate for moderately thick plates.

Three-Dimensional Instabilities in Flow Past a Rotating Cylinder

Abstract: Flow past a spinning circular cylinder placed in a uniform stream is investigated via three-dimensional computations. A stabilized finite element method is utilized to solve the incompressible Navier-Stokes equations in the primitive variables formulation. The Reynolds number based on the cylinder diameter and freestream speed of the flow is 200. The nondimensional rotation rate, α, (ratio of the surface speed and freestream speed) is 5. It is found that although the two-dimensional flow for α=5 is stable, centrifugal instabilities exist along the entire span in a three-dimensional set-up. In addition, a "no-slip" side-wall can result in separation of flow near the cylinder ends. Both these effects lead to a loss in lift and increase in drag. The end conditions and aspect ratio of the cylinder play an important role in the flow past a spinning cylinder. It is shown that the Prandtl's limit on the maximum lift generated by a spinning cylinder in a uniform flow does not hold.

Dynamic Instability of an Elastic Disk Under the Action of a Rotating Friction Couple

Abstract: This paper investigates the instability of the transverse vibration of a disk excited by two corotating sliders on either side of the disk. Each slider is a mass-spring-damper system traveling at the same constant speed around the disk. There are friction forces acting in the plane of the disk at the contact interfaces between the disk and each of the two sliders. The equation of motion of the disk is established by taking into account the bending couple acting in the circumferential direction produced by the different friction forces on the two sides of the disk. The normal forces and the friction couples produced by the rotating sliders are moving loads and are seen to bring about dynamic instability. Regions of instability for parameters of interest are obtained by the method of state space. It is found that the moving loads produced by the sliders are a mechanism for generating unstable parametric resonances in the subcritical speed range. The existence of stable regions in the parameter space of the simulated example suggests that the disk vibration can be suppressed by suitable assignment of the parameter values of the sliders.

A Continuum Theory That Couples Creep and Self-Diffusion

Abstract: In a single-component material, a chemical potential gradient or a wind force drives self-diffusion. If the self-diffusion flux has a divergence, the material deforms. We formulate a continuum theory to be consistent with this kinematic constraint. When the diffusion flux is divergence-free, the theory decouples into Stokes's theory for creep and Herring's theory for self-diffusion. A length emerges from the coupled theory to characterize the relative rate of self-diffusion and creep. For a flow in a film driven by a stress gradient, creep dominates in thick films, and self-diffusion dominates in thin films. Depending on the film thickness, either stress-driven creep or stress-driven diffusion prevails to counterbalance electromigration. The transition occurs when the film thickness is comparable to the characteristic length of the material.

A Geometrically Nonlinear Shear Deformation Theory for Composite Shells

Abstract: geometrically nonlinear shear deformation theory has been developed for elastic shells to accommodate a constitutive model suitable for composite shells when modeled as a two-dimensional continuum. A complete set of kinematical and intrinsic equilibrium equations are derived for shells undergoing large displacements and rotations but with small, two-dimensional, generalized strains. The large rotation is represented by the general finite rotation of a frame embedded in the undeformed configuration, of which one axis is along the normal line. The unit vector along the normal line of the undeformed reference surface is not in general normal to the deformed reference surface because of transverse shear It is shown that the rotation of the frame about the normal line is not zero and that it can be expressed in terms of other global deformation variables. Based on a generalized constitutive model obtained from an asymptotic dimensional reduction from the three-dimensional energy, and in the form of a Reissner-Mindlin type theory, a set of intrinsic equilibrium equations and boundary conditions follow. It is shown that only five equilibrium equations can be derived in this manner because the component of virtual rotation about the normal is not independent. It is shown, however, that these equilibrium equations contain terms that cannot he obtained without the use of all three components of the finite rotation vector.

Mechanical Response of a Metallic Aortic Stent--Part I: Pressure-Diameter Relationship

Abstract: The mechanical response of a metallic stent is considered in this series of two papers. In Part I, the development of a test method for the characterization of the mechanical response of a metallic aortic stent subjected to internal or external pressure, and a model that captures the relationship between the pressure and diameter of the stent based on slender rod theory are described. The axial and radial deformation of a bare-metal stent were measured as the stent was subjected to loading ranging from an external pressure of about 80 mm of Hg to an internal pressure of about 160 mm of Hg. The pressure was applied using a polyethylene bag; the method of applying the pressure and measuring the strains was found to provide an accurate determination of the mechanical behavior of the stent. The stent was shown to exhibit two stiff limiting states corresponding to the fully collapsed and fully expanded diameters and an intermediate range between the two where the stiffness was an order of magnitude smaller than the typical stiffness of an aorta. A complete mathematical characterization of the pressure-diameter response of the wire stent was also developed; this model is a straightforward application of the theory of slender rods to the problem of the stent. Excellent agreement with the experimental measurements is indicated, opening the possibility for modeling of the coupled response of the stent and the vessel into which it is inserted. In Part II, we consider the effect of variations of pressure over the length of the stent that introduce changes in the diameter along the length of the stent which leads naturally to the formulation of the coupled problem of the scent within the blood vessel.

A Superposition Framework for Discrete Dislocation Plasticity

Abstract: A superposition technique is introduced that allows for the application of discrete dislocation (DD) plasticity to a wide range of thermomechanical problems with reduced computational effort. Problems involving regions of differing elastic and/or plastic behavior are solved by superposing the solutions to i) DD models only for those regions of the structure where dislocation phenomena are permitted subject to either zero traction or displacement at every point on the boundary and ii) an elastic (EL) (or elasticlcohesivezone) model of the entire structure subject to all desired loading and boundary conditions. The DD subproblem is solved with standard DD machinery for an elastically homogeneous material. The EL subproblem requires only a standard elastic or elasticlcohesivezone finite element (FE) calculation. The subproblems are coupled: the negative of the tractions developed at the boundaries of the DD subproblem are applied as body forces in the EL subproblem, while the stressfield of the EL subproblem contributes a driving force to the dislocations it? the DD subproblem structure. This decomposition and the generic boundary conditions of the DD subproblem permit the DD machinery to be easily applied as a "black-box" constitutive material description in an otherwise elastic FE formulation and to be used in a broader scope of applications due to the overall enhanced computational efficiency. The method is validated against prior results for crack growth along a plastic/rigid bimaterial interface. Preliminary results for crack growth along a metal/ceramic bimaterial interface are presented.

Direct Computational Simulations for Internal Condensing Flows and Results on Attainability/Stability of Steady Solutions, Their Intrinsic Waviness, and Their Noise Sensitivity

Abstract: The paper presents a new two-dimensional computational approach and results for laminar/laminar internal condensing flows. Accurate numerical solutions of the full governing equations are presented for steady and unsteady film condensation flows on a sidewall inside a vertical channel. It is found that exit conditions and noise sensitivity are important. Even for stable steady solutions obtained for nearly incompressible vapor phase flows associated with unconstrained exit conditions, the noise sensitivity to the condensing surface's minuscule transverse vibrations is high. The structure of waves, the underlying characteristics, and the growth/damping rates for the disturbances are discussed. A resonance condition for high growth rates is proposed and its efficacy in significantly enhancing wave motion and heat transfer rates is computationally demonstrated. For the unconstrained exit cases, the results make possible a separately reported study of the effects of shear, gravity and surface tension on noise sensitive stable solutions.

Reciprocity Theorems for Diffusion, Flow, and Waves

Abstract: Diffusion, flow, and wave phenomena can each be captured by a unified differential equation in matrix-vector form. This equation forms the basis for the derivation of unified reciprocity theorems for diffusion, flow and wave phenomena.

Nonlinear Elasticity for Modeling Fracture of Isotropic Brittle Solids

Abstract: A softening hyperelastic continuum model is proposed for analysis of brittle fracture. Isotropic material is characterized by two standard parameters-shear and bulk modulus-and an additional parameter of the volumetric separation work. The model can be considered as a volumetric generalization of the concept of the cohesive surface. The meaning of the proposed constitutive equations is clarified by the examples of simple shear and hydrostatic pressure. It is emphasized that the proposed constitutive model includes only smooth functions and the necessary computational techniques are those of nonlinear elasticity.

A Nondimensional Number to Classify Composite Compressive Failure

Abstract: A new nondimensional number (η) to predict the dominant failure mechanism of fiber reinforced composites under compression loading is presented. Results from previous experimental investigations on the failure of glass fiber reinforced and carbon fiber reinforced vinylester matrix composites, respectively, were used to motivate and develop η. Experimental results available in the open literature are used to compare the predictions of η. This number can be used as a design tool to develop new composite materials with a preferred failure mode. The exercise of developing such a number provides insight into parameters that control the compressive strength of fiber reinforced composite materials.