Showing papers in "Journal of Applied Mechanics in 2007"

The response of metallic sandwich panels to water blast

Abstract: Metallic sandwich panels subject to underwater blast respond in a manner dependent on the relative time scales for core crushing and water cavitation. This article examines the response at impulses representative of an (especially relevant) domain: wherein the water cavitates before the core crushes. Three core topologies (square honeycomb, I-core, and corrugated) have been used to address fundamental issues affecting panel design. Their ranking is based on three performance metrics: the back-face deflection, the tearing susceptibility of the faces, and the loads transmitted to the supports. The results are interpreted by comparing with analytic solutions based on a three-stage response model. In stage I, the wet face acquires its maximum velocity with some water attached. In stage II, the core crushes and all of the constituents (wet and dry face and core) converge onto a common velocity. In stage III, the panel deflects and deforms, dissipating its kinetic energy by plastic bending, stretching, shearing, and indentation. The results provide insight about three aspects of the response. (i) Two inherently different regimes have been elucidated, designated strong (STC) and soft (SOC), differentiated by a stage II/III time scale parameter. The best overall performance has been found for soft-core designs. (ii) The foregoing analytic models are found to underestimate the kinetic energy and, consequently, exaggerate the performance benefits. The discrepancy has been resolved by a more complete model for the fluid/structure interaction. (iii) The kinetic energy acquired at the end of the second stage accounts fully for the plastic dissipation occurring in the third stage, indicating that the additional momentum acquired after the end of the second stage does not affect panel performance.

Analytical Derivation of Cosserat Moduli via Homogenization of Heterogeneous Elastic Materials

Abstract: Why do experiments detect Cosserat-elastic effects for porous, but not for stiff-particlereinforced, materials? Does homogenization of a heterogeneous Cauchy-elastic material lead to micropolar (Cosserat) effects, and if so, is this true for every type of heterogeneity? Can homogenization determine micropolar elastic constants? If so, is the homogeneous (effective) Cosserat material determined in this way a more accurate representation of composite material response than the usual effective Cauchy material? Direct answers to these questions are provided in this paper for both two- (2D) and three-dimensional (3D) deformations, wherein we derive closed-form formulae for Cosserat moduli via homogenization of a dilute suspension of elastic spherical inclusions in 3D (and circular cylindrical inclusions in 2D) embedded in an isotropic elastic matrix. It is shown that the characteristic length for a homogeneous Cosserat material that best mimics the heterogeneous Cauchy material can be derived (resulting in surprisingly simple formulae) when the inclusions are less stiff than the matrix, but when these are equal to or stiffer than the matrix, Cosserat effects are shown to be excluded. These analytical results explain published experimental findings, correct, resolve and extend prior contradictory theoretical (mainly numerical and limited to two-dimensional deformations) investigations, and provide both a general methodology and specific results for determination of simple higher-order homogeneous effective materials that more accurately represent heterogeneous material response under general loading conditions. In particular, it is shown that no standard (Cauchy) homogenized material can accurately represent the response of a heterogeneous material subjected to a uniform plus linearly varying applied traction, while a homogenized Cosserat material can do so (when inclusions are less stiff than the matrix).

On the Stoney Formula for a Thin Film/Substrate System With Nonuniform Substrate Thickness

Abstract: Current methodologies used for the inference of thin film stress through system curvature measurements are strictly restricted to stress and curvature states which are assumed to remain uniform over the entire film/substrate system. Recently Huang, Rosakis, and co-workers [Acta Mech. Sinica, 21, pp. 362–370 (2005); J. Mech. Phys. Solids, 53, 2483–2500 (2005); Thin Solid Films, 515, pp. 2220–2229 (2006); J. Appl. Mech., in press; J. Mech. Mater. Struct., in press] established methods for the film/substrate system subject to nonuniform misfit strain and temperature changes. The film stresses were found to depend nonlocally on system curvatures (i.e., depend on the full-field curvatures). These methods, however, all assume uniform substrate thickness, which is sometimes violated in the thin film/substrate system. Using the perturbation analysis, we extend the methods to nonuniform substrate thickness for the thin film/substrate system subject to nonuniform misfit strain.

Hierarchical Corrugated Core Sandwich Panel Concepts

Abstract: The transverse compression and shear collapse mechanisms of a second order, hierarchical corrugated truss structure have been analyzed. The two competing collapse modes of a first order corrugated truss are elastic buckling or plastic yielding of the truss members. In second order trusses, elastic buckling and yielding of the larger and smaller struts, shear buckling of the larger struts, and wrinkling of the face sheets of the larger struts have been identified as the six competing modes of failure. Analytical expressions for the compressive and shear collapse strengths in each of these modes are derived and used to construct collapse mechanism maps for second order trusses. The maps are useful for selecting the geometries of second order trusses that maximize the collapse strength for a given mass. The optimization reveals that second order trusses made from structural alloys have significantly higher compressive and shear collapse strengths than their equivalent mass first order counterparts for relative densities less than about 5%. A simple sheet metal folding and dip brazing method of fabrication has been used to manufacture a prototype second order truss with a relative density of about 2%. The experimental investigation confirmed the analytical strength predictions of the second order truss, and demonstrate that its strength is about ten times greater than that of a first order truss of the same relative density. DOI: 10.1115/1.2198243

Analytical Solution for Size-Dependent Elastic Field of a Nanoscale Circular Inhomogeneity

Abstract: Two-dimensional elastic field of a nanoscale circular hole/inhomogeneity in an infinite matrix under arbitrary remote loading and a uniform eigenstrain in the inhomogeneity is investigated. The Gurtin-Murdoch surface/interface elasticity model is applied to take into account the surface/interface stress effects. A closed-form analytical solution is obtained by using the complex potential function method of Muskhelishvili. Selected numerical results are presented to investigate the size dependency of the elastic field and the effects of surface elastic moduli and residual surface stress. Stress state is found to depend on the radius of the inhomogeneity/hole, surface elastic constants, surface residual stress, and magnitude of far-field loading.

On the Analytic Solution of Magnetohydrodynamic Flow of a Second Grade Fluid Over a Shrinking Sheet

Abstract: In this study, we derive an analytical solution describing the magnetohydrodynamic boundary layer flow of a second grade fluid over a shrinking sheet. Both exact and series solutions have been determined. For the series solution, the governing nonlinear problem is solved using the homotopy analysis method. The convergence of the obtained solution is analyzed explicitly. Graphical results have been presented and discussed for the pertinent parameters.

Size-Dependent Elastic State of Ellipsoidal Nano-Inclusions Incorporating Surface∕Interface Tension

Abstract: The determination of elastic states of an embedded inclusion is of considerable importance in a wide variety of physical problems. In the classical elasticity context this problem was first solved rigorously by 1. The latter work, both with and without modifications, has been employed to tackle a diverse set of problems: Localized thermal heating, residual strains, dislocationinduced plastic strains, phase transformations, overall or effective elastic, plastic and viscoplastic properties of composites, damage in heterogeneous materials, quantum dots, interconnect reliability, microstructural evolution, to name a few. The classical solution of an embedded inclusion neglects the presence of surface or interface energies and indeed, the effects of those are negligible except in the size range of tens of nanometers, where one contends with a significant surface-to-volume ratio. Clearly, the influence of surface/interface energies only extends to the nanoscale regime, as illustrated by various mechanical and optoelectronic applications

Kinking of transversal interface cracks between fiber and matrix

Abstract: Under loads normal to the direction of the fibers, composites suffer failures that are known as matrix or interfiber failures, typically involving interface cracks between matrix and fibers, the coalescence of which originates macrocracks in the composite. The purpose of this paper is to develop a micromechanical model, using the boundary element method, to generate information aiming to explain and support the mechanism of appearance and propagation of the damage. To this end, a single fiber surrounded by the matrix and with a partial debonding is studied. It has been found that under uniaxial loading transversal to the fibers direction the most significant phenomena appear for semidebonding angles in the interval between 60 deg and 70 deg. After this interval the growth of the crack along the interface is stable (energy release rate (ERR) decreasing) in pure Mode II, whereas it is plausibly unstable in mixed mode (dominated by Mode I for semidebondings smaller than 30 deg) until it reaches the interval. At this interval the direction of maximum circumferential stress at the neighborhood of the crack tip is approximately normal to the applied load. If a crack corresponding to a debonding in this interval leaves the interface and penetrates into the matrix then: (a) the growth through the matrix is unstable in pure Mode I; (b) the value of the ERR reaches a maximum (in comparison with other debonding angles); and (c) the ERR is greater than that released if the crack continued growing along the interface. All this suggests that it is in this interval of semidebondings (60-70 deg) that conditions are most appropriate for an interface crack to kink. Experiments developed by the authors show an excellent agreement between the predictions generated in this paper and the evolution of the damage in an actual composite.

Mechanical Steering Compensators for High-Performance Motorcycles

Abstract: This paper introduces the idea of using mechanical steering compensators to improve the dynamic behavior of high-performance motorcycles. These compensators are seen as possible replacements for a conventional steering damper and comprise networks of springs, dampers, and a less familiar component called the inerter. The inerter was recently introduced to allow the synthesis of arbitrary passive mechanical impedances, and finds a potential application in the present work. The design and synthesis of these compensation systems make use of the analogy between passive electrical and mechanical networks. This analogy is reviewed alongside the links between passivity, positive reality, and network synthesis. Compensator design methods that are based on classical Bode-Nyquist frequency-response ideas are presented. Initial designs are subsequently optimized using a sequential quadratic programing algorithm. This optimization process ensures improved performance over the machine’s entire operating regime. The investigation is developed from an analysis of specific mechanical networks to the class of all biquadratic positive real functions. This aspect of the research is directed to answering the question: “What is the best possible system performance achievable using any simple passive mechanical network compensator?” The study makes use of computer simulations, which exploit a state-of-the-art motorcycle model whose parameter set is based on a Suzuki GSX-R1000 sports machine. The results show that, compared to a conventional steering damper, it is possible to obtain significant improvements in the dynamic properties of the primary oscillatory modes, known as “wobble” and “weave.” DOI: 10.1115/1.2198547

Parametric formulation of the finite-volume theory for functionally graded materials-Part I: Analysis

Abstract: In Part I of this communication, the finite-volume theory for functionally graded materials was further extended to enable efficient analysis of structural components with curved boundaries, as well as efficient modeling of continuous inclusions with arbitrarily-shaped cross sections of a graded material's microstructure, previously approximated using discretizations by rectangular subcells. This was accomplished through a parametric formulation based on mapping of a reference square subcell onto a quadrilateral subcell resident in the actual microstructure. In Part II, the parametric formulation is verified through comparison with analytical solutions for homogeneous and graded curved structural components subjected to transient thermal and steady-state thermomechanical loading. Grading is modeled using piecewise uniform thermoelastic moduli assigned to each discretized region. Results for a heterogeneous microstructure in the form of a single inclusion embedded in the matrix phase of large dimensions are also generated and compared with the exact analytical solution, as well as with the results obtained using the standard version of the finite-volume theory based on rectangular discretization and the finite-element method. It is demonstrated that the parametric finite-volume theory is a very competitive alternative to the finite-element method based on the quality of results and execution time.

The Eshelby Tensors in a Finite Spherical Domain—Part I: Theoretical Formulations

Abstract: This work is concerned with the precise characterization of the elastic fields due to a spherical inclusion embedded within a spherical representative volume element (RVE) The RVE is considered having finite size, with either a prescribed uniform displacement or a prescribed uniform traction boundary condition Based on symmetry and group theoretic arguments, we identify that the Eshelby tensor for a spherical inclusion admits a unique decomposition, which we coin the “radial transversely isotropic tensor” Based on this notion, a novel solution procedure is presented to solve the resulting Fredholm type integral equations By using this technique, exact and closed form solutions have been obtained for the elastic disturbance fields In the solution two new tensors appear, which are termed the Dirichlet‐Eshelby tensor and the Neumann‐Eshelby tensor In contrast to the classical Eshelby tensor they both are position dependent and contain information about the boundary condition of the RVE as well as the volume fraction of the inclusion The new finite Eshelby tensors have far-reaching consequences in applications such as nanotechnology, homogenization theory of composite materials, and defects mechanics DOI: 101115/12711227

Friction Induced Vibrations in Moving Continua and Their Application to Brake Squeal

Abstract: Considerable effort is spent in the design and testing of disk brake systems installed in modern passenger cars. This effort can be reduced if appropriate mathematical-mechanical models are used for studying the dynamics of these brakes. In this context, the mechanism generating brake squeal in particular deserves closer attention. The present paper is devoted to the modeling of self-excited vibrations of moving continua generated by frictional forces. Special regard is given to an accurate formulation of the kinematics of the frictional contact in two and three dimensions. On the basis of a travelling Euler-Bernoulli beam and a rotating annular Kirchhoff plate with frictional point contact the essential properties of the contact kinematics leading to self-excited vibrations are worked out. A Ritz discretization is applied and the obtained approximate solution is compared to the exact one of the traveling beam. A minimal disk brake model consisting of the discretized rotating Kirchhoff plate and idealized brake pads is analyzed with respect to its stability behavior resulting in traceable design proposals for a disk brake.

The Underwater Blast Resistance of Metallic Sandwich Beams With Prismatic Lattice Cores

Abstract: The finite element method is used to evaluate the underwater blast resistance of monolithic beams and sandwich beams containing prismatic lattice cores (Y-frame and corrugated core) and an ideal foam core. Calculations are performed on both free-standing and end-clamped beams, and fluid-structure interaction effects are accounted for. It is found that the degree of core compression in the free-standing sandwich beam is sensitive to core strength, yet the transmitted impulse is only mildly sensitive to the type of sandwich core. Clamped sandwich beams significantly outperform clamped monolithic beams of equal mass, particularly for stubby beams. The Fleck and Deshpande analytical model for the blast response of sandwich beams is critically assessed by determining the significance of cross-coupling between the three stages of response: in stage I the front face is accelerated by the fluid up to the point of first cavitation, stage II involves compression of the core until the front and back faces have an equal velocity, and in stage III the sandwich beam arrests by a combination of beam bending and stretching. The sensitivity of the response to the relative magnitude of these time scales is assessed by appropriately chosen numerical simulations. Coupling between stages I and II increases the level of transmitted impulse by the fluid by 20‐30% for a wide range of core strengths, for both the free-standing and clamped beams. Consequently, the back face deflection of the clamped sandwich beam exceeds that of the fully decoupled model. For stubby beams with a Y-frame and corrugated core, strong coupling exists between the core compression phase (stage II) and the beam bending/stretching phase (stage III); this coupling is beneficial as it results in a reduced deflection of the back (distal) face. In contrast, the phases of core compression (stage II) and beam bending/stretching (stage III) are decoupled for slender beams. The significance of the relative time scales for the three stages of response of the clamped beams are summarized on a performance map that takes as axes the ratios of the time scales. DOI: 10.1115/1.2198549

Dynamic Compressive Response of Stainless-Steel Square Honeycombs

Abstract: The dynamic out-of-plane compressive response of stainless-steel square honeycombs has been investigated for impact velocities ranging from quasi-static values to 300 ms -1 . Square-honeycomb specimens of relative density 0.10 were manufactured using a slotting technique, and the stresses on the front and back faces of the dynamically compressed square honeycombs were measured using a direct impact Kolsky bar. Three-dimensional finite element simulations of the experiments were performed to model the response and to help interpret the experimental results. The study has identified three distinct factors governing the dynamic response of the square honeycombs: material rate sensitivity, inertial stabilization of the webs against buckling, and plastic wave propagation. Material rate sensitivity and inertial stabilization of the webs against buckling cause the front and back face stresses to increase by about a factor of two over their quasi-static value when the impact speed is Increased from 0 to 50 ms -1 . At higher impact velocities, plastic wave effects cause the front face stress to increase linearly with velocity whereas the back face stress is almost independent of velocity. The finite element predictions are in reasonable agreement with the measurements.

Combined Torsional-Bending-Axial Dynamics of a Twisted Rotating Cantilever Timoshenko Beam With Contact-Impact Loads at the Free End

Abstract: In this paper, consideration is given to the dynamic response of a rotating cantilever twisted and inclined airfoil blade subjected to contact loads at the free end. Starting with the basic geometrical relations and energy formulation for a rotating Timoshenko beam constrained at the hub in a centrifugal force field, a system of coupled partial differential equations are derived for the combined axial, lateral and twisting motions which includes the transverse shear, rotary inertia, and Coriolis effects, as well. In the mathematical formulation, the torsion of the thin airfoil also considers a very general case of shear center not being coincident with the CG (center of gravity) of the cross section, which allows the equations to be used also for analyzing eccentric tip-rub loading of the blade. Equations are presented in terms of axial load along the longitudinal direction of the beam which enables us to solve the dynamic pulse buckling due to the tip being loaded in the longitudinal as well as transverse directions of the beam column. The Rayleigh-Ritz method is used to convert the set of four coupled-partial differential equations into equivalent classical mass, stiffness, damping, and gyroscopic matrices. Natural frequencies are computed for beams with varying "slenderness ratio" and "aspect ratio" as well as "twist angles." " Dynamical equations account for the full coupling effect of the transverse flexural motion of the beam with the torsional and axial motions due to pretwist in the airfoil. Some transient dynamic responses of a rotating beam repeatedly rubbing against the outer casing is shown for a typical airfoil with and without a pretwist.

Flow Analysis and Modeling of Field-Controllable, Electro- and Magneto-Rheological Fluid Dampers

Abstract: This study combines a fluid mechanics-based approach and the Herschel-Bulkley constitutive equation to develop a theoretical model for predicting the behavior of field-controllable, magneto-rheological (MR), and electro-rheological (ER) fluid dampers. The goal is to provide an accurate theoretical model for analysis, design, and development of control algorithms of MR/ER dampers. Simplified explicit expressions for closed-form solution of the pressure drop across a MR fluid valve are developed. The Herschel-Bulkley quasi-steady flow analysis is extended to include the effect of fluid compressibility to account for the nonlinear dynamic behavior of MR/ER fluid dampers. The advantage of this model is that it only depends on geometric and material properties of the MR/ER material and the device. The theoretical results are validated by an experimental study. It is demonstrated that the proposed model can effectively predict the nonlinear behavior of field-controllable fluid dampers.

Quasi-periodic response regimes of linear oscillator coupled to nonlinear energy sink under periodic forcing

Abstract: Quasi-periodic response of a linear oscillator attached to nonlinear energy sink with relatively small mass under external sinusoidal forcing in a vicinity of main (1:1) resonance is studied analytically and numerically. It is shown that the quasi-periodic response is exhibited in well-defined amplitude-frequency range of the external force. Two qualitatively different regimes of the quasi-periodic response are revealed. The first appears as a result of linear instability of the steady-state regime of the oscillations. The second one occurs due to interaction of the dynamical flow with invariant manifold of damped-forced nonlinear normal mode of the system, resulting in hysteretic motion of the flow in the vicinity of this mode. Parameters of external forcing giving rise to the quasi-periodic response are predicted by means of simplified analytic model. The model also allows predicting that the stable quasi-periodic regimes appear for certain range of damping coefficient..All findings of the simplified analytic model are verified numerically and considerable agreement is observed.

Thermal Buckling of Multi-Walled Carbon Nanotubes by Nonlocal Elasticity

Abstract: The small internal length scales of nanomaterials/nano-devices may call the direct application of classical continuum models into question. In this research, a nonlocal elastic shell model, which takes the small scale effects into account, is developed to study the thermal buckling behavior of multi-walled carbon nanotubes. The multi-walled carbon nanotubes are considered as concentric thin shells coupled with the van der Waals forces between adjacent nanotubes. Closed form solutions are formulated for two types of thermal buckling of a double-walled carbon nanotube: Radial thermal buckling (as in a shell under external pressure) and axial thermal buckling. The effects of small scale effects are demonstrated, and a significant influence of internal characteristic parameters such as the length of the C-C bond has been found on the thermal buckling critical temperature. The study interestingly shows that the axial buckling is not likely to happen, while the "radial" buckling may often take place when the carbon nano-tubes are subjected to thermal loading. Furthermore, a convenient method to determine the material constant, "e o " and the internal characteristic parameter, "a," is suggested.

Fluid-structure interaction effects in the dynamic response of free-standing plates to uniform shock loading

Abstract: The problem of uniform shocks interacting with free-standing plates is studied analytically and numerically for arbitrary shock intensity and plate mass. The analysis is of interest in the design and interpretation of fluid-structure interaction (FSI) experiments in shock tubes. In contrast to previous work corresponding to the case of incident blast profiles of exponential distribution, all asymptotic limits obtained here are exact. The contributions include the extension of Taylor's FSI analysis for acoustic waves, the exact analysis of the asymptotic limits of very heavy and very light plates for arbitrary shock intensity, and a general formula for the transmitted impulse in the intermediate plate mass range. One of the implications is that the impulse transmitted to the plate can be expressed univocally in terms of a single nondimensional compressible FSI parameter.

New First-Order Shear Deformation Plate Theories

Abstract: First-order shear deformation theories, one proposed by Reissner and another one by Mindlin, are widely in use, even today, because of their simplicity. In this paper, two new displacement based first-order shear deformation theories involving only two unknown functions, as against three functions in case of Reissner’s and Mindlin’s theories, are introduced. For static problems, governing equations of one of the proposed theories are uncoupled. And for dynamic problems, governing equations of one of the theories are only inertially coupled, whereas those of the other theory are only elastically coupled. Both the theories are variationally consistent. The effectiveness of the theories is brought out through illustrative examples. One of the theories has striking similarity with classical plate theory.

Vibration Characteristics of Multiwalled Carbon Nanotubes Embedded in Elastic Media by a Nonlocal Elastic Shell Model

Abstract: In this paper, the vibrational behavior of the multiwalled carbon nanotubes (MWCNTs) embedded in elastic media is investigated by a nonlocal shell model. The nonlocal shell model is formulated by considering the small length scales effects, the interaction of van der Waals forces between two adjacent tubes and the reaction from the surrounding media, and a set of governing equations of motion for the MWCNTs are accordingly derived. In contrast to the beam models in the literature, which would only predict the resonant frequencies of bending vibrational modes by taking the MWCNT as a whole beam, the current shell model can find the resonant frequencies of three modes being classified as radial, axial, and circumferential for each nanotube of a MWCNT. Big influences from the small length scales and the van der Waals' forces are observed. Among these, noteworthy is the reduction in the radial frequencies due to the van der Waals' force interaction between two adjacent nanotubes. The numerical results also show that when the spring constant k 0 of the surrounding elastic medium reaches a certain value, the lowest resonant frequency of the double walled carbon nanotube drops dramatically.

Towards the Design of an Optimal Energetic Sink in a Strongly Inhomogeneous Two-Degree-of-Freedom System

Abstract: Analytical, numerical, and experimental results of energy pumping in a strongly inhomogeneous two-degree-of-freedom system are to be presented in this study. The latter is based both on efficient analytical solution and comparative analysis for various types of energetic sinks. Considering the efficient pumping process as damped beating with strong energy transfer, it is shown that we can design the sinks with amplitude-phase variables which provide the most efficient result. In this study, the main types of energetic sinks are to be compared. Computer simulation has confirmed the analytical predictions which had been obtained. Experimental verification of the analytical prediction is considered for a particular type of sink.

Nonstationary Response Envelope Probability Densities of Nonlinear Oscillators

Abstract: The nonstationary random response of a class of lightly damped nonlinear oscillators subjected to Gaussian white noise is considered. An approximate analytical method for determining the response envelope statistics is presented. Within the framework of stochastic averaging, the procedure relies on the Markovian modeling of the response envelope process through the definition of an equivalent linear system with response-dependent parameters. An approximate solution of the associated Fokker-Planck equation is derived by resorting to a Galerkin scheme. Specifically, the nonstationary probability density function of the response envelope is expressed as the sum of a time-dependent Rayleigh distribution and of a series expansion in terms of a set of properly selected basis functions with time-dependent coefficients. These functions are the eigen-functions of the boundary-value problem associated with the Fokker-Planck equation governing the evolution of the probability density function of the response envelope of a linear oscillator The selected basis functions possess some notable properties that yield substantial computational advantages. Applications to the Van der Pol and Duffing oscillators are presented. Appropriate comparisons to the data obtained by digital simulation show that the method, being nonperturbative in nature, yields reliable results even for large values of the nonlinearity parameter.

Stochastic Finite Element Buckling Analysis of Laminated Plates With Circular Cutout Under Uniaxial Compression

Abstract: A generalized stochastic buckling analysis of laminated composite plates, with and without centrally located circular cutouts having random material properties, is presented under uniaxial compressive loading. In this analysis, the layerwise plate model is used to solve both prebuckling and buckling problems. The stochastic analysis is done based on mean centered first-order perturbation technique. The mean buckling strength of composite plates is validated with results available in the literature. It has been observed that the present analysis can predict buckling load accurately even for plates with large cutouts. Micromechanics based approach is used to study the effect of variation in microlevel constituents on the effective macrolevel properties like elastic moduli. Consequently, the effect of uncertainty in these material properties on the buckling strength of the laminated plates is studied. Parametric studies are carried out to see the effect of hole size, layups, and boundary conditions on the mean and variance of plate buckling strength.

An Asymptotic Framework for the Analysis of Hydraulic Fractures: The Impermeable Case

Abstract: This paper presents a novel asymptotic framework to obtain detailed solutions describing the propagation of hydraulic fractures in an elastic material. The problem consists of a system of nonlinear integro-differential equations and a free boundary problem. This combination of local and nonlocal effects leads to transitions on a small scale near the crack tip, which control the behavior across the whole fracture profile. These transitions depend upon the dominant physical process(es) and are identified by simultaneously scaling the associated parameters with the distance from the tip. A smooth analytic solution incorporating several physical processes in the crucial tip region can be constructed using this new framework. In order to clarify the exposition of the new methodology, this paper is confined to considering the impermeable case in which only the two physical processes of viscous dissipation and structure energy release compete.

T-Stresses Across Static Crack Kinking

Abstract: This paper is concerned with the T-stress change before and after crack kinking in two-dimensional elastic solids. By using asymptotic analysis and the Westergaard stress function method, approximate analytical formulas for calculating the T-stress as well as stress intensify factors of an infinitesimal kink are given. Contributions from the T-stress before crack kinking, to the T-stress and the stress intensity factors of the kinked crack, are clearly described. It is noted that since the sign of the T-stress of a kinked open crack might be different from that of a main crack, simply using the sign of the T-stress before crack kinking is not sufficient to determine crack growth stability as observed in recent experiments.

The Eshelby Tensors in a Finite Spherical Domain—Part II: Applications to Homogenization

Abstract: In this part of the work, the Eshelby tensors of a finite spherical domain are applied to various homogenization procedures estimating the effective material properties of multiphase composites. The Eshelby tensors of a finite domain can capture the boundary effect of a representative volume element as well as the size effect of the different phases. Therefore their application to homogenization does not only improve the accuracy of classical homogenization methods, but also leads to some novel homogenization theories. This paper highlights a few of them: a refined dilute suspension method and a modified Mori-Tanaka method, the exterior eigenstrain method, the dual-eigenstrain method, which is a generalized self-consistency method, a shell model, and new variational bounds depending on the different boundary conditions. To the best of the authors' knowledge, this is the first time that a multishell model is used to evaluate the Hashin-Shtrikman bounds for a multiple phase composite (n≥3), which can distinguish some of the subtleties of different microstructures.

Measurement of the Total Energy Release Rate for Cracks in PZT Under Combined Mechanical and Electrical Loading

Abstract: Four-point-bending V-notched specimens of lead zirconate titanate (PZT) poled parallel to the long axis are fractured under conditions of controlled crack growth in a custom-made device. In addition to the mechanical loading electric fields, up to 500 V/mm are applied parallel and anti-parallel to the poling direction, i.e., perpendicular to the crack surface. To determine the different contributions to the total energy release rate, the mechanical and the piezoelectric compliance, as well as the electrical capacitance of the sample, are recorded continuously using small signal modulation/demodulation techniques. This allows for the calculation of the mechanical, the piezoelectric, and the electrical part of the total energy release rate due to linear processes. The sum of these linear contributions during controlled crack growth is attributed to the intrinsic toughness of the material. The nonlinear part of the total energy release rate is mostly associated to domain switching leading to a switching zone around the crack tip. The measured force-displacement curve, together with the modulation technique, enables us to determine this mechanical nonlinear contribution to the overall toughness of PZT. The intrinsic material toughness is only slightly dependent on the applied electric field (10% effect), which can be explained by screening charges or electrical breakdown in the crack interior. The part of the toughness due to inelastic processes increases from negative to positive electric fields by up to 100%. For the corresponding nonlinear electric energy change during crack growth, only a rough estimate is performed.

Null-Field Approach for the Multi-inclusion Problem Under Antiplane Shears

Abstract: In this paper, we derive the null-field integral equation for an infinite medium containing circular holes and/or inclusions with arbitrary radii and positions under the remote antiplane shear. To fully capture the circular geometries, separable expressions of fundamental solutions in the polar coordinate for field and source points and Fourier series for boundary densities are adopted to ensure the exponential convergence. By moving the null-field point to the boundary, singular and hypersingular integrals are transformed to series sums after introducing the concept of degenerate kernels. Not only the singularity but also the sense of principle values are novelly avoided. For the calculation of boundary stress, the Hadamard principal value for hypersingularity is not required and can be easily calculated by using series sums. Besides, the boundary-layer effect is eliminated owing to the introduction of degenerate kernels. The solution is formulated in a manner of semi-analytical form since error purely attributes to the truncation of Fourier series. The method is basically a numerical method, and because of its semi-analytical nature, it possesses certain advantages over the conventional boundary element method. The exact solution for a single inclusion is derived using the present formulation and matches well with the Honein et al. 's solution by using the complex-variable formulation (Honein, E., Honein, T, and Hermann, G., 1992, Appl. Math., 50, pp. 479-499). Several problems of two holes, two inclusions, one cavity surrounded by two inclusions and three inclusions are revisited to demonstrate the validity of our method. The convergence test and boundary-layer effect are also addressed. The proposed formulation can be generalized to multiple circular inclusions and cavities in a straightforward way without any difficulty.

The analysis of tensegrity structures for the design of a morphing wing

Abstract: Current attempts to build fast, efficient, and maneuverable underwater vehicles have looked to nature for inspiration. However, they have all been based on traditional propulsive techniques, i.e., rotary motors. In the current study a promising and potentially revolutionary approach is taken that overcomes the limitations of these traditional methods-morphing structure concepts with integrated actuation and sensing. Inspiration for this work comes from the manta ray (Manta birostris) and other batoid fish. These creatures are highly maneuverable but are also able to cruise at high speeds over long distances. In this paper, the structural foundation for the biomimetic morphing wing is a tensegrity structure. A preliminary procedure is presented for developing morphing tensegrity structures that include actuating elements. To do this, the virtual work method has been modified to allow for individual actuation of struts and cables. The actuation response of tensegrity beams and plates are studied and results are presented. Specifically, global deflections resulting from actuation of specific elements have been calculated with or without external loads. Finally, a shape optimization analysis of different tensegrity structures to the biological displacement field will be presented.