bluuebunny/crossref_metadata_2025 huggingface dataset:
Instability of Gradient Dependent Viscoplastic Model for Clay Saturated With Water and FEM Analysis
Authors: Oka Fusao , Yashima Atsushi , Adachi Toshihisa , Aifantis E. C.
Published: April 2009

For the last two decade, several constitutive models have been proposed for geomaterials and applied to practical problems. There remains, however, still some outstanding issues to be resolved. One of them is the formation of shear band before and after failure. This problem is strongly connected to the strain localization phenomenon. Recently, the importance of simulation of post localization regime has been pointed out. For this problem an interesting approach has been proposed by Aifantis and co-workers based on the introduction of higher order strain gradients into constitutive equation. The purpose of this paper is to propose a strain gradient dependent elasto-viscoplastic model for clay and study the instability condition of the constitutive theory. The model is then implemented into FEM code to simulate the clay behavior under plane strain condition by considering the transport of pore water based on Biot’s theory of solid-fluid mixture.
Characterization of the Flow Localization History in Dynamic Viscoplasticity
Authors: Shawki T. G. , Sherif R. A. , Cherukuri H. P.
Published: April 2009

The evolution of narrow regions of intense plastic flow during the dynamic deformation of rate–sensitive materials is an outstanding problem in mechanics. A unified framework for the analysis of the pre–localization regime was recently presented by Shawki (1991a, b). In the former work, the onset of flow localization was tied to the increased importance of inertial effects. An energy criterion was developed for the characterization of localization initiation. On the other hand, the aforementioned criterion does not provide the critical strain associated with severe localization. The current work examines the extension of the energy criterion towards the determination of the critical strain for the onset of the so–called “stage III” of the localization evolution history. The onset of severe localization appears to be tied to the attainment of an inflection point in the total system kinetic energy evolution profile. Fully nonlinear numerical solutions of the governing system of coupled, dynamic and thermo–mechanical equations are carried out to the late–time, post–localization regime. The foregoing numerical solutions establish the role of the total kinetic energy as a possible single parameter for the characterization of the full localization history.
On the Formability/Instability of Stretch-Forming Sheet Metals
Authors: Bayoumi A. E. , Joshi R.
Published: April 2009

Manufacturing processes of aircraft, automobile and electronic components involve a lot of stretch-forming of sheet metals. The processes contain a large amount of straining which, in turn, may lead to plastic instabilities such as necking, slip formation or shear banding. Understanding the instability phenomenon requires the development of constitutive description of material characterizing the plastic instability and post uniform deformation behavior. The previous work on plastic instability usually lacks the experimental verification of the theoretical models. This may be owing to the complexity involved in designing a suitable experimental methodology for accurate measurements of strain in the locally deforming zone as the deformation progresses rather rapidly once the local neck sets in. A review of the important methodologies and analyses that were and are used in investigating instability of sheet metal in uniaxial tension is presented in this paper. Some supporting results are also presented.
Fault Growth and Acoustic Emissions in Confined Granite
Authors: Lockner David A. , Byerlee James D.
Published: April 2009

The failure process in a brittle granite was studied by using acoustic emission techniques to obtain three dimensional locations of the microfracturing events. During a creep experiment the nucleation of faulting coincided with the onset of tertiary creep, but the development of the fault could not be followed because the failure occurred catastrophically. A technique has been developed that enables the failure process to be stabilized by controlling the axial stress to maintain a constant acoustic emission rate. As a result the post-failure stress-strain curve has been followed quasi-statically, extending to hours the fault growth process that normally would occur violently in a fraction of a second. The results from the rate-controlled experiments show that the fault plane nucleated at a point on the sample surface after the stress-strain curve reached its peak. Before nucleation, the microcrack growth was distributed throughout the sample. The fault plane then grew outward from the nucleation site and was accompanied by a gradual drop in stress. Acoustic emission locations showed that the fault propagated as a fracture front (process zone) with dimensions of 1 to 3 cm. As the fracture front passed by a given fixed point on the fault plane, the subsequent acoustic emission would drop. When growth was allowed to progress until the fault bisected the sample, the stress dropped to the frictional strength. These observations are in accord with the behavior predicted by Rudnicki and Rice’s bifurcation analysis but conflict with experiments used to infer that shear localization would occur in brittle rock while the material is still hardening.
Analyses of Plastic Flow Localization in Metals
Authors: Needleman A. , Tvergaard V.
Published: April 2009

The continuum mechanics framework for analyzing plastic flow localization is reviewed. The prediction of the localization of deformation into shear bands is sensitive to the constitutive description. The classical isotropic hardening elastic-plastic solid with a smooth yield surface and normality is very resistant to localization, but deviations from these idealizations have a strong effect. Thus, a material that forms a sharp vertex on the yield surface, as predicted by crystal plasticity, shows flow localization at quite realistic levels of strain, and even the formation of a rounded vertex on the yield surface has an important influence. Also softening induced by material damage or by the heating due to plastic dissipation have significant influence in promoting the onset of flow localization. In a practical situation one effect, such as thermal softening under high deformation rates, may be the dominant cause of localization, but often the interaction of different effects appears to be the more realistic explanation of observed flow localization. Some relevant constitutive models are reviewed and the effect of the different material models on localization predictions is illustrated. Important information on localization behavior in uniformly strained solids is obtained by a relatively simple material stability analysis, but often failure by flow localization occurs in nonuniformly strained regions, where numerical solution procedures are necessary to obtain theoretical predictions. The numerical results reviewed cover localization under dynamic as well as quasi-static loading conditions.
The Phenomenon of Shear Strain Localization in Dynamic Viscoplasticity
Authors: Shawki T. G.
Published: April 2009

This article addresses shear flow localization during high rates of deformation of thermal viscoplastic materials. An overview of several efforts towards an improved understanding of shear band formation is given. This paper aims at extracting a unified framework towards the analysis of shear band formation for the considered class of deformations. For this purpose, we present a number of rigorous exact solutions for the one–dimensional simple shearing deformation of a general class of thermal viscoplastic material response. These solutions are used as benchmarks for the validation of both analytical and computational procedures. The interactive roles of inertia, rate–sensitivity, heat conduction, perturbation geometry, boundary conditions, thermal softening, strain hardening and constitutive description as regards the initiation and further intensification of flow localization are thoroughly addressed. We also examine the delicate questions concerning the notion of shear localization and the related mathematical characterization, length and time scales as well as the connection between localization and catastrophic failure.
Plastic Flow of Random Media: Micromechanics, Markov Property and Slip-Lines
Authors: Ostoja-Starzewski Martin
Published: April 2009

The classical method of slip-lines (characteristics) of planar flow of perfectly-plastic media is generalized to a stochastic setting. The media are charaterized by space-homogeneous statistics of the yield limit k, whose derivation is outlined on the basis of micromechanics. The field equations of the random continuum approximation lead to a stochastic hyperbolic system. This system, when stated in a finite difference form, displays a Markov property for the forward evolution. On that basis, two methods of solution of boundary value problems - an exact one and a mean-field one - are outlined through an example of a Cauchy problem. The principal observation is that even for a weak material randomness the stochastic solution may differ qualitatively from that of a homogeneous deterministic medium and have a strong scatter.
Multiphase Poroelastic Finite Element Models for Soft Tissue Structures
Authors: Simon Bruce R.
Published: April 2009

During the last two decades, biological structures with soft tissue components have been modeled using poroelastic or mixture-based constitutive laws, i.e., the material is viewed as a deformable (porous) solid matrix that is saturated by mobile tissue fluid. These structures exhibit a highly nonlinear, history-dependent material behavior; undergo finite strains; and may swell or shrink when tissue ionic concentrations are altered. Given the geometric and material complexity of soft tissue structures and that they are subjected to complicated initial and boundary conditions, finite element models (FEMs) have been very useful for quantitative structural analyses. This paper surveys recent applications of poroelastic and mixture-based theories and the associated FEMs for the study of the biomechanics of soft tissues, and indicates future directions for research in this area. Equivalent finite-strain poroelastic and mixture continuum biomechanical models are presented. Special attention is given to the identification of material properties using a porohyperelastic constitutive law and a total Lagrangian view for the formulation. The associated FEMs are then formulated to include this porohyperelastic material response and finite strains. Extensions of the theory are suggested in order to include inherent viscoelasticity, transport phenomena, and swelling in soft tissue structures. A number of biomechanical research areas are identified, and possible applications of the porohyperelastic and mixture-based FEMs are suggested.
Addendum to: Bibliography of Monographs and Surveys on Shells
Authors: Pietraszkiewicz W.
Published: April 2009

The bibliography collected by Ahmed K Noor, Bibliography of monographs and surveys on shells, Applied Mechanics Reviews 43(9) 223–234 (1990), ASME Book No AMR078, contains 411 books, 98 conference proceedings and 23 survey papers. In this report additional bibliography of monographs, books, conference proceedings, and survey papers on shells is collected, including a fairly complete additional list of books and survey papers by Polish authors and some early books by Love (1892–93), Rayleigh (1894), Cosserat (1909) and Timoshenko (1914–16), where shell theory is extensively covered.
Romanian Sources on Applied Mechanics
Authors: Popescu Mihail E.
Published: April 2009

This note provides a list of journals and recent books published in Romania covering topics in applied mechanics, with information on how to obtain them.
Geometrically Exact Analysis of Spatial Frames
Authors: Pimenta Paulo M. , Yojo Takashi
Published: April 2009

A fully nonlinear, geometrically exact, finite strain rod model is derived from basic kinematical assumptions. The model incorporates shear distortion in bending and can take account of torsion warping. Rotation in 3D space is handled with the aid of the Euler-Rodrigues formula. The accomplished parametrization is simple and does not require update algorithms based on quaternions parameters. Weak and strong forms of the equilibrium equations are derived in terms of cross section strains and stresses, which are objective and suitable for constitutive description. As an example, an invariant linear elastic constitutive equation based on the small strain theory is presented. The attained formulation is very convenient for numerical procedures employing Galerkin projection like the finite element method and can be readily implemented in a finite element code. A mixed formulation of Hu-Washizu type is also derived, allowing for independent interpolation of the displacement, strain and stress fields within a finite element. An exact expression for the Fre´chet derivative of the weak form of equilibrium is obtained in closed form, which is always symmetric for conservative loading, even far from an equilibrium state and is very helpful for numerical procedures like the Newton method as well as for stability and bifurcation analysis. Several numerical examples illustrate the usefulness of the formulation in the lateral stability analysis of spatial frames. These examples were computed with the code FENOMENA, which is under development at the Computational Mechanics Laboratory of the Escola Polite´cnica.
Determination of Stress Concentration Factors for Shallow and Sharp V-Notches Using a Hybrid Method
Authors: Freire Jose´ L. F. , Carvalho Eduardo A. , Cavaco Marco A. M.
Published: April 2009

Stress distributions near the root of shallow and sharp V-notches are determined through a hybrid method which associates the isochromatic photoelastic response with the analytical description of the stress state for the points studied.
Micromechanics as a Basis of Stochastic Finite Elements and Differences: An Overview
Authors: Ostoja-Starzewski M.
Published: April 2009

A generalization of conventional deterministic finite element and difference methods to deal with spatial material fluctuations hinges on the problem of determination of stochastic constitutive laws. This problem is analyzed here through a paradigm of micromechanics of elastic polycrystals and matrix-inclusion composites. Passage to a sought-for random meso-continuum is based on a scale dependent window playing the role of a Representative Volume Element (RVE). It turns out that the microstructure cannot be uniquely approximated by a random field of stiffness with continuous realizations, but, rather, two random continuum fields may be introduced to bound the material response from above and from below. Since the RVE corresponds to a single finite element, or finite difference cell, not infinitely larger than the crystal size, these two random fields are to be used to bound the solution of a given boundary value problem at a given scale of resolution. The window-based random continuum formulation is also employed in analysis of rigid perfectly-plastic materials, whereby the classical method of slip-lines is generalized to a stochastic finite difference scheme. The present paper is complemented by a comparison of this methodology to other existing stochastic solution methods.
Dynamic Post-Buckling Behavior of Thin-Walled Structures With Flexible Knife-Edge Supports
Authors: Souza M. A.
Published: April 2009

The paper discusses the influence that changes of the simply supported boundary condition during the loading process have on the dynamic post-buckling behavior of elastic thin-walled structures. Of special interest is the knife-edge type of support which is associated to the free-to-rotate boundary condition. The results presented show how changes of the free-to-rotate condition during the loading process can dramatically alter the response of thin-walled structures. This fact is highlighted by the equilibrium paths and the characteristic curves presented. The former relate the applied compressive load and the lateral displacement, whereas, the latter relate the compressive load and the square of the corresponding natural frequency of vibration. The importance of an adquate design of the supports is stressed in view of the observed dramatic changes. The work is done in the scope of the elastic stability and damping is not included in the analysis.
Stability and Bifurcations of Nonlinear Multibody Systems
Authors: Kreuzer Edwin J.
Published: April 2009

Many technical systems are adequately described only by means of nonlinear mathematical models. Multibody systems became the most important mechanical models for analyzing engineering dynamics problems. The long-term or steady-state behavior of such systems can have a periodic, quasi-periodic, or chaotic character. Changes of the qualitative behavior are characterized by local and global bifurcations. This paper deals with stability problems in multibody system dynamics and explains different bifurcation phenomena as well as methods for analyzing them. Results from a simple oscillator prove the applicability of the methods.
Modal Analysis of a Flexible Three-Link System in Variable Configurations
Authors: Benner J. W. , Sinha S. C. , Wiens G. J.
Published: April 2009

In this paper, some experimental results of modal tests performed on a large three-link flexible system are reported. These modal tests were conducted at the NASA’s LSS GTF (Large Space Structures Ground Test Facility) located at MSFC (Marshall Space Flight Center). The experimental results were obtained for various configurations and compared with those obtained using the Component Mode Synthesis technique. The mode functions were selected to keep the computation as simple as possible without compromising the accuracy. The results obtained from the dynamic software simulation package called TREETOPS have also been included for completeness. It is found that the experimental results are in excellent agreement with those obtained by the use of component mode techniques for the aforementioned structures. The average percent change in the frequencies is observed to be 6.09%, while the average mode shape correspondence is noted as 94.5%.
Coupled Motion in the Dynamic Analysis of a Three Block Structure
Authors: Sinopoli A. , Sepe V.
Published: April 2009

A mathematical model is presented for the in-plane dynamic analysis of a structure composed of three rigid blocks, simply supported on each other, in presence of dry friction. In order to investigate the dynamics excited by a given ground motion, a Lagrangian formulation is proposed, with displacements, velocities and reactive forces restricted in bounded fields, due to the incompenetrability of the elements. Special attention is devoted to the modelling of the impacts, and to the role of Coulomb friction during the smooth dynamics. Different failure modes are obtained, characterized by a different participation factor of the degrees of freedom. Regions of coupling between rocking and sliding-displacements can be identified, as a function of the features of the excitation and of the friction coefficients. Survival domains decreasing with time can be obtained. They seem to indicate that, in presence of an earthquake, excessive relative displacements in the contact surfaces between the elements would be the most probable cause of failure of such a structure.
Knowledge-Based Shock-Wave Modeling by GENESIS
Authors: Hunt Barry , Adamson Arthur P.
Published: April 2009

GENESIS—GEneralized Nonlinear Extension of Surface Integral Schemes—offers the prospect of extending existing 3-D panel codes, originally developed for linear flows over complex configurations, to the general re´gime of flows governed by the unsteady Euler equation—without significant increases in computational time or resources. The boundary representation of a shock discontinuity exploits its causal link with conditions at the sonic point to suppress, non-dissipatively, the physically-impossible formation of an expansion shock. Three approaches are described, two approximate and one nominally exact, for solving the transonic Euler equation on conventional computers; some 2-D transonic results are presented, obtained on a PC in about one second.
Variational-Asymptotical Analysis of Initially Curved and Twisted Composite Beams
Authors: Cesnik Carlos E. S. , Hodges Dewey H.
Published: April 2009

An asymptotically exact methodology, based on geometrically nonlinear, three-dimensional elasticity, is presented for cross-sectional analysis of initially curved and twisted, nonhomogeneous, anisotropic beams. Through accounting for all possible deformation in the three-dimensional representation, the analysis correctly accounts for the complex elastic coupling phenomena in anisotripic beams associated with shear deformation. The analysis is subject only to the restrictions that the strain is small relative to unity and that the maximum dimension of the cross section is small relative to the wave length of the deformation and to the minimum radius of curvature and/or twist. The resulting cross-sectional elastic constants exhibit first-order dependence on the initial curvature and twist. As is well known, the associated geometrically-exact, one-dimensional equilibrium and kinematical equations also depend on initial twist and curvature. Present numerical results show that it is insufficient to account for initial twist and curvature in the beam equations only. The corrections to the stiffness model derived herein are also necessary in general for proper representation of anisotropic beams.
Compressive Strength and Failure Time Based on Local Buckling in Viscoelastic Composites
Authors: Schapery R. A.
Published: April 2009

The axial compressive strength and failure time of unidirectional, viscoelastic composites are investigated. Effects of nonlinear shear behavior and fiber misalignment are emphasized because they are important strength-limiting factors in those strongly anisotropic composites which fail by local buckling in the shear mode of deformation. We first describe the basic buckling model and then, neglecting hereditary effects, predict the compressive strengths of an untoughened and a rubber-toughened carbon/epoxy composite. Next, using a nonlinear viscoelastic constitutive equation for shear behavior, failure time for constant load and compressive strength for increasing load history are predicted by a numerical method. Additionally, approximate analytical formulas are developed which enable one to easily estimate buckling response as a function of initial fiber misalignment angle as well as loading and material parameters.
Estimation of Lyapunov Exponents Using a Semi-Discrete Formulation
Authors: To¨ro¨k Josef S.
Published: April 2009

Lyaponov exponents are a generalization of the eigenvalues of a dynamical system at an equilibrium point. They are used to determine the stability of any type of steady-state behavior, including chaotic solutions. More specifically, Lyapunov exponents measure the exponential rates of divergence or convergence associated with nearby trajectories. This paper presents an efficient method of estimating the Lyapunov spectrum of continuous dynamical systems. Based on the Lie series expansion of the flow, the technique can be readily implemented to estimate the Lyapunov exponents of dynamical systems governed by ordinary differential equations.
Large-Amplitude Plate Vibration in an Elevated Thermal Environment
Authors: Lee Jon
Published: April 2009

At elevated temperatures the dynamics of vibrating plate (or shell) must include the three thermal effects: (i) the global expansion by uniform plate temperature, (ii) the local expansion by temperature variation over the plate, and (iii) the thermal moment induced by temperature gradient across the plate thickness. For the single-mode prototype model of Galerkin representation, (i) and (ii) give rise to the combined stiffness that is responsible for thermal buckling, whereas (iii) contributes to the combined forcing of acoustic and thermal excitations. For the high-temperature sonic fatigue test facility at the Wright Lab, the present study is devoted to the mean square estimates on transverse displacement and normal stress/strain by the equivalent linearization technique.
Hybrid Pade´-Galerkin Technique for Differential Equations
Authors: Geer James F. , Andersen Carl M.
Published: April 2009

A three-step hybrid analysis technique, which successively uses the regular perturbation expansion method, the Pade´ expansion method, and then a Galerkin approximation, is presented and applied to some model boundary value problems. In the first step of the method, the regular perturbation method is used to construct an approximation to the solution in the form of a finite power series in a small parameter ε associated with the problem. In the second step of the method, the series approximation obtained in step one is used to construct a Pade´ approximation in the form of a rational function in the parameter ε. In the third step, the various powers of ε which appear in the Pade´ approximation are replaced by new (unknown) parameters {δj}. These new parameters are determined by requiring that the residual formed by substituting the new approximation into the governing differential equation is orthogonal to each of the perturbation coordinate functions used in step one. The technique is applied to model problems involving ordinary or partial differential equations. In general, the technique appears to provide good approximations to the solution even when the perturbation and Pade´ approximations fail to do so. The method is discussed and topics for future investigations are indicated.
Method of Virtual Power Applied to Cosserat Surfaces With Deformable Directors
Authors: Alves Boris Krajnc , Lubliner Jacob
Published: April 2009

Following a brief outline of the method of virtual power, the local equations of motion for a Cosserat surface with inextensible directors are derived by means of this method. The model obtained coincides with the results derived from three-dimensional theory by Simo and Fox. Subsequently the model is extended so as to account for deformable directors. Besides the linear-momentum and moment-of-momentum balance equations, one additional scalar equation is derived. This equation replaces the director-momentum balance equation of Naghdi and therefore eliminates the necessity of introducing constitutive restrictions. The equivalence between the model derived by the virtual-power method and the results from the direct method of Naghdi are finally noted.
Experimental Determination of Stress Intensity Factor Distributions in Engineering Problems
Authors: Smith C. W.
Published: April 2009

Following a brief introduction of the concept of stress intensity factor from fracture mechanics and the frozen stress method from photoelasticity, an algorithm is developed from fracture mechanics equations and the stress-optic law for converting stress fringe measurements into a form useful for determining the stress intensity factor. This algorithm covers all three local modes of deformation and is used to analyse frozen stress slices along the border of cracks to obtain distributions for stress intensity factors K1, K2 and K3. The use of the method is illustrated by three examples from practical engineering problems and results are compared with the literature where possible.
Damping of Vibrations of Layered Elastic-Viscoelastic Beams
Authors: Hetnarski Richard B. , West Ray A. , Torok Joseph S.
Published: April 2009

A five-layer cantilever beam consisting of an elastic core, two symmetric viscoelastic layers, and two elastic constraining layers is considered. The viscoelastic effects are incorporated in the Euler-Bernoulli beam theory. If the contraction and extension of the constraining layers is neglecterd a fourth order differential equation of motion is received. Inclusion of contraction and extension of the constraining layers results in a more accurate sixth order differential equation. Appropriate boundary conditions are derived. Laplace transforms are used extensively. Both the analytical solution and the numerical results are presented.
Green’s Functions in Generalized Micropolar Thermoelasticity
Authors: Dhaliwal Ranjit S. , Wang Jun
Published: April 2009

General solution of the generalized micropolar thermoelastic equations has been obtained for arbitrary distribution of the body couples, body forces, and heat sources in an infinite body. Short time solutions have been obtained for the cases of impulsive body force and heat source acting at a point. Numerical values of the short time solutions have been displayed graphically.
Principles and the Uncertainty Principles of the Probabilistic Strength of Materials and Their Applications to Seismology
Authors: Kittl P. , Di´az G. , Marti´nez V.
Published: April 2009

The principles of Fracture-Statistics Mechanics are presented using two functional equations, namely one for the cumulative probability of fracture, and another for the local probability of fracture. These two functional equations are independent and they become compatible only when the volume considered is very small. The determination of the specific-risk function can be made by means of integral equations, without having to specify the analytical expression for this function. This two principles give two principles of uncertainty. Some applications to seismology are given where it is shown that the possibilities of predicting the instant of occurrence and the magnitude of an earthquake are null. Only the probability of occurrence of an earthquake of a given magnitude in a given place can be known. The instant of occurrence, the magnitude and the location are aleatory.
Passive Vibration Control: A Probabilistic Approach
Authors: Jensen Hector A. , Setareh Mehdi
Published: April 2009

This paper is concerned with the behavior of vibration absorbers attached to systems with uncertain properties. The uncertainties of the main system properties are modeled in a probabilistic sense by means of a Bayesian probabilistic interpretation. The structural systems considered in this study are simple systems modeled as one-degree-of-freedom oscillators subjected to a white noise base excitation. Due to the uncertainty of the main system properties, the classical deterministic minimization problem becomes a stochastic optimization problem. An optimization technique is implemented to solve this non-classical problem, and the absorber parameters as well as the optimum response of the system are obtained. These results are then used to assess the performance of the vibration absorber. It is found that parameter uncertainties may have a significant effect on its effectiveness. Finally, an alternative approach that improves the absorber efficiency, when uncertainties in the main system properties are considered, is presented in this paper.
Flowing Polymers Through Porous Media: An Experimental Study of Flow Distribution, Polymer Degradation, and Molecular Weight Effects
Authors: Mu¨ller A. J. , Medina L. I. , Pe´rez-Martin O. , Rodriguez S. , Romero C. , Sargenti M. L. , Sa´ez A. E.
Published: April 2009

The flow of aqueous poly(ethylene oxide) solutions through nonconsolidated porous media has been experimentally investigated. Three aspects of practical relevance have been addressed: the effect of polymer on flow distribution under nonuniform flow conditions, the mechanical degradation of the polymer in the porous media, and the effect of molecular weight on flow resistance. The nonuniform flow results indicate that, although the presence of polymer changes the distribution of the flow by affecting the region of the medium that is swept by the fluid, a significant increase in flow resistance is still observed above a critical Reynolds number, as it happens under uniform flow conditions. The degradation experiments show that the polymer is significantly degraded only in the region where a sizable increase in flow resistance is obtained with respect to the Newtonian behavior. The most significant effect of the molecular weight of the polymer is the fact that an increase in that parameter results in a substantial reduction of the Reynolds number at which the increased flow resistance is observed. Furthermore, the rate of change of this onset Reynolds number with polymer concentration appears to be independent of molecular weight. The results presented here indicate that the increase in flow resistance is not exclusively determined by the shear viscosity of the polymer solution.
Analysis of Cylindrically Curved Panels Based on a Two Field Variable Variational Principle
Authors: Bismarck-Nasr Maher N.
Published: April 2009

A variational formulation of thin cylindrically curved panels having transverse displacement and Airy stress function as field variable is presented. Euler-Lagrange equations and boundary conditions are obtained. A finite element based on this variational principle preserving C(1) continuity is formulated. Applications for free vibrations, buckling, and supersonic panel flutter analyses are given. Several numerical calculations are presented. The results obtained are discussed and are compared with previous analytical solutions, numerical calculations, and experimental findings.
Recent Results on the Elasticity Theory of Inclusions
Authors: Huang Jin H. , Mura T.
Published: April 2009

A method drawing from variational method is presented for the purpose of investigating the behavior of inclusions and inhomogeneities embedded in composite materials. The extended Hamilton’s principle is applied to solve many problems pertaining to composite materials such as constitutive equations, fracture mechanics, dislocation theory, overall elastic moduli, work hardening and sliding inclusions. Especially, elastic fields of sliding inclusions and workhardening rate of composite materials are presented in closed forms. For sliding inclusion problems, the sliding is modeled by adding the Somigliana dislocations along a matrix-inclusion interface. Exact formula are exploited for both Burgers vector and the disturbances in stress and strain due to sliding. The resulting expressions are obtained by utilizing the principle of minimum strain energy. Finally, explicit expressions are obtained for work-hardening rate of composite materials. It is verified that the work-hardening rate and yielding stress are independent on the size of inclusions but are dependent on the shape and the volume fraction of inclusions.
Simulation of Microcrack Propagation in Creeping Polycrystals Due to Diffusive Grain Boundary Cavitation
Authors: van der Burg M. W. D. , van der Giessen E.
Published: April 2009

Creep rupture in random polycrystalline aggregates is investigated numerically in terms of multi-grain cell studies using a Delaunay network modelling technique. The model involves a representation of the crystalline aggregate by means of special purpose elements attributed to each grain facet. These Delaunay elements account for elastic and creep deformations of the grains, free grain boundary sliding, as well as for the nucleation and diffusive growth of grain boundary cavities until coalescence leads to a facet microcrack. Damage accumulation is simulated numerically, until an excessive number of microcracks cause des-integration of the polycrystal. Primary attention is on the influence of randomness in the microstructure on creep rupture, either in terms of random variations of the size and shape of hexagonal grains, or in terms of random variations in the nucleation properties of grain boundaries. It is found that randomness always tends to decrease the life time. In particular, it is found that the life time depends sensitively on random variations of the geometry of the microstructure.
On the Possibly Multifractal Properties of Dissipated Energy in Brittle Materials
Authors: Frantziskonis G.
Published: April 2009

The paper reports an analytical study on the properties of fracture networks in brittle materials. Micro-deformation gradients are considered random fields and/or scaling fields. Under dynamic crack propagation conditions the possibly fractal properties of the (macro) crack pattern are governed by the interplay of fluctuations and spatial correlations. For “slow” crack propagation they are governed by the kinematic fields in the vicinity of crack or notch tips. The spatial distribution of dissipated energy, due to fracture, is evaluated. It is shown that there is a strong possibility that the dissipated energy is multifractal. Here, its properties are characterized in a fashion similar to the so-called p-model where p herein denotes normalized dissipated energy. For the three cases analyzed - uniaxial tension, pure shear, and dilatation - the dissipated energy under pure shear shows the strongest disorder, the one under dilatation the weakest, and the tension case is always between these two.
Effective Moduli of Solids With Cavities of Various Shapes
Authors: Kachanov M. , Tsukrov I. , Shafiro B.
Published: April 2009

Effective elastic properties of solids with cavities of various shapes are derived in two approximations: the approximation of non-interacting cavities and the approximation of the average stress field (Mori-Tanaka’s scheme); the latter appears to be appropriate when mutual positions of defects are random. We construct the elastic potential of a solid with cavities. Such an approach covers, in a unified way, cavities of various shapes and any mixture of them. No degeneracies (or a need in a special limiting procedure) arise when cavities shrink to cracks. It also provides a unified description of both isotropic and anisotropic effective properties and recovers results available in the literature for special cases. Elastic potentials dictate the choice of proper parameters of cavity density. These parameters depend on defect shapes. Even in the case of random orientations, the isotropic overall properties cannot be characterized in terms of porosity alone; for elliptical holes, for example, a second parameter - “eccentricity” - is needed.
Spatial Variability in Concrete: Nature, Structure, and Consequences
Authors: Breysse D. , Fokwa D. , Drahy F.
Published: April 2009

The failure process of concrete is a complex phenomenon in which the material inhomogeneities play an important role. Different ways of accounting for material disorder are commented on and examples are exhibited, showing the difficulties related to inhomogeneous material modeling. In a first part, results and limits via phenomenological probabilistic models (a probabilistic model of damage and a probabilistic numerical model of cracking) are pointed out. Then, results obtained on numerical simulations on lattices are studied. It is shown that the knowledge of the local disorder is a key factor for a better understanding of the global response (localization, size-effect, ...), even if these results can only be taken as qualitative ones. It appears that studies using numerical discrete models for concrete can lead to spurious results if the bias introduced by the discretization itself is not recognized and correctly accounted for. Finally it is shown with two examples (casted concrete and microcracked medium) how the structure of disorder can be identified and modelled. Some indications are given about the cases in which it seems useful to analyze the material at this micro-scale. The main interest seems to be their use for building phenomenological and material-related rules describing the response at a higher scale. The conclusion tries to separate the problems one has to treat in four main classes and to propose for each type of problem a better way to account for material disorder.
Elastic Moduli of Two Dimensional Materials With Polygonal and Elliptical Holes
Authors: Jasiuk I. , Chen J. , Thorpe M. F.
Published: April 2009

We study the effective elastic moduli of two-dimensional composite materials containing polygonal holes. In the analysis we use a complex variable method of elasticity involving a conformal transformation. Then we take a far field result and derive the effective elastic constants of composites with a dilute concentration of polygonal holes. In the discussion we use the recently-stated Cherkaev-Lurie-Milton theorem, which gives general relations between the effective elastic constants of two-dimensional composites. We also discuss known results for elliptical holes in the context of the present work.
Estimates of Elastic Modulus for Media of Randomly Packed Granules
Authors: Chang Ching S. , Liao Ching L.
Published: April 2009

The model of static hypothesis is not readily available for granular material treated as a collection of particles. Unlike other types of material, the internal stresses in a granular system are concentrated at discrete inter-particle contacts. In this paper, we propose a static hypothesis and a micromechanical description of strain considering the packing structure. The upper and lower estimates of the elastic moduli for granular materials are derived in explicit terms of the inter-particle properties.
Voronoi Cell Finite Element Model for Thermoelastoplastic Deformation in Random Heterogeneous Media
Authors: Moorthy Suresh , Ghosh Somnath , Liu Yunshan
Published: April 2009

A finite element model has been developed for analysis of heterogeneous media, in which second phase inclusions are arbitrarily dispersed within a matrix. A mesh generator based on Dirichlet tessellation, discretizes the heterogeneous domain, accounting for the arbitrariness in location, shape and size of the second phase. This results in a network of convex “Voronoi” polygons which form the elements in a finite element mesh. An assumed stress hybrid formulation has been implemented for accommodating arbitrary multi-sided elements in the finite element model. Composite element formulations have been developed to incorporate the effect of second phase within each element. Formulations have been developed for thermo-elasticity, micropolar elasticity and elasto-plasticity.
Properties of Random Polycrystalline Two-Phase Materials
Authors: Werner E. , Siegmund T. , Weinhandl H. , Fischer F. D.
Published: April 2009

The physical properties of polycrystalline two-phase alloys depend on the properties and the amounts of the constituent phases and on the geometrical arrangement of the grains in the two-phase microstucture. Establishing microstructure-property relationships for two-phase materials requires the correct quantitative characterization of all topological features of the microstructure. Stereology and quantitative metallography provide the means to analyse both real and idealized model microstructures with this respect. The two most important quantitative parameters involved in the formulation of microstructure-property relationships are the contiguity C and the fraction of clusters r which quantify the continuity of the phases and to which extent the phases are present as matrix or as inclusion, respectively. Idealized random model microstructures closely approximating real microstructures are generated and joined with continuum and micromechanical models. The essence of the micromechanical model is the unit cell approach combined with finite element calculations. Properties computed for the unit cell are then representative for the overall microstructure. With this method four important physical properties of a ferritic-austenitic stainless duplex steel are modeled successfully: the magnetic permeability, the diffusion of hydrogen, the thermal expansion behavior and the mechanical properties at elevated temperatures. From these examples the relevance of the parameters C and r is evident. Furthermore, the linear rule of mixture is not appropriate to describe both experimentally obtained properties and the results from the numerical analyses for the respective entity.
Behavior of the Poisson Ratio of a Two-Phase Composite Material in the High-Concentration Limit
Authors: Zimmerman Robert W.
Published: April 2009

The behavior of the Poisson ratio of a material filled with spherical inclusions is studied in the high-concentration limit, using the Mori-Tanaka and the differential effective medium theories. When the inclusions are either much stiffer or much softer than the matrix, both theories predict the existence of a boundary layer near c = 1 in the graph of the Poisson ratio ν as a function of inclusion concentration c. As c increases, ν first approaches some fixed point ν* that depends only on the matrix properties. In a localized region near c = 1, ν then varies rapidly so as to equal the Poisson ratio of the inclusions at c = 1. The results therefore show a qualitative distinction between, for example, the effect of very hard inclusions and infinitely rigid inclusions. The results also illustrate the extent to which the Poisson ratio fails to obey a mixing law of the Voigt or Reuss type, in that the effective Poisson ratio is not bounded between the Poisson ratios of the matrix and inclusion phases.
The Elastoplastic Behavior of a Class of Two-Phase Composites Containing Rigid Inclusions
Authors: Bhattacharyya A. , Weng G. J.
Published: April 2009

The theoretical principle for the determination of the overall elastoplastic behavior for three types of two-phase composites reinforced with rigid spheroidal inclusions is established. In the first type the inclusions are aligned unidirectionally (1-D) whereas in the second type they are randomly oriented on a plane (2-D), both leading to transversely isotropic composites. The third type of composite involves a 3-D random orientation leading to a globally isotropic material. The theory is based on the energy approach recently proposed by Qiu and Weng (1992) and, while intended only for a modest concentration of inclusions, it can cover a wide range of inclusion shapes, from discs to spheres and all the way to needles (or fibers). It is shown, among others, that the axial response of the 1-D composite is the strongest when reinforced with fibers whereas discs provide the strongest reinforcement under the transverse loading. The outcome is reversed for the 2-D composite. As a consequence of a uniform boundary displacement, the 3-D isotropic composite reinforced with the extreme shapes of rigid needles (aspect ratio → ∞) or discs (aspect ratio → 0) turns out to be also ideally rigid with the entire external stress being carried by the rigid inclusions. For other inclusion shapes, the elastoplastic behavior with prolate inclusions are almost always stiffer as compared to those with oblate shapes with a reciprocal aspect ratio. The asymptotic moduli of the two-phase composites containing the two extreme inclusion shapes are given in terms of the disc and needle density parameters, and the overall elastoplastic behavior for the three different microgeometries are also given as a function of these parameters.
Elastic Moduli of Composites With Random, Rigid Inclusions
Authors: Davis L. C. , Hass K. C. , Chen J. , Thorpe M. F.
Published: April 2009

The elastic moduli of composite materials consisting of an isotropic, elastic matrix with perfectly rigid inclusions have been studied near random close packing. In two dimensional systems of uniform sized disks, the moduli have been determined by computer simulations. A theory of the bulk modulus k is developed by assuming that the elastic energy of the neck regions is minimized subject to the constraint that average local strain, <εi>, equals the macroscopic strain. Here the change in center-to-center distance to the ith nearest neighbor disk is δri=εiri. We show that εi ∝ √ wi, where wi is the gap (ri−2R, R=disk radius). This prediction has been verified by the simulations, which also confirm our theory. Our findings appear to be the first example of local geometry dominating the strain near close packing. Predictions for the bulk modulus K in three dimensional systems of rigid spheres (radius = R) are also made. In this case, εi ∝ 1/log(R/wi).