bluuebunny/crossref_metadata_2025 huggingface dataset:
Measurements and Analysis of Flow Velocity and Sediment Concentration at the Seabed
Authors: Myrhaug D. , Slaattelid O. H. , Soulsby R. L. , Lambrakos K. F.
Published: April 2009

A review of flow velocity and sediment concentration measurements on field sites is given, but the main emphasis is on the data analysis results of near-bottom measurements of flow velocities and suspended sediment concentrations over a sandy bottom during four storms in the central North Sea. The water depth was 70 meters and the seafloor consisted of fine sand of 0.20 mm average diameter. The measurements included sediment concentrations, flow velocity in the boundary layer on the seafloor, steady current over the water column, wave heights, and photographs of the seafloor. The paper presents the variation of the sediment concentrations, waves and currents during the storms. Results from the logarithmic boundary layer flow model fit to the current measurements using the roughness (z0) and friction velocity (u*) as fitting parameters are also given. It also gives limited comparisons of model predictions with the data. The predictions are obtained from a wave-current interaction model combined with three different moveable bed models, which predict ripple size and sediment transport effects on the bed roughness.
Modeling Sediment-Turbulent Flow Interactions
Authors: Villaret C. , Davies A. G.
Published: April 2009

Models of widely differing complexity have been used in recent years to quantify sediment transport processes for engineering applications. This paper presents a review of these model types, from simple eddy viscosity models involving the “passive scalar hypothesis” for sediment predication, to complex two-phase flow models. The specific points addressed in this review include, for the suspension layer, the bottom boundary conditions, the relationship between the turbulent eddy viscosity and particle diffusivity, the damping of turbulence by vertical gradients in suspended sediment concentration, and hindered settling. For the high-concentration near-bed layer, the modeling of particle interactions is discussed mainly with reference to two-phase flow models. The paper concludes with a comparison between the predictions of both a classical, one-equation, turbulence k-model and a two-phase flow model, with “starved bed” experimental data sets obtained in steady, open-channel flow.
Regularization Techniques Applied to Boundary Element Methods
Authors: Tanaka Masataka , Sladek Vladimir , Sladek Jan
Published: April 2009

This review article deals with the regularization of the boundary element formulations for solution of boundary value problems of continuum mechanics. These formulations may be singular owing to the use of two-point singular fundamental solutions. When the physical interpretation is irrelevant for this topic of computational mechanics, we consider various mechanical problems simultaneously within particular sections selected according to the main topic. In spite of such a structure of the paper, applications of the regularization techniques to many mechanical problems are described. There are distinguished two main groups of regularization techniques according to their application to singular formulations either before or after the discretization. Further subclassification of each group is made with respect to basic principles employed in individual regularization techniques. This paper summarizes the substances of the regularization procedures which are illustrated on the boundary element formulation for a scalar potential field. We discuss the regularizations of both the strongly singular and hypersingular integrals, occurring in the boundary integral equations, as well as those of nearly singular and nearly hypersingular integrals arising when the source point is near the integration element (as compared to its size) but not on this element. The possible dimensional inconsistency (or scale dependence of results) of the regularization after discretization is pointed out. Finally, we discuss the numerical approximations in various boundary element formulations, as well as the implementations of solutions of some problems for which derivative boundary integral equations are required.
Review of Three Dimensional Dynamic Analyses of Circular Cylinders and Cylindrical Shells
Authors: Soldatos Kostas P.
Published: April 2009

There is an increasing usefulness of exact three-dimensional analyses of elastic cylinders and cylindrical shells in composite materials applications. Such analyses are considered as benchmarks for the range of applicability of corresponding studies based on two-dimensional and/or finite element modeling. Moreover, they provide valuable, accurate information in cases that corresponding predictions based on that later kind of approximate modeling is not satisfactory. Due to the complicated form of the governing equations of elasticity, such three-dimensional analyses are comparatively rare in the literature. There is therefore a need for further developments in that area. A survey of the literature dealing with three-dimensional dynamic analyses of cylinders and open cylindrical panels will serve towards such developments. This paper presents such a survey within the framework of linear elasticity.
Impact on Laminated Composites: Recent Advances
Authors: Abrate Serge
Published: April 2009

Impact damage in structures made out of composite materials is a major concern since such damage can be introduced during the life of the structure, and its mechanical properties can be drastically reduced as a result. In a previous review of the literature on impact on composite materials, this author considered 285 published before 1989. In this article over 300 articles most of which appeared after 1989 are reviewed. These figures indicate that this is a very active area of research, and the present paper seeks to present a comprehensive view of the latest developments. Taken together, these two reviews present a comprehensive view of the state of knowledge in the area. Most the current research effort is focused on low velocity impact damage and, in particular, the damage predictions and the evaluation and prediction of residual properties of damaged laminates. A significant number of papers deal with ballistic impacts on laminated composites and the use of composite materials in designing light armor.
Theory of Representations for Tensor Functions—A Unified Invariant Approach to Constitutive Equations
Authors: Zheng Q.-S.
Published: April 2009

Representations in complete and irreducible forms for tensor functions allow general consistent invariant forms of the nonlinear constitutive equations and specify the number and type of the scalar variables involved. They have proved to be even more pertinent in attempts to model mechanical behavior of anisotropic materials, since here invariant conditions predominate and the number and type of independent scalar variables cannot be found by simple arguments. In the last few years, the theory of representations for tensor functions has been well established, including three fundamental principles, a number of essential theorems and a large amount of complete and irreducible representations for both isotropic and anisotropic tensor functions in three- and two-dimensional physical spaces. The objective of the present monograph is to summarize and recapitulate the up-to-date developments and results in the theory of representations for tensor functions for the convenience of further applications in contemporary applied mechanics. Some general topics on unified invariant formulation of constitutive laws are investigated.
Analytical Solutions of Contact Impact Problems
Authors: Jaeger J.
Published: April 2009

In this article, analytical solutions of the normal and tangential impact of half-spaces at low velocities are formulated. After a brief introduction, a classification of contact problems is proposed and some publications about impact are mentioned. The basic contact laws for monotonously increasing normal, tangential, and torsional contact have been found decades ago, while the general analytical solutions for tangential and torsional load histories, which are necessary for impact calculations, have only been found recently. Insertion of these contact laws into the equations of motion yields a system of nonlinear differential equations, which are uncoupled in the case of the oblique central impact. The normal solution of the uncoupled equations for Hertzian and some axisymmetric surfaces can be written as a hypergeometric function, which generalizes earlier solutions. Solutions in tangential direction for the compression phase and the restitution phase can be found for the case of complete adhesion. Finally, the kinematic coefficient of restitution is shown. This solutions may help to understand some open problems of the collision of rigid bodies, which are in contact on a small elastic domain, where a part of the kinetic energy is transformed into elastic energy and reconverted into kinetic energy in normal and tangential directions.
Contact-Impact Problems: A Review With Bibliography
Authors: Zhong Zhi-Hua , Mackerle Jaroslav
Published: April 2009

Contact-impact problems are of great interest in many engineering fields, eg automotive industry, aircraft industry, nuclear industry, defence industry, and ocean engineering etc. Much research work, both theoretical and experimental, has been carried out on the problem. The fast development of computational mechanics and computing techniques has made it possible to attack extremely complicated contact-impact problems with great success. It is the purpose of this paper to review the contact-impact problems and some recent developments in numerical studies on the problem. General descriptions and variational formulation of the problem are first given. Then, general finite element procedures and various techniques to solve the problem are discussed. Special attention is paid to the treatment of contact-impact interfaces. Finally, a bibliography on the contact-impact problem is presented, listing about five hundred reports, papers and books which have been published retrospectively from 1980.
Recent Advances and Applications of Reduction Methods
Authors: Noor Ahmed K.
Published: April 2009

The focus of this review is on the basic idea and useful interpretations of reduction methods; multiple-parameter reduction methods; treatment of nonconservative loadings (unsymmetric systems); and application of reduction methods in conjunction with operator splitting. The literature reviewed is devoted to the mathematical aspects of reduction methods, as well as to the following seven application areas: eigenvalue problems; nonlinear vibrations; linear and nonlinear dynamic analysis (initial/boundary value problems); linear systems analyzed by using semi-analytic numerical discretization procedures; reanalysis techniques; sensitivity analysis; and optimum design. Sample numerical results are presented showing the effectiveness of reduction methods in a recent application. Hybrid analytical techniques which share some of the key elements with reduction techniques are highlighted. Some of the future directions for research on reduction methods are outlined.
Theories and Computational Models for Composite Laminates
Authors: Reddy J. N. , Robbins D. H.
Published: April 2009

A review of equivalent–single–layer and layerwise laminated plate theories and their finite element models is presented. The layerwise theory advanced by the senior author is presented and a variable displacement finite element model and mesh superposition techniques are described. A simultaneous multiple model approach that is based on the variable kinematic theory and the mesh superposition method are also described. The objective of the simultaneous multiple model approach is to match the most appropriate mathematical model with each subregion based on the physical characteristics, applied loading, expected behavior, and level of solution accuracy desired in that subregion. Thus solution economy is maximized without sacrificing the solution accuracy.
Numerical Modeling of Friction-Induced Vibrations and Dynamic Instabilities
Authors: Tworzydlo W. W. , Becker E. B. , Oden J. T.
Published: April 2009

A numerical study of dynamic instabilities and vibrations of mechanical systems with friction is presented. Of particular interest are friction-induced vibrations, self-excited oscillations and stick-slip motion. A typical pin-on-disk apparatus is modeled as the assembly of rigid bodies with elastic connections. An extended version of the Oden-Martins friction model is used to represent properties of the interface. The mechanical model of the frictional system is the basis for numerical analysis of dynamic instabilities caused by friction and of self-excited oscillations. Coupling between rotational and normal modes is the primary mechanism of resulting self-excited oscillations. These oscillations combine with high-frequency stick-slip motion to produce a significant reduction of the apparent kinetic coefficient of friction. As a particular study model, a pin-on-disk experimental setup has been selected. A good qualitative and quantitative correlation of numerical and experimental results is observed.
Friction in Servo Machines: Analysis and Control Methods
Authors: Armstrong-He´louvry Brian , Dupont Pierre , Canudas de Wit Carlos
Published: April 2009

Analysis tools and compensation methods for the automatic control of systems with friction are surveyed. The literature reviewed is principally that of the controls and mechanics communities, and the perspective taken is that of the controls engineer. Over 180 papers are cited. The analysis tools discussed are describing functions, algebraic analysis, phase plane analysis and simulation. All major compensation techniques are described including both those which employ friction models (fixed and adaptive feedforward compensation) and those which do not (stiff PD, integral, dither, impulsive and dual mode control). A summary of current engineering practice in industry is reported and a paradigm for future research is proposed.
Internal Variable Formulations of Problems in Elastoplasticity: Constitutive and Algorithmic Aspects
Authors: Reddy B. D. , Martin J. B.
Published: April 2009

This work surveys a broad range of related issues in quasistatic elastoplasticity, beginning with a development of an internal variable constitutive theory. The initial-boundary value problem is then considered, and the remainder of the work is concerned with the properties of the time-discrete problem. It is shown how this discrete problem has associated with it a holonomic constitutive law (that is, one relating stress to strain or strain increment), and this holonomic law in turn forms the basis of a solution algorithm. Conditions for the convergence of the algorithm are discussed. The entire treatment applies to the spatially continuous problem.
Linearization in Analysis of Nonlinear Stochastic Systems
Authors: Socha Leslaw , Soong T. T.
Published: April 2009

The purpose of this paper is to provide a review and an assessment of the state-of-the-art in the area of statistical and equivalent linearization in the analysis of nonlinear stochastic systems. Included in the discussion are systems subjected to stationary and nonstationary excitations as well as parametrically excited systems. A variety of linearization criteria are discussed together with accuracy associated with these procedures. This review also includes some applications of equivalent linearization to the study of dynamics of mechanical and structural systems subjected to environmental loads such as wave loads and earthquake excitations. Limitations of current procedures of equivalent linearization are mentioned and suggestions for areas of further research are made.
Biomimetics: Advancing Man-Made Materials Through Guidance From Nature
Authors: Srinivasan A. V. , Haritos G. K. , Hedberg F. L.
Published: April 2009

“The X–29 and HI–MAT use on–board computers to provide greater flexibility. Designers hope that someday these techniques will give man–made flying machines the agility of a dragonfly, which can hover and change direction almost instantly in its search for food.” (Footnote on a display at the National Air & Space Museum, Washington, D.C., August 1990) Future technological advances are becoming increasingly dependent on our ability to design and produce materials with specific thermomechanical and electronic properties. The projected structural and electronic performance requirements for materials are unprecedented. The realization of corresponding technological goals will require significant scientific and technical breakthroughs fueled by innovative thinking. Biomimetics attempts to tap a virtually inexhaustible source of ideas and inspiration: naturally–evolved systems. Mankind has long marveled at the efficiency and effectiveness of biologically–evolved structural systems. Biologists have studied exhaustively the time–proven processes that natural systems employ for synthesizing multifunctional materials with unparalleled precision, thus enabling the species to survive and prosper. The prospect of mimicking biological synthesis in producing man–made materials has generally appeared to be an impossible task. In recent years, however, revolutionary advances in our ability to probe the fabric of materials down to their atomic structures and in the processing control of advanced materials’ microstructures have fueled a renewed interest in imitating natural processes, initially in the laboratory, and ultimately, at the industrial scale. Engineering and scientific communities have a fundamental role to play in this new revolutionary and promising endeavor. The benefits to specific thermomechanical properties resulting from each microstructural feature designed into the biological system have to be understood and quantitatively catalogued. Recommendations for incorporating architectural features encountered in nature in customized man–made systems must be based on engineering analysis of the property enhancement resulting from each observed physical mechanism. This paper addresses a few specific examples of nature’s ingenuity in building–in features which advance properties such as strength, impact resistance, damage control through multiple fracture–energy absorbing paths, and built–in damage–assessment and repair–activating sensors. Potential benefits to advanced artificial materials through inspiration derived from understanding the function of natural materials are also discussed.
Hydroacoustics of Transitional Boundary-Layer Flow
Authors: Lauchle Gerald C.
Published: April 2009

Transitional boundary layers exist on surfaces and bodies operating in viscous fluids at speeds such that the critical Reynolds number based on the distance from the leading edge is exceeded. The transition region is composed of a simultaneous mixture of both laminar and turbulent regimes occurring randomly in space and time. The turbulent regimes are known as turbulent spots, they grow rapidly with downstream distance, and they ultimately coalesce to form the beginning of fully-developed turbulent boundary-layer flow. It has been long suspected that such a region of unsteadiness may give rise to local pressure fluctuations and radiated sound that are different from those created by the fully-developed turbulent boundary layer at equivalent Reynolds number. This article reviews the available literature on this subject. The emphasis of this literature is on natural and artificially created transitional boundary layers under mostly incompressible conditions; hence, the word hydroacoustics in the title. The topics covered include the dynamics and local wall pressure fluctuations due to the passage of turbulent spots created in a deterministic way, the pressure fluctuations under transitioning boundary layers where the formation and location of spots are random, and the acoustic radiation from transition and its pre-cursor, the Tollmien-Schlichting waves. The majority of this review is for zero-pressure gradient flat plate flows, but the limited literature on axisymmetric body and plate flows with pressure gradient is included.
Rough-Wall Turbulent Boundary Layers
Authors: Raupach M. R. , Antonia R. A. , Rajagopalan S.
Published: April 2009

This review considers theoretical and experimental knowledge of rough-wall turbulent boundary layers, drawing from both laboratory and atmospheric data. The former apply mainly to the region above the roughness sublayer (in which the roughness has a direct dynamical influence) whereas the latter resolve the structure of the roughness sublayer in some detail. Topics considered include the drag properties of rough surfaces as functions of the roughness geometry, the mean and turbulent velocity fields above the roughness sublayer, the properties of the flow close to and within the roughness canopy, and the nature of the organized motion in rough-wall boundary layers. Overall, there is strong support for the hypothesis of wall similarity: At sufficiently high Reynolds numbers, rough-wall and smooth-wall boundary layers have the same turbulence structure above the roughness (or viscous) sublayer, scaling with height, boundary-layer thickness, and friction velocity.
Effect of Loading Sequence on the Fatigue Life of Notched Specimens Made From Steel and Aluminium Alloys
Authors: Buxbaum Otto , Kla¨tschke Hartmut , Oppermann Helge
Published: April 2009

A statistical parameter which can be derived from the Markov matrix has been defined in order to characterize the intermixture of random loading fluctuations. By means of this intermixture parameter, load sequences for fatigue tests can be generated closer to reality, and thus more reliable effects as well as effects resulting from loading sequences can be taken into account quantitatively in life calculations. The intermixture parameter has been calculated for 17 test load sequences. The corresponding fatigue test results obtained for notched specimens (Ki = 1.4–3.6) made from steels or aluminium alloys, either under bending or axial loading, led to a general relation between intermixture and fatigue life, being primarily influenced by the stress ratio.
Random Heterogeneous Media: Microstructure and Improved Bounds on Effective Properties
Authors: Torquato S.
Published: April 2009

The purpose of the present article is to review recent advances made in the determination and calculation of improved bounds on the effective properties of random heterogeneous media that depend upon the microstructure via n-point correlation functions. New breakthroughs made in the quantitative characterization of the microstructure of heterogeneous materials are also reviewed. The following four different effective properties shall be studied: (i) effective conductivity tensor (which includes, by mathematical analogy, the dielectric constant, magnetic permeability, and diffusion coefficient); (ii) effective stiffness tensor; (iii) diffusion-controlled trapping constant; and (iv) fluid permeability tensor. It shall be demonstrated that improved upper and lower bounds can provide a relatively sharp estimate of the effective property even when the bounds diverge from one another. Although this article reviews state-of-the-art advances in the field, an attempt will be made to elucidate methods and principles for the nonexpert.
Influence of Stress State on the Failure Behavior of Cracked Components Made of Steel
Authors: Clausmeyer H. , Kussmaul K. , Roos E.
Published: April 2009

One of the decisive factors influencing the safety of components is the capacity for plastic deformation of the material employed. This depends not only on the actual material properties, such as reduction of area or notch impact energy, but also on the stress conditions prevailing in the component. With sufficiently sharp transitions of geometrical form, or at cracks, such high multiaxial stress states can arise in components, that in spite of excellent plastic deformation capability of the malterial, practically deformationless fractures are inevitable. If one generates from the principal normal stresses (σ1, σ2, σ3) the multiaxiality quotient q, which represents a characteristic quantity for the degree of multiaxiality of the stress state, the effect of the stress states on the strength and deformation behavior of a component can be estimated. With the aid of the Sandel fracture theory, which includes the von Mises yield theory as a special case, the critical q value qc, which characterises the stress conditions leading to cleavage fracture if q < qc, can be calculated. The fracture mechanics evaluation of the sharply notched specimens of dimensions similar to components shows no dependence of the effective crack initiation value on the specimen size or stress state, since at the load free crack tip, plane stress conditions generally prevail. The further failure process after crack initiation in the form of stable crack extension is very strongly controlled by the stress state. This phase could also be estimated from consideration of the pattern of the q value in the remaining cross section. The investigations have shown that the multiaxiality quotient q, which characterizes the degree of multiaxiality of the stress state, represents a characteristic quantity with which, in combination with fracture mechanics methods, the failure behavior of components may be estimated, even with respect to stable crack extension.
Impact on Laminated Composite Materials
Authors: Abrate Serge
Published: April 2009

Laminated composite materials are used extensively in aerospace and other applications. With their high specific modulus, high specific strength, and the capability of being tailored for a specific application, these materials offer definite advantages compared to more traditional materials. However, their behavior under impact is a concern, since impacts do occur during manufacture, normal operations, or maintenance. The situation is critical for impacts which induce significant internal damage, undetectable by visual inspection, that cause large drops in the strength and stability of the structure. Impact dynamics, including the motion of both the impactor and the target and the force developed at the interface, can be predicted accurately using a number of models. The state of stress in the vicinity of the impact is very complex and requires detailed analyses. Accurate criteria for predicting initial failure are generally not available, and analyses after initial failure are questionable. For these reasons, it can be said that a general method for estimating the type and size of impact damage is not available at this time. However, a large amount of experimental data has been published, and several important features of impact damage have been identified. In particular, interply delaminations are known to occur at the interface between plies with different fiber orientation. Their shape is generally elongated in the direction of the fibers in the lower ply at that interface. The delaminated area is known to increase linearly with the kinetic energy of the impactor after a certain threshold value has been reached. The effect of impact damage on the properties of the laminate has obvious implications for design and inspection of actual structures. Experimental results concerning the residual strength of impact damaged specimens subjected to tension, compression, shear, bending, and both static and fatigue loading are available. Analyses concentrate primarily on predicting residual tensile and compressive strength. In order to fully understand the effect of foreign object impact damage, one should understand impact dynamics and be able to predict the location, type, and size of the damage induced and the residual properties of the laminate. This article is organized along these lines and presents a comprehensive review of the literature on impact of laminated composites, considering both experimental and analytical approaches.
Simulation of Stochastic Processes by Spectral Representation
Authors: Shinozuka Masanobu , Deodatis George
Published: April 2009

The subject of this paper is the simulation of one-dimensional, uni-variate, stationary, Gaussian stochastic processes using the spectral representation method. Following this methodology, sample functions of the stochastic process can be generated with great computational efficiency using a cosine series formula. These sample functions accurately reflect the prescribed probabilistic characteristics of the stochastic process when the number N of the terms in the cosine series is large. The ensemble-averaged power spectral density or autocorrelation function approaches the corresponding target function as the sample size increases. In addition, the generated sample functions possess ergodic characteristics in the sense that the temporally-averaged mean value and the autocorrelation function are identical with the corresponding targets, when the averaging takes place over the fundamental period of the cosine series. The most important property of the simulated stochastic process is that it is asymptotically Gaussian as N → ∞. Another attractive feature of the method is that the cosine series formula can be numerically computed efficiently using the Fast Fourier Transform technique. The main area of application of this method is the Monte Carlo solution of stochastic problems in engineering mechanics and structural engineering. Specifically, the method has been applied to problems involving random loading (random vibration theory) and random material and geometric properties (response variability due to system stochasticity).
Generalized Galerkin Methods for Convection Dominated Transport Phenomena
Authors: Donea J.
Published: April 2009

A brief survey is made of recent advances in the development of finite element methods for convection dominated transport phenomena. Because of the nonsymmetric character of convection operators, the standard Galerkin formulation of the method of weighted residuals does not possess optimal approximation properties in application to problems in this class. As a result, numerical solutions are often corrupted by spurious node-to-node oscillations. For steady problems describing convection and diffusion, spurious oscillations can be precluded by the use of upwind-type finite element approximations that are constructed through a proper Petrov-Galerkin weighted residual formulation. Various upwind finite element formulations are reviewed in this paper, with a special emphasis on the major breakthroughs represented by the so-called streamline upwind Petrov-Galerkin and Galerkin least-squares methods. The second part of the paper is devoted to a review of time-accurate finite element methods recently developed for the solution of unsteady problems governed by first-order hyperbolic equations. This includes Petrov-Galerkin, Taylor-Galerkin, least-squares, and various characteristic Galerkin methods. The extension of these methods to deal with unsteady convection-diffusion problems is also considered.
Circular Cylinder Wake Configurations: A Flow Visualization Survey
Authors: Coutanceau Madeleine , Defaye Jean-Rene´
Published: April 2009

The survey starts with the presentation of the general principles underlying the different types of techniques which are most often used in wake visualization with their advantages, but also their respective limits. Then information deduced from flow pictures collected from the literature from the beginning of the century up to the present has been used to characterize the wake structure of a circular cylinder (at rest or submitted to various motions) and its evolution with the Reynolds number for an extended range (0 < Re < 107). Incompressible flow has been more particularly considered, both in the quasi-established phase (ten regimes are differentiated and extensively described) and in the transient phase (specific features are pointed out). Special attention has been paid to three-dimensional and memory effects by a combined presentation of crosswise and spanwise observations of the wake phenomena as well as their evolution with time. The influence of compressibility in the high-speed regime and of superimposed periodic motions, either on the cylinder or on the stream, have been also investigated and the main characteristics of the lock-in regime have been described. The survey is illustrated by 40 figures and completed by a table in which are reported the successive studies related to the flow around a circular cylinder based upon visualization, including a brief account of the experimental setups and methods, as well as a description of the main phenomena observed in the corresponding pictures.
Domain of Influence Results in Generalized Thermoelasticity—A Survey
Authors: Ignaczak Jozef
Published: April 2009

The aim of the article is to review a number of results on finite wave speeds of thermoelastic disturbances that are based on two different models of a thermoelastic solid, and which were obtained mostly by the present author and his collaborators during the past 10 years. The two models discussed are the L–S model proposed, among others, by Lord and Shulman in 1967 and the G–L model introduced into the technical literature by Green and Lindsay in 1972. Each of the two models is a generalization of the classical one, and it has been introduced, among other reasons, in an attempt to eliminate the paradox of an infinite velocity of thermoelastic disturbances inherent in the classical model. A stress is made on the domain of influence theorems for arbitrary anisotropic and nonhomogeneous thermoelastic bodies in which the thermoelastic coupling cannot be ignored. Apart from the general results concerning the initial-boundary value problems in terms of various pairs of mechanical and thermal variables, some particular potential–temperature and one-dimensional results are discussed. The article should prove useful for those researchers who try to understand an effect of thermoelastic coupling on speed of thermoelastic waves in a nonhomogeneous and anisotropic medium as well as for those working on modeling of waves of more complex nature such as electromagneto-thermoelastic waves and others.
Statics of Laminated and Fibrous Composites With Curved Structures
Authors: Akbarov S. D. , Guz’ A. N.
Published: April 2009

A broad and detailed review is presented on problems of statics of mechanics of laminated and fibrous composite materials with curved structures. Studies are discussed which were carried out based on the piecewise-homogeneous body model using exact three-dimensional equations of deformable solid body mechanics. The classification was made according to the type of composite (laminated, fibrous), the form of bending in the structure of composites considered, the materials properties (isotropic, anisotropic), the properties of binder and filler, and their models (elastic, viscoelastic). The formulation of the problem is presented for laminated and fibrous composites with bent, curved structures. Two types of bending are distinguished according to the forms of reinforcing elements bending: (1) periodic; (2) local. For every type of bending, solution methods of corresponding problems are presented. Moreover, according to the form of the location of neighboring curved, bent layers, with respect to each other, two types of bending are distinguished—the monophasic and the antiphasic. Detailed presentation is given of some very significant specific results, illustrating the influence of reinforcing element bending on local distribution of stresses in every component of the composite material. Tables and graphs are presented from publications on this subject. Some applications are presented of results based on the piecewise-homogeneous body model in composite mechanics. In conclusion, some areas of future research are proposed. The situations presented prove the theoretical and practical importance of investigations discussed in the review. In the analysis of strength problems, in many cases information is needed on the local distribution of the stress-deformed state in every component of the composite material with bent, curved structures. Information of this type could be obtained only within the framework of the piecewise-homogeneous body model using exact three-dimensional equations of deformable solid body mechanics.
Stability of Fibrous Composites
Authors: Babich I. Yu. , Guz’ A. N.
Published: April 2009

In this review article the three-dimensional linearized theory is presented of the internal and the surface instability of fibrous composite materials. The possible mechanisms of the stability loss in the structure of these materials are investigated. In this investigation the strict model is used of the nonlinearly elastic compressible and incompressible piecewise-homogeneous medium with the arbitrary form of the elastic potential for the theory of finite deformation and for two variants of the theory of small precritical deformations. Problems for a single fiber (fibrous materials with low concentration of the filler, when at stability loss the interaction between fibers is not accounted for), for two fibers (fibrous materials with low concentration of the filler, when as a result of the structure irregularity at the stability loss two neighbouring fibers may interact) for the infinite row and for a doubly periodic system of fibers (fiber materials with nonsmall filler concentration, taking into account fiber interaction), in the infinite and semiinfinite matrix, are considered. Results are obtained for these cases, predominantly when conditions are satisfied of the complete contact on the fiber and matrix polymer or metal interfaces. In the case of the metal matrix at plastic deformations the conception of continuing loading is used, and the change of the unloading zones in the process of stability loss is not accounted for. The influence of the inhomogeneity of the precritical stressed state, resulting from the difference of coefficients of the transverse expansion, of the mechanical properties, and of the volume concentrations of the fibers and the matrix, on the critical parameters is investigated. Application is presented of the obtained results in the fracture mechanics of fibrous composite materials under compression along the reinforcing elements.
Effective Stiffness of Cracked Elastic Solids
Authors: Fares N.
Published: April 2009

This paper discusses the elastic stiffness reduction that accompanies cracking. Basic results are illustrated using simple examples and general approaches of determining the effective stiffness of cracked solids are reviewed. Various approximate methods of obtaining the effective stiffness of cracked solids are demonstrated for the case of aligned uniform cracks. These methods include the dilute approximation, self-consistent method, Mori-Tanaka’s method, differential scheme and shear lag model. Finally, recent numerical results of 3-D periodically cracked solids with high interaction are presented and discussed.
Crack Tip Shielding in Ceramic and Cementitious Materials Subjected to Monotonic and Cyclic Loading
Authors: Hu Xiaozhi , Mai Yiu-Wing
Published: April 2009

Crack tip shielding due to crack-interface bridging in a cellulose fiber reinforced cement, plain mortar and a coarse-grained alumina is studied in terms of a novel compliance function φ-curve concept proposed recently by the authors. The simplicity and versatility of the approach are demonstrated through evaluation of the crack tip shielding influence under both monotonic and cyclic loading with compliance measurements. Crack-tip shielding degradation due to either successive saw-cutting or repetitive crack-face abrasion can also be quantitatively determined.
Conditions for Pseudo Strain-Hardening in Fiber Reinforced Brittle Matrix Composites
Authors: Li Victor C. , Wu Hwai-Chung
Published: April 2009

Apart from imparting increased fracture toughness, one of the useful purposes of reinforcing brittle matrices with fibers is to create enhanced composite strain capacity. This paper reviews the conditions underwhich such a composite will exhibit the pseudo strain-hardening phenomenon. The presentation is given in a unified manner for both continuous aligned and discontinuous random fiber composites. It is demonstrated that pseudo strain-hardening can be practically designed for both types of composites by proper tailoring of material structures.
Dynamics of Periodic and Near-Periodic Structures
Authors: Li Dong , Benaroya Haym
Published: April 2009

A brief review of linear waves and dynamic behavior of both periodic and near-periodic structures is presented in this paper. Emphasis is placed on a summary of more recent studies of engineering structures subject to wave motion and the effects of near-periodicity on their dynamic behavior. Conclusions drawn regarding linear waves and dynamics serve as a foundation for further investigation into the area of nonlinear waves and dynamics of these structures.
Thermal Buckling of Plates and Shells
Authors: Thornton Earl A.
Published: April 2009

This review discusses research on thermal buckling of plates and shells since the first work in the 1950s. Elastic thermal buckling of metallic as well as composite plates and shells is described. The role of material thermal properties on thickness and spatial temperature gradients is demonstrated first. Then thermal buckling and postbuckling research for plates, shallow shells and curved panels, cylindrical and conical shells is presented. Analytical, computational and experimental studies are described. Governing equations and formulas for critical buckling temperatures are presented for several practical applications. An assessment of past research is made, and future research needs are highlighted.
Qualitative Aspects of Nonlinear Wave Motion: Complexity and Simplicity
Authors: Engelbrecht J.
Published: April 2009

The nonlinear wave processes possess many qualitative properties which cannot be described by linear theories. In this presentation, an attempt is made to systematize the main aspects of this fascinating area. The sources of nonlinearities are analyzed in order to understand why and how the nonlinear mathematical models are formulated. The technique of evolution equations is discussed then as a main mathematical tool to separate multiwave processes into single waves. The evolution equations give concise but in many cases sufficient description of wave processes in solids permitting to analyze spectral changes, phase changes and velocities, coupling of waves, and interaction of nonlinearities with other physical effects of the same order. Several new problems are listed. Knowing the reasons, the seemingly complex problems can be effectively analyzed.
Conservative Formulation of Large Deformation Plasticity
Authors: Glimm James G. , Plohr Bradley J. , Sharp David H.
Published: April 2009

We explain several ideas which may, either singly or in combination, help achieve high resolution in simulations of large-deformation plasticity. Because of the large deformations, we work in the Eulerian picture. The governing equations are written in a fully conservative form, which are correct for discontinuous as well as continuous solutions. Models of shear bands are discussed. These models describe the internal dynamics of a developed shear band in terms of time-asymptotic states; in other words, the smooth internal structure is replaced by a jump discontinuity, and the shear band evolution is determined by jump relations. This analysis is useful for high resolution numerical methods, including both shock capturing and shock tracking schemes, as well as for the understanding and validation of computations, independently of the underlying method. Preliminary computations, which illustrate the feasibility of these ideas, are presented.
Nonlinear Hyperbolic Waves in Hyperelastic Solids
Authors: Haddow J. B.
Published: April 2009

This paper considers hyperbolic, one spatial dimension nonlinear wave propagation in a hyperelastic solid, and a discussion of the basic theory is presented. Constitutive relations for compressible rubberlike materials, whose internal energies can be expressed as the sum of a function of specific volume only and a function of temperature only, are discussed. These relations are assumed for the analysis of a class of plane wave problems and similarity solutions are obtained. Thermal effects, including the effect of the jump in entropy across a shock for a problem of uncoupled longitudinal wave propagation, are taken into account, however heat conduction is neglected. Solutions for a piezotropic model, which is a model for which mechanical and thermal effects are uncoupled, are obtained for comparison purposes. An axisymmetric problem is also discussed.
Analysis of Failure Waves in Glasses
Authors: Clifton R. J.
Published: April 2009

Recent plate impact experiments have been interpreted as indicating the existence of “failure waves” during the compression of glass by impact at sufficiently high velocities. In experiments on soda-lime glass, Brar et al. (1991) reported the propagation of a wave across which the shearing strength dropped sharply from 2 GPa to 1 GPa, and the spall strength dropped from 3 GPa to zero. Such a drop in spall strength has also been reported by Raiser et al. (1993) in an aluminosilicate glass. Kanel et al. (1993) interpreted a small jump in the rear surface particle velocity in experiments on K19 glass as the reflection of a recompression wave from a wavefront propagating at approximately the speed reported for “failure waves”. In this paper, such “failure waves” are interpreted within the context of nonlinear wave theory. In this theory the “failure wave” corresponds to a propagating phase boundary—called a transformation shock. The theory is analogous to the theory of liquifaction shocks in fluids.
Mathematical Modeling of Transport Phenomena During Alloy Solidification
Authors: Beckermann C. , Viskanta R.
Published: April 2009

Mathematical modeling of mass, momentum, heat, and species transport phenomena occurring during solidification of metal alloys is reviewed. Emphasis is placed on the incorporation of the effects of the solid structure and the interactions between the solid and liquid phases on a microscopic scale into a (macroscopic) model of the transport phenomena occurring at the system scale. Both columnar and equiaxed growth structures, as well as laminar convection of liquid and solid crystals are considered. The macroscopic conservation equations are introduced via a volume averaging approach and commonly made simplifications are examined. Basic constitutive relations for the phase interactions occurring in alloy solidification are presented. Recent progress in including nucleation, microsegregation, undercooling and other microscopic phenomena in the macroscopic equations is reviewed. The specific areas where future theoretical and experimental research is needed are identified.
Perturbation Techniques in Phase Change Heat Transfer
Authors: Aziz A. , Lunardini V. J.
Published: April 2009

Heat transfer with change of phase (freezing or melting) is important in numerous scientific and engineering applications. Since the pioneering works of Neumann and Stefan, a number of analytical and numerical techniques have been developed to deal with freezing and melting problems. One such analytical tool is the method of perturbation expansions, which is the main focus of this work. The article begins with a review of the perturbation theory and outlines the regular perturbation method, the method of strained coordinates, the method of matched asymptotic expansions, and the recently developed method of extended perturbation series. Next, the applications of these techniques to phase change problems in Cartesian, cylindrical, and spherical systems are discussed in detail. Although the bulk of the discussion is confined to one-dimensional situations, the report also includes two- and three-dimensional cases where admittedly the success of these techniques has so far been limited. The presentation is sufficiently detailed so that even the reader who is unfamilar with the perturbation theory can understand the material without much difficulty. However, at the same time, the discussion covers the latest literature on the subject and therefore should serve as the state-of-the-art review.