Showing papers in "Applied Mechanics Reviews in 1992"

Effective Elastic Properties of Cracked Solids: Critical Review of Some Basic Concepts

Abstract: The problem of effective moduli of cracked solids is critically reviewed. Various approaches to the problem are discussed; they are further assessed by comparing their predictions to results for sample deterministic arrays. These computer experiments indicate that the approximation of noninteracting cracks has a wider than expected range of applicability. Some of the deficiencies of various approximate schemes seem to be related to inadequacy of the conventionally used crack density parameter (insensitive to mutual positions of cracks). An alternative parameter that has this sensitivity, is suggested. Finally, the problem of effective moduli is discussed in the context of {open_quotes}damage mechanics{close_quotes}. It is argued that, contrary to the spirit of many damage models, there is no direct quantitative correlation between progression of a microcracking solid towards fracture and deterioration of its stiffness; thus, the effective moduli may not always serve as a reliable indicator of damage. 84 refs., 14 figs.

Remarks on Crack-Bridging Concepts

Abstract: The article draws upon recent work by us and our colleagues on metal and ceramic matrix composites for high temperature engines. The central theme here is to deduce mechanical properties, such as toughness, strength and notch-ductility, from bridging laws that characterize inelastic processes associated with fracture. A particular set of normalization is introduced to present the design charts, segregating the roles played by the shape, and the scale, of a bridging law. A single material length, {gamma}{sub 0}E/{sigma}{sub 0}, emerges, where {gamma}{sub 0} is the limiting-separation, {sigma}{sub 0} the bridging-strength, and E the Young`s modulus of the solid. It is the huge variation of this length-from a few manometers for atomic bond, to a meter for cross-over fibers - that underlies the richness in material behaviors. Under small-scale bridging conditions, {gamma}{sub 0}E/{sigma}{sub 0} is the only basic length scale in the mechanics problem and represents, with a pre-factor about 0.4, the bridging zone size. A catalog of small-scale bridging solutions is compiled for idealized bridging laws. Large-scale bridging introduces a dimensionless group, a/({gamma}{sub 0}E/{sigma}{sub 0}), where a is a length characterizing the component. The group plays a major role in all phenomena associated with bridging, and provides a focus ofmore » discussion in this article. For example, it quantifies the bridging scale when a is the unbridged crack length, and notch-sensitivity when a is hole radius. The difference and the connection between Irwin`s fracture mechanics and crack bridging concepts are discussed. It is demonstrated that fracture toughness and resistance curve are meaningful only when small-scale bridging conditions prevail, and therefore of limited use in design with composites. Many other mechanical properties of composites, such as strength and notch-sensitivity, can be simulated by invoking large-scale bridging concepts. 37 refs., 21 figs., 3 tabs.« less

Conditions for Pseudo Strain-Hardening in Fiber Reinforced Brittle Matrix Composites

Abstract: 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 gills of composites by proper tailoring of material structures. 18 refs., 8 figs., 2 tabs.

Computational Models for High-Temperature Multilayered Composite Plates and Shells

Abstract: The focus of this review is on the hierarchy of composite models, predictor-corrector procedures, the effect of temperature-dependence of material properties on the response, and the sensitivity of the thermomechanical response to variations in material parameters. The literature reviewed is devoted to the following eight application areas: heat transfer; thermal stresses; curing, processing and residual stresses; bifurcation buckling; vibrations of heated plates and shells; large deflection and postbuckling problems; and sandwich plates and shells. Extensive numerical results are presented showing the effects of variation in the lamination and geometric parameters of temperature-sensitive angle-ply composite plates on the accuracy of thermal buckling response, and the sensitivity derivatives predicted by nine different modeling approaches (based on two-dimensional theories). The standard of comparison is taken to be the exact three-dimensional thermoelasticity solutions. Some future directions for research on the modeling of high-temperature multilayered composites are outlined. 448 ref., 16 figs., 11 tabs.

Multiphase Poroelastic Finite Element Models for Soft Tissue Structures

Abstract: 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. Give 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 ans 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 areasmore » are identified, and possible applications of the porohyperelastic and mixture-based FEMs are suggested. 62 refs., 11 figs., 3 tabs.« less

Analyses of Plastic Flow Localization in Metals

Abstract: 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 bymore » 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. 81 refs., 16 figs.« less

Effect of Loading Path and Porosity on the Failure Mode of Porous Rocks

Abstract: Grain crushing and pore collapse are the dominant compaction mechanisms in high porosity clastic rocks. These micromechanical processes control the evolution of strain hardening during cataclastic flow, and they can also result in embrittlement of the rock. The mechanics of the transition from brittle fracture to homogeneous cataclastic flow for the Berea and Kayenta sandstones were investigated in the laboratory. The mechanical data show that the transition is sensitively dependent on the stress state as well as the porosity. In the stress space, the complete locus for brittle failure by shear localization can be determined by tests on normally consolidated and overconsolidated samples along different loading paths. Using porosity as the hardening parameter, the evolution of the inelastic yield locus with strain hardening can be mapped out in the stress space. This yield locus expands with decreasing porosity. Scanning electron microscope and acoustic emission measurements were used to elucidate the micromechanics. The onset of grain crushing and pore collapse was marked by a surge in acoustic emission activity. A Hertzian fracture mechanics model was formulated to analyze the roles of porosity, grain size and fracture toughness in controlling the onset of hydrostatic and shear-enhanced compaction. Stereological measurements of the microcrack density show that significant stress-induced anisotropy was induced by shear-enhanced compaction, with preferred orientations of the stress-induced microcracks subparallel to the maximum compression direction.

Optimum Dimensions of Extended Surfaces Operating in a Convective Environment

Abstract: This article is devoted to the review of the literature on optimum dimensions of extended surfaces losing heat by pure convection to the surroundings. The review covers straight (longitudinal) fins, annular (radial) fins, and spines of different profile shapes. The optimum dimensions for each shape are given both in terms of the volume of the material as well as the heat dissipation. The effects of tip heat loss, variable heat transfer coefficient, internal heat generation, temperature dependent thermal conductivity, base convection, and primary surface thickness on the optimum dimensions are discussed. The optimization procedure is illustrated with several numerical examples. Areas of extended surface technology where further optimization studies are needed are identified. It is hoped that the article would serve the dual purpose of the state-of-the-art as well as a pedagogical review. 24 refs., 22 figs., 9 tabs.

Microbubble drag reduction in liquid turbulent boundary layers

Abstract: The interactions between a dense cloud of small bubbles and a liquid turbulent boundary layer are reviewed on the basis of available experimental observations to understand and quantify their capability for reducing skin friction. Gas bubbles are generally introduced into the boundary layer by injection through a porous surface or by electrolysis. After injection, the bubbles stay near the wall in boundary-layer-like fashion giving rise to strong gradients in both velocity and gas concentration. In general, the magnitude of the skin friction reduction increases as the volume of bubbles in the boundary layer is increased until a maximum skin friction reduction of typically 80–90% of the undisturbed skin friction level is reached. The volumetric gas flow required for this maximum is nominally equal to the volume flow of the liquid in the boundary layer. Bubble size estimates indicate that in most microbubble experiments the bubbles have been intermediate in size between the inner and outer scales of the undisturbed boundary layer. Additional studies with other nondimensional bubble sizes would be useful. However, the bubble size is most likely controlled by the injection process, and considerably different conditions would be required to change this ratio appreciably. The trajectories of the bubble clouds are primarily determined by the random effects of turbulence and bubble-bubble interactions. The effects of buoyancy represent a weaker effect. The trajectories are unlike the deterministic trajectory of an individual bubble in a time-averaged boundary layer. Bubbles are most effective in high speed boundary layers and, for the bubble sizes tested to date, produce an effect that persists for some one hundred boundary layer thicknesses. Modeling suggests that microbubbles reduce skin friction by increasing the turbulence Reynolds number in the buffer layer in a manner similar to polymers. Although the effects of microbubbles are consistent and reproducible, their primary practical limitation is the volume of gas needed. Studies aimed at reducing the volumetric gas flow requirements are recommended. Potential applications would favor high speed vehicles operating near the surface where pumping work is minimized.

Extensile Cracking in Porous Rock Under Differential Compressive Stress

Abstract: Under differential compressive stress rocks exhibit nonlinear deformation that includes initial compaction, near-linear elastic behavior, and strain-hardening followed by strain-softening and dilation (or compaction in clastic rocks) and localization. This behavior derives largely from changes in the microstructure of the rocks. Much of it has been attributed to the growth of extensile microcracks. The stress-induced microstructural changes brought about by successively more complicated states of stress produced by uniaxial and triaxial compression of circular cylinders, axisymmetric stresses in hollow cylinders, and indentation by hemispheres in Indiana limestone and Berea sandstone have been preserved using Wood`s metal porosimetry. In this technique molten Wood`s metal at about 100{degrees}C is used as a pore fluid at a pressure of about 10 MPa, and the experiments are conducted using the concepts of effective stress. At the deformation state of interest, the temperature is lowered to solidify the metal, thereby preserving the microstructure as it exists under load and facilitating subsequent preparation of the specimen for microscopic study. Mode I microcrack growth is observed to occur by a variety of mechanisms such as bending, point loading and sliding cracks. The effects of this are analyzed using an elastic continuum within which Mode II displacement acrossmore » microcracks and Mode I microcrack growth results from heterogeneous stress concentrations that produce local tensile stresses. While the continuum model replicates many of the observations, it fails to account for localization by en echelon arrays of extensile microcracks that precede macroscopic shear faulting. Using a {open_quotes}zero order{close_quotes} continuum approximation, the spatially stochastic distribution of grains in clastic rocks is shown to be important in the formation of the en echelon arrays of microcracks that form shear bands. 63 refs., 26 figs., 1 tab.« less

Overview of Micro Heat Pipe Research and Development

Abstract: The concept of a micro heat pipe was first proposed in 1984. Since that time, numerous analytical and experimental investigations have been conducted to determine the fundamental parameters that govern the operation of these devices. Micro heat pipes ranging in size from 1 mm in diameter and 60 mm in length to 30 {mu}m in diameter and 10 mm in length have been analyzed, modelled, and fabricated. The following review describes the historical development of these devices, along with the analytical and numerical techniques used to model and predict their performance and the results of several recent experimental investigations. Because of recent advances in the development of micro heat pipes fabricated as an integral part of semiconductor waters, particular emphasis has been placed on various construction and charging methods currently under investigation. 43 refs., 25 figs.

Finite Element Analysis of Aeroelasticity of Plates and Shells

Abstract: A review of the finite element method applied to the problem of supersonic aeroelastic stability of plates and shells is presented. The review is limited to linear models. Some new contributions in the field are presented and future trends are discussed. 105 refs., 18 figs., 6 tabs.

Phenomenological Theories of Elastoplasticity and Strain Localization at High Strain Rates

Abstract: In this paper certain fundamental concepts underlying the phenomenological theories of elastic-plastic deformations at finite strains and rotations are presented, and some of the commonly discussed theories are summarized, emphasizing the constitutive parameters which influence strain localization and material instability often observed in finite deformation of ductile materials. Particular attention is paid to the thermodynamic basis of inelastic deformation. Conditions for the existence of inelastic potentials are discussed. The results are presented in terms of a general material strain and its conjugate stress, and then specialized for particular applications, emphasizing quantities and theories which are reference- and strain measure-independent. Rate-independent and rate-dependent elastoplasticity relations are developed, starting from a finite deformation version of the J{sub 2}-plasticity with isotropic and kinematic hardening, and leading to theories which include dilatancy, pressure sensitivity, frictional effects, and the noncoaxiality of the plastic strain and the stress deviator. A class of commonly used deformation plasticity theories is then examined and its relation to nonlinear elasticity is discussed. The question of plastic spin, and its relation to the decomposition of the deformation gradient into elastic and plastic constituents, is reviewed in some detail, and it is shown that this decomposition yields explicit relations which uniquely definemore » all spins in terms of the velocity gradient and the elastic and plastic deformation rates, hence requiring no additional constitutive relations for the plastic spin. The phenomenon of strain localization at high strain rates is illustrated and discussed, and a series of numerical results are given. Finally, a recent breakthrough in elastoplastic explicit computational algorithms for large-strain, large-strain-rate problems is briefly reviewed. 144 refs., 6 figs.« less

Dynamics and control of coherent structure in turbulent jets

Abstract: Current understanding of coherent structure dynamics in incompressible turbulent jets as explained by the nonlinear stability theory is reviewed, focusing on nonswirling turbulent jets. Topics addressed include hydrodynamic stability theory and coherent structures; dynamics of energy transfers among different scales of motion; nonlinear development of amplitude; development of single-frequency coherent mode; fundamental-subharmonic interaction and vortex pairing; and reversal of Reynolds stresses. Attention is also given to the effect of initial phase-difference angle between fundamental and subharmonic, conditions for resonance interaction, modulation of spreading rate by controlling coherent structure, turbulence enhancement or suppression due to excitation, 3D effects, jet noise, and swirling jets.

Recent Developments in the Force Method of Structural Analysis

Abstract: The development of the force method of structural analysis has been hindered by the difficulty of generating a suitable maximal set of independent self-equilibrating stress systems, known as statical or null basis. Recent developments to overcome this problem can be classified as topological, combinatorial, algebraic, mixed and integrated force methods. Combinatorial methods are efficient and provide insight to the problems involved, however, further research is needed before a unified formulation can be made. Algebraic methods are simple and general in nature, however, their automation requires considerable amount of operations and storage. The insight to the problems are not present in these methods. Mixed methods incorporate the efficiency of the existing combinatorial methods and generality of the algebraic approaches. 88 refs., 10 figs.

Dynamics of periodic and near-periodic structures

Abstract: 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.

Finite Strain Plasticity and Damage in Constitutive Modeling of Metals With Spin Tensors

Abstract: The analysis of damage and plastic deformation in metals is very important towards the full understanding of the various damage mechanisms in these materials. A coupled theory of damage mechanics and finite strain plasticity is proposed. The theory is based on a sound mathematical and mechanical background and is thermodynamically consistent. It is formulated using spatial coordinates utilizing a von Mises type yield criterion with both isotropic and kinematic hardening. The derivation is based on the concept of effective stress that was originally proposed by Kachanov for the case of uniaxial tension. The plasticity model is first formulated in a fictitious undamaged configuration of the body. Then certain transformation equations are derived to transform this model into a damage-plasticity model in the damaged configuration of the body. Certain assumptions are made in order to make this transformation possible. These assumptions include small elastic strains and the hypothesis of elastic energy equivalence. 39 refs., 6 figs.

Stress Minimum Forms for Elastic Solids

Abstract: This article concerns the problem of determining shapes of minimum stress concentration. Special emphasis is place upon the mathematically precise formulation of these problems and upon the study of cases in which the optimum shape can be found in a highly explicit form. For all the cases discussed, a mathematical proof of the optimality is given. 40 refs., 6 figs., 1 tab.

Statics of laminated and fibrous composites with curved structures

Abstract: 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.

A Micromechanics-Based Model for Creep Behavior of Rock

Abstract: Recently, various ideas on underground development have been proposed and associated technical problems have been studied. One of the issues of concern is the prediction of the long-term behavior of rock, such as creep phenomena and fatigue. The mechanical behavior of rock is known to be greatly affected by temperature, confining pressure, pore fluid pressure and pH. It is necessary to establish a prediction method for creep deformation and creep failure of rock in order to ensure the long-term safety of the underground structures such as vaults for nuclear waste and power stations. Studies with the scanning electron microscope revealed that the mechanisms of creep deformation and creep failure is the growth of microcrack nucleated at a pre-existing defect. Under compression below the failure strength, the microcrack gradually grows and the rock specimen fails after a certain time. The mechanism of time-dependent crack growth is understood as the stress corrosion at the crack tips. The objective of this study is to establish a prediction method of creep behavior. It is necessary to understand the governing mechanism of phenomena and to build a model for the reproduction of creep behavior. In this study, an analytical model of microcrack growth under compressionmore » on the basis of micromechanics is proposed. The analytical results of the proposed model are compared with the experimental results. It appears that the experimental data are reproduced by the model. Moreover, a constitutive equation is derived from the proposed micromechanical model and is implemented into a finite element program to analyze the creep behavior of underground structures. As an example, a problem of elliptical excavation under hydrothermal conditions is analyzed and a crack length field is predicted as a function of time at different temperatures. It is concluded that the results of the finite element analysis indicate the possibility that rock may fail due to the effect of high temperature.« less

Fault Growth and Acoustic Emissions in Confined Granite

Abstract: 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 acousticmore » 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.« less

Nonlinear analysis techniques for shear band formation at high-strain-rates

Abstract: One of the most striking manifestations of instability in solid mechanics is the localization of shear strain into narrow bands during high speed, plastic deformations of metals. According to one theory, the formation of shear bands is attributed to effective strain-softening response, which results at high strain rates as the net outcome of the influence of thermal softening on the, normally, strain-hardening response of metals. Our objective is to review some of the insight obtained by applying nonlinear analysis techniques on simple models of nonlinear partial differential equations simulating this scenario for instability. First, we take up a simple system, intended as a paradigm, that describes isothermal shear deformations of a material exhibiting strain softening and strain-rate sensitivity. As it turns out, for moderate amounts of strain softening strain-rate sensitivity exerts a dissipative effect and stabilizes the motion. However, once a threshold is exceeded, the response becomes unstable and shear strain localization occurs. Next, we present extensions of these results to situations where explicit thermal effects are taken into account. 35 refs., 2 figs.

The Structure of Shear Bands in Idealized Granular Materials

Abstract: The structure of shear bands in granular materials was investigated by numerically simulating an idealized assembly of two-dimensional particles. Flexible stress-controlled boundaries were used instead of periodic boundaries to avoid constraining the motion of particles within the tested specimen. The particle displacement, particle rotations and rotations of the particle neighborhoods (macro-rotation) were examined within the shear band. The shear band width was found to decrease with axial strain from 18 and 15 times the average particle radius. The particle rotations and macro-rotations were concentrated inside the shear bands. The numerical simulations suggest that the particle rotations are induced by macro-rotations, and support the use of the micropolar theory for examining instable phenomena within granular materials. 18 refs., 6 figs.

Dynamics of laminated and fibrous composites

Abstract: In the present review investigation results are presented on the elastic wave propagation in laminated and fibrous unidirectional composite materials modeled by the piecewise-homogeneous medium (the structural model). In contrast to continual theories, the model of such a type does not essentially impose additional restrictions (other than those postulated by solid deformable body mechanics) on frequencies and gradients of the spatial alteration of the wave processes investigated. However, it should be stressed that, within the framework of this approach, it is necessary to solve complicated boundary-value or initial-boundary-value problems, which considerably complicate investigations in this area. Currently, regularly laminated materials are most thoroughly investigated. A detailed, comprehensive analysis is given of bulk, surface, and normal waves. The rule of selection, choice of modes, is formulated for piecewise-inhomogeneous spectra, the structure of the pass bands zones for bulk, shear and longitudinal–transverse waves is described with its dependence of the relative thickness and mechanical properties of layers, and vibration modes on transmission zone boundaries are determined. The theory of Love- and Rayleigh-type surface waves is presented. These waves may propagate in regularly laminated composites at frequencies corresponding to the stop band zones of bulk waves. A highly significant influence of the correspondence of the set of frequency and other composition properties to the pass band or stop band zones for bulk waves in the reflecting materials is noted on the reflection character of shear and longitudinal–transverse plane waves. The existence of frequency intervals and several incidence angles in the cases of the complete internal wave reflection is shown. Penetration of surface disturbances deep into the regularly laminated materials was investigated on plane cylindrical and spherical interface surfaces of properties. The character of the displacements and the stress attenuation is essentially different for pass band and stop band zones of bulk longitudinal and transverse waves in the medium with plane boundaries. Results are also presented for thermoelastic, magnetoelastic and electroelastic (acoustoelectric) waves. The application of the superposition principle and the summation theorems for cylindrical functions for unidirectional fibrous materials with regular packing allows us to construct formal solutions both for doubly periodic media and for the separately situated row of elastic inclusions with periodic location. Solutions of such a type may be extended to smooth inclusions of noncircular cylindrical form. In all cases boundary value problems are reduced to infinite systems of algebraic equations with complex coefficients containing cylindrical functions. For the row of periodically located fibers, the informal character of solutions is shown, and infinite systems of equations are investigated. Specific quantitative results are also obtained. The diffraction of shear and longitudinal-transverse waves on solid and hollow fibers was analyzed. In the discrete frequency spectrum, the existence of resonance effects of the Wood-anomaly type is shown. For shear waves on separately located inclusion, the influence of the noncircular fiber form on the stress distribution was investigated. The prospects for development of wave theory are pointed out within the framework of the structural composite model.

Stability of Fibrous Composites

Abstract: 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 continuingmore » 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. 78 refs., 20 figs., 11 tabs.« less

Instability of Gradient Dependent Viscoplastic Model for Clay Saturated With Water and FEM Analysis

Abstract: 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 elastoviscoplastic 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. 22 refs., 7 figs.

The Phenomenon of Shear Strain Localization in Dynamic Viscoplasticity

Abstract: 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. 41 refs., 4 figs., 6 tabs.

Effective stiffness of cracked elastic solids

Abstract: 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. 40 refs., 9 figs.