Linear Elasticity

Conventional methods for road and airport pavement analyses, such as BISAR and GAMES, were developed based on a cylindrical coordinate system. Because of the loading symmetry due to the assumption that a circular uniformly distributed load is acting on the pavement surface, it was useful to use a cylindrical coordinate system. However, depending on the magnitude of the tire load, several research reports on tire-pavement contact stresses have shown that the contact patch is predominantly rectangular and not circular in shape. Based on this observation and the fact that it may be difficult for most multi-layer linear elastic software packages to make use of the field measured tire-pavement contact stresses, which are rectangular in shape, this paper presents the development of a method for pavement structural analysis considering both uniform and non-uniform loads acting over a rectangular area. In this approach, three components of displacements, which satisfy Navier's equations, are expressed using Neuber-Papkovich functions.Worked examples for vertical and horizontal loads acting over rectangular area are presented in this paper. In order to verify the validity of the solutions obtained, the results are compared with those obtained from freeware GAMES software, which analyses loads acting over a circular area and is widely used in Japan and South Africa and a number of institutions in Australia, Europe and US.

Displacement profiles for isolated normal faults are most often triangular rather than semi-elliptical as predicted for linear elastic materials. Simple modelling indicates that triangular displacement profiles can arise from GutenbergeRichter earthquakes randomly distributed on fault surfaces of constant dimensions. Near-triangular profiles are generated after a small number of earthquake cycles and for earthquake magnitude ranges as small as 0.5. The results are only weakly dependent on the shape of earthquake slip profiles, and reproduce the geometry of displacement profiles on the non-propagating active Cape Egmont Fault in New Zealand. By contrast, growth models in which fault displacement and length increase in proportion result in unrealistic displacement profiles for realistic slip profiles irrespective of whether earthquake populations are Characteristic or GutenbergeRichter.

A problem of reflection and transmission of obliquely incident plane transverse wave at a plane interface between two porous elastic half-spaces in welded contact is investigated. The theory developed by Cowin and Nunziato [S.C. Cowin, J.W. Nunziato, Linear elastic materials with voids, Journal of Elasticity 13 (1983) 125-147] has been used to write down the equations of motion and constitutive relations for the elastic medium with voids. Potential method is used to obtain the reflection and transmission coefficients. It is found that these coefficients are functions of angle of incident, elastic constants, void parameters and that of the frequency of the incident wave. Numerical computations have been performed for a particular model and the results obtained are depicted graphically. The results of Ciarletta and Sumbatyan [M. Ciarletta, M.A. Sumbatyan, Reflection of plane waves by the free boundary of a porous elastic half-space, Journal of Sound and Vibration 259 (2) (2003) 253-264] have been reduced as a special case of the present formulation. The expression for the partition of energy at the interface during transmission and reflection of waves have also been presented.

The behavior of plane harmonic waves in a linear elastic material with voids is analyzed. There are two dilational waves in this theory, one is predominantly the dilational wave of classical linear elasticity and the other is predominantly a wave carrying a change in the void volume fraction. Both waves are found to attenuate in their direction of propagation, to be dispersive and dissipative. At large frequencies the predominantly elastic wave propagates with the classical elastic dilational wave speed, but at low frequencies it propagates at a speed less than the classical speed. It makes a smooth but relatively distinct transition between these wave speeds in a relatively narrow range of frequency, the same range of frequency in which the specific loss has a relatively sharp peak. Dispersion curves and graphs of specific loss are given for four particular, but hypothetical, materials, corresponding to four cases of the solution.

In this paper, a strategy for developing self-learning ®nite element codes is presented. At the heart of these codes is a neural network based constitutive model (NNCM). In contrast to the normal practice of training neural networks for constitutive models with the data from homogenous material tests, training is accomplished here with stresses and strains at certain calibrating points in tests on structures where the stress/strain states are not homogenous. This strategy has a distinct advantage since a considerable eort is devoted by the experimentalists to achieve as homogenous state of stress/strain as possible. In many situations this is impractical for many reasons such as the samples being too small, precious or may require expensive methods of preparation.

The present paper deals with the problem of the determination of the in-plane behavior of masonry material. The masonry is considered as a composite material composed by a regular distribution of blocks connected by horizontal and vertical mortar joints. The overall constitutive relationships of the regular masonry are derived by a rational micromechanical and homogenization procedure. Linear elastic constitutive relationship is considered for the blocks, while a new special nonlinear constitutive law is proposed for the mortar joints. In particular, a mortar constitutive law, which accounts for the coupling of the damage and friction phenomena occurring during the loading history, is proposed; the developed model is based on an original micromechanical analysis of the damage process of the mortar joint. Then, an effective nonlinear homogenization procedure, representing the main novelty of the paper, is proposed; it is based on the transformation field analysis, using the technique of the superposition of the effects and the finite element method. The presented methodology is implemented in a numerical code. Finally, numerical applications are performed in order to assess the performances of the proposed procedure in reproducing the mechanical behavior of masonry material.

... Reina Mercedes, Seville 41012, Spain (Received 23 January 1995; revised version received 13 February 1995; accepted 2 March 1995) A method to calculate the ... 1, we can express the kth layer as: ak(Zk) = Tk(Zk)hk(O) + Rk(Zk) (10) where matrix T and vector R are given in ...

The stress inversion method is developed to find a stress field which satisfies the equation of equilibrium for a body in a state of plane stress. When one stress-strain relation is known and data on the strain distribution on the body and traction along the boundary are provided, the method solves a well-posed problem, which is a linear boundary value problem for Airy's stress function, with the governing equation being the Poisson equation and the boundary conditions being of the Neumann type. The stress inversion method is applied to the Global Positioning System (GPS) array data of the Japanese Islands. The stress increment distribution, which is associated with the displacement increment measured by the GPS array, is computed, and it is found that the distribution is not uniform over the islands and that some regions have a relatively large increment. The elasticity inversion method is developed as an alternative to the stress inversion method; it is based on the assumption of linear elastic deformation with unknown elastic moduli and does not need boundary traction data, which are usually difficult to measure. This method is applied to the GPS array data of a small region in Japan to which the stress inversion method is not applicable. To cite this article: M. Hori et al., C. R. Mecanique 336 (2008). Résumé Méthode d'inversion des contraintes et analyse des données GPS. La méthode d'inversion est développée pour trouver un champ de contraintes satisfaisant les équations d'équilibre pour un corps en situation de contrainte plane. La relation entre contrainte et déformation étant connue et les données de distribution de déformation sur le corps et de traction sur le bord étant fournies, la méthode résout un problème bien posé, qui consiste en un problème aux limites linéaire pour la fonction de contrainte d'Airy, comprenant l'équation de Poisson et des conditions aux limites de type Neumann. La méthode d'inversion est appliquée aux données GPS (Global Positioning System) concernant les îles japonaises. Les incréments de contraintes associés aux incréments de déplacements mesurés par le système GPS sont calculés, et l'on trouve que leur distribution n'est pas uniforme sur les îles, certaines régions présentant un incrément relativement grand. La méthode d'inversion élastique est développée comme alternative à la méthode d'inversion des contraintes ; elle est fondée sur l'hypothèse d'une déformation linéaire élastique avec des coefficients d'élasticité inconnus, et ne requiert pas de données concernant les tractions au bord, généralement difficilement mesurables. La méthode est appliquée aux données GPS d'une petite région du Japon pour laquelle la méthode d'inversion des contraintes n'est pas utilisable. Pour citer cet article : M. Hori et al., C. R. Mecanique 336 (2008).

An automated structural design methodology has been devised which simultaneously considers design criteria associated with both linear elastic and crashworthiness loading conditions. This method is developed within the context of a nonlinear mathematical programming based structural optimization capability using an efficient two-phased crashworthiness analysis technique. Specially constructed nonlinear approximations for the crashworthiness constraints are employed to further reduce the computational burden during the optimization process. This methodology is demonstrated on an automobile structural design problem. It is shown that more mass efficient designs can be obtained by simultaneously considering elastic and crashworthiness design criteria as compared to a sequential approach in which the structure is first designed for the elastic loads and then modified to satisfy the crashworthiness criteria.

In the analysis and design of framed structures, the traditional methods are based on the simplified assumption that the joints are completely either pinned or rigid. However, the experimental investigations show that the frame connections present an intermediate behaviour between these two extreme cases. The present work is concerned with the dynamic elastic analysis of semi-rigid plane frames subjected to

The effect of different precracking methods on the results of linear elastic K Ic fracture toughness testing with medium-density polyethylene (MDPE) was investigated. Cryogenic conditions were imposed in order to obtain valid K Ic values from specimens of suitable size. Most conservative K Ic values were obtained by slow pressing a fresh razor blade at the notch root of the specimen. Due to the low deformation level imposed on the crack tip region, the slow pressing razor blade technique also produced less scatter in fracture toughness results. It has been shown that the slow stable crack growth preceding catastrophic brittle failure during K Ic tests in MDPE under cryogenic conditions should not be disregarded as it has relevant physical meaning and may affect the fracture toughness results.

The indentation of single crystals by a periodic array of flat rigid contacts is analyzed using discrete dislocation plasticity. Plane strain analyses are carried out with the dislocations all of edge character and modeled as line singularities in a linear elastic solid. The limiting cases of frictionless and perfectly sticking contacts are considered. The effects of contact size, dislocation source density, and dislocation obstacle density and strength on the evolution of the mean indentation pressure are explored, but the main focus is on contrasting the response of crystals having dislocation sources on the surface with that of crystals having dislocation sources in the bulk. When there are only bulk sources, the mean contact pressure for sufficiently large contacts is independent of the friction condition, whereas for sufficiently small contact sizes, there is a significant dependence on the friction condition. When there are only surface dislocation sources the mean contact pressure increases much more rapidly with indentation depth than when bulk sources are present and the mean contact pressure is very sensitive to the strength of the obstacles to dislocation glide. Also, on unloading a layer of tensile residual stress develops when surface dislocation sources dominate.

The first-order shear deformation plate theory can be used in the small strain and moderate rotation non-linear elasticity by defining correctly the displacement vector form. In this paper, the problem of the consistency between the displacement vector form and the finite strain tensor approximation is analysed. Then, a new moderate rotation theory is proposed. The variational form of the governing equations is derived for the beam and the plate problems in a consistent way. Then, an iterative numerical procedure based on the finite element method and the secant striffness matrix is developed in order to solve the non-linear differential equation problem. Computations are made for one-and two-dimensional structures, in order to assess the performance of the von Karman, finite elasticity, classical and the proposed moderate rotation theories.

In this paper we present an equilibrium model of commodity spot (s t ) and futures (f t ) prices, with finite elasticity of arbitrage services and convenience yields. By explicitly incorporating and modelling endogenously the convenience yield, our theoretical model is able to capture the existence of backwardation or contango in the long-run spot-futures equilibrium relationship, s t = β 2 f t + β 3 . When the slope of the cointegrating vector β 2 > 1(β 2 < 1) the market is under long run backwardation (contango). It is the first time in this literature in which the theoretical possibility of finding a cointegrating vector different from the standard β 2 = 1 is formally considered.

The elastic moduli of single layer graphene sheet (SLGS) have been a subject of intensive research in recent years. Calculations of these effective properties range from molecular dynamic simulations to use of structural mechanical models. On the basis of mathematical models and calculation methods, several different results have been obtained and these are available in the literature. Existing mechanical models employ Euler-Bernoulli beams rigidly jointed to the lattice atoms. In this paper we propose truss-type analytical models and an approach based on cellular material mechanics theory to describe the in-plane linear elastic properties of the single layer graphene sheets. In the cellular material model, the C-C bonds are represented by equivalent mechanical beams having full stretching, hinging, bending and deep shear beam deformation mechanisms. Closed form expressions for Young's modulus, the shear modulus and Poisson's ratio for the graphene sheets are derived in terms of the equivalent mechanical C-C bond properties. The models presented provide not only quantitative information about the mechanical properties of SLGS, but also insight into the equivalent mechanical deformation mechanisms when the SLGS undergoes small strain uniaxial and pure shear loading. The analytical and numerical results from finite element simulations show good agreement with existing numerical values in the open literature. A peculiar marked auxetic behaviour for the C-C bonds is identified for single graphene sheets under pure shear loading.

A semi-analytical analysis for the transient elastodynamic response of an arbitrarily thick simply supported beam due to the action of an arbitrary moving transverse load is presented, based on the linear theory of elasticity. The solution of the problem is derived by means of the powerful state space technique in conjunction with the Laplace transformation with respect to the time coordinate. The inversion of Laplace transform has been carried out numerically using Durbin’s approach based on Fourier series expansion. Special convergence enhancement techniques are invoked to completely eradicate spurious oscillations and obtain uniformly convergent solutions. Detailed numerical results for the transient vibratory responses of concrete beams of selected thickness parameters are obtained and compared for three types of harmonic moving concentrated loads: accelerated, decelerated and uniform. The effects of the load velocity, pulsation frequency and beam aspect ratio on the dynamic response are examined. Also, comparisons are made against solutions based on Euler–Bernoulli and Timoshenko beam models. Limiting cases are considered, and the validity of the model is established by comparison with the solutions available in the existing literature as well as with the aid of a commercial finite element package.

The present paper presents a novel finite element formulation for static analysis of linear elastic spatial frame structures extending the formulation given by Simo and Vu-Quoc [A geometrically-exact rod model incorporating shear and torsion-warping deformation, Int. J. Solids Structures 27 (3) (1991) 371-3931, along the lines of the work on the planar beam theory presented by Saje [A variational principle for finite planar deformation of straight slender elastic beams, Internat. J. Solids and Structures * Corresponding author. 0045-7825/95/$09.50 0 1995 Elsevier Science S.A. All rights reserved SSDI 0045-7825(94)00056-S 132 G. JeleniC, M. Saje I Comput. Methods Appl. Mech. Engrg. 120 (1995) 131-161

In this chapter we consider reduced basis (RB) approximation and a posteriori error estimation for linear functional outputs of affinely parametrized linear parabolic partial differential equations. The essential ingredients are Galerkin projection onto a low-dimensional space associated with a smooth parametrically induced manifolddimension reduction; efficient and effective POD-Greedy RB sampling methods for identification of optimal and numerically stable approximations spaces -rapid convergence; rigorous and sharp a posteriori error bounds for the linear-functional outputs of interest -certainty; and Offline-Online computational decomposition strategies -minimum marginal cost. The RB approach is effective in the real-time context in which the expensive Offline stage is deemed unimportant -for example parameter estimation and control; the RB approach is also effective in the many-query context in which the expensive Offline stage is asymptotically negligible -for example design

The aim of this paper is to give the title theory of shearable plates a precise and exact position with respect to three-dimensional linear elasticity. We assume that the Reissner-Mindlin representation of the displacement field hold in a 3-D body in the shape of a plate, and discuss how a constitutive response consistent with such a representation should be chosen. We find that the Reissner-Mindlin plate theory results from mere integration over the thickness of the equilibrium equations of a cylindrical body made of a linearly elastic material which is both transversely inextensible and transversely isotropic.

This article presents the state of the art in passive devices for enhancing limb movement in people with neuromuscular disabilities. Both upper-and lower-limb projects and devices are described. Special emphasis is placed on a passive functional upper-limb orthosis called the Wilmington Robotic Exoskeleton (WREX). The development and testing of the WREX with children with limited arm strength are described. The exoskeleton has two links and 4 degrees of freedom. It uses linear elastic elements that balance the effects of gravity in three dimensions. The experiences of five children with arthrogryposis who used the WREX are described.

This study proposes a new method to determine the mechanical properties of human skin by the use of the indentation test [Pailler-Mattei, 2004. Caractérisation mécanique et tribologique de la peau humaine in vivo, Ph.D. Thesis, ECL-no. 2004-31; Pailler-Mattei, Zahouani, 2004. Journal of Adhesion Science and Technology 18, 1739-1758]. The principle of the measurements consists in applying an in vivo compressive stress [Zhang et al., 1994. Proceedings of the Institution of Mechanical Engineers 208, 217-222; Bosboom et al., 2001. Journal of Biomechanics 34, 1365-1368; Oomens et al., 1984. Selected Proceedings of Meetings of European Society of Biomechanics, pp. 227-232; Oomens et al., 1987. Journal of Biomechanics 20(9), 877-885] on the skin tissue of an individual's forearm. These measurements show an increase in the normal contact force as a function of the indentation depth. The interpretation of such results usually requires a long and tedious phenomenological study. We propose a new method to determine the mechanical parameters which control the response of skin tissue. This method is threefold: experimental, numerical, and comparative. It consists combining experimental results with a numerical finite elements model in order to find out the required parameters. This process uses a scheme of extended Kalman filters (EKF) [Gu et al., 2003. Materials Science and Engineering A345, 223-233; Nakamura et al., 2000. Acta Mater 48, 4293-4306; Leustean and Rosu, 2003. Certifying Kalman filters. RIACS Technical Report 03.02, 27pp. http://gureni.cs.uiuc.edu/~grosu/download/luta + leo.pdf; Welch and Bishop, An introduction to Kalman filter, University of North Carolina at Chapel Hill, 16p. http://www.cs.unc.edu/~welch/kalman/]. The first results presented in this study correspond to a simplified numerical modeling of the global system. The skin is assumed to be a semi-infinite layer with an isotropic linear elastic mechanical behavior [Zhang et al., 1994. Proceedings of the Institution of Mechanical Engineers 208, 217-222] This analysis will be extended to more realistic models in further works.

In this paper the results of 2D FE analyses of the seismic ground response of a clayey deposit, performed adopting linear visco-elastic and visco-elasto-plastic constitutive models, are presented. The viscous and linear elastic parameters are selected according to a novel calibration strategy, leading to FE results comparable to those obtained by 1D equivalent-linear visco-elastic frequency-domain analyses. The influence of plasticity on the numerical results is also investigated, with particular reference to the relation between the hysteretic and viscous damping effects. Finally, different boundary conditions, spatial discretisation and time integration parameters are considered and their role on the FE results discussed.

A linear theory of elastic materials with voids is presented. This theory differs significantly from classical linear elasticity in that the volume fraction corresponding to the void volume is taken as an independent kinematical variable. Following a discussion of the basic equations, boundary-value problems are formulated, and uniqueness and weak stability are established for the mixed problem. Then, several applications of the theory are considered, including the response to homogeneous deformations, pure bending of a beam, and small-amplitude acoustic waves. In each of these applications, the change in void volume induced by the deformation is determined. In the final section of the paper, the relationship between the theory presented and the effective moduli approach for porous materials is discussed.

This paper presents a finite element program, for the modelling of rutting of flexible pavements. In its present version, the program incorporates a permanent deformation model for unbound granular materials based on the concept of the shakedown theory developed by Zarka for metallic structures under cyclic loadings and has been used to estimate the permanent deformations of unbound granular materials (UGM) subjected to traffic loading. The calculation is performed in two steps: the first step consists in modelling the resilient behaviour of the pavement in 3D, using non-linear elastic models, to determine the stress field in the pavement. Then stress paths are derived and used to calculate the permanent deformations and the displacements, using a Drucker-Prager yield surface. An application to the prediction of the permanent deformations of experimental pavements with an unbound granular base, tested on the LCPC pavement testing facility is presented.

This is the second paper in a series of three papers generated from a recent study on crack-opening-area analysis of circumferentially cracked pipes for leak-before-break applications. This paper (Part II-Model Validations) focuses on the evaluation of current analytical models, discussed in the first paper (Part I-Analytical Models) as well as finite element models for conducting crack-opening-area analyses of pipes with circumferential through-wall cracks. The evaluation was performed by direct comparisons of the predicted results with the test data from full-scale pipe fracture experiments. The results from 25 full-scale pipe fracture experiments, conducted in the Degraded Piping Program, the International Piping Integrity Research Group Program and the Short Cracks in Piping and Piping Welds Program, were used to verify the analytical models. The main objective was the evaluation of engineering analysis procedures (estimation methods) as well as the ability of the finite element method to predict crack-opening displacements and shapes in pipes with circumferential through-wall cracks. Statistics were developed to quantify the accuracy of the current predictive models. A wide variety of pipe fracture tests involving cracks in base metals, weld metals and bimetallic weld metals were analyzed. Pipes containing both simple through-wall cracks and complex cracks were evaluated. ᭧ 1998 Elsevier Science Ltd. All rights reserved 1. the GE/EPRI method [2-4]; 2. the Paris/Tada method [5]; 3. the LBB.NRC method; [6] 4. the LBB.ENG2 method [7-9]; 5. the LBB.ENG3 method [10-12].

A technique for finding the stiffnesses and shear flows in multi-cell thin-walled girders subjected to linear elastic torsion is proposed. The girder is thought as the superposition of elementary closed tracks, just like open girders are the juxtaposition of thin strips. For each track there is a uniform value of the stress flow function, found by means of a linear system of compatibility equations resembling those for the redundant reactions in statically indeterminate frames. The connection between the proposed approach and fundamental properties of graphs is discussed; the advantages with respect to the standard procedures are also enlightened referring to two sample cross-sections.

PROBLEMS LUCA PLACIDI (ABSTRACT) We use the semi-inverse method to solve a St. Venant and an Almansi-Michell problem for a prismatic body made of a homogeneous and isotropic elastic material that is stress free in the reference configuration. In the St. Venant problem, only the end faces of the prismatic body are loaded by a set of self-equilibrated forces. In the Almansi-Michell problem self equilibrated surface tractions are also applied on the mantle of the body. The St. Venant problem is also analyzed for the following two cases: (i) the reference configuration is subjected to a hydrostatic pressure, and (ii) stress-strain relations contain terms that are quadratic in displacement gradients. The Signorini method is also used to analyze the St. Venant problem. Both for the St. Venant and the Almansi-Michell problems, the solution of the three dimensional problem is reduced to that of solving a sequence of two dimensional problems. For the St. Venant problem involving a second-order elastic material, the first order deformation is assumed to be an infinitesi-mal twist. In the solution of the Almansi-Michell problem, surface tractions on the mantle of the cylindrical body are expressed as a polynomial in the axial coordinate. When solving the problem by the semi-inverse method, displacements are also expressed as a polynomial in the axial coordinate. An explicit solution is obtained for a hollow circular cylindrical body with surface tractions on the mantle given by an affine function of the axial coordinate iii

This paper presents the theorem proposed by Luigi Federico Menabrea to study linear elastic redundant systems. Some of Menabrea's papers on the subject are examined, as well as the criticism and the corrections brought to his first proof. We consider Menabrea's work in the frame of the studies of his contemporaries; we try to provide a historical and epistemological background for Menabrea's theorem and for its consequences in modern mechanics.

In this paper, the most critical physical properties for the greenhouse covering materials are reviewed. The physical properties considered include the radiometric properties (transmissivity, re#ectivity and absorptivity) over several radiation bands and also the K-value (the overall heat transfer coe$cient). Only a few standard methods for testing these physical properties of covering materials for greenhouses exist. Usually, some of the testing methods used for plastics in general, are also applied to greenhouse covers despite important functional di!erences. These testing methods are reviewed with regard to their suitability for application to greenhouse covering materials. Also, reported values of the most important physical properties of greenhouse covering materials are presented and reviewed. The values presented are found to vary considerably among the materials considered. These variations are attributed mainly to the testing method employed and also to the type of the material. Existing testing methods are used arbitrarily and technical information is presented in a rather confusing way. Modi"cation of existing testing methods is required because, in most cases, they are insu$cient for greenhouse covering materials. Also new testing methods should be elaborated, and specially designed for greenhouse covering materials.

This paper presents a newly developed design method for non-encased and encased 27 stone columns. The developed analytical closed form solution is based on previous 28 solutions, initially developed for non-encased columns and for non-dilating rigid-plastic 29 column material. In the present method, the initial stresses in the soil/column are taken 30 into account, with the column considered as an elasto-plastic material with constant 31 dilatancy, the soil as an elastic material and the geosynthetic encasement as a linear-32 elastic material. To check the validity of the assumptions and the ability of the method 33 to give reasonable predictions of settlements, stresses and encasement forces, 34 comparative elasto-plastic finite element analyses have been performed. The agreement 35 between the two methods is very good, which was the reason that the new method was 36 used to generate a parametric study in order to investigate various parameters, such as 37 soil/column parameters, replacement ratio, load level and geosynthetic encasement 38 stiffness on the behaviour of the improved ground. The results of this study show the 39 influence of key parameters and provide a basis for the rational predictions of settlement 40 response for various encasement stiffnesses, column arrangements and load levels. The 41 practical use of the method is illustrated through the design chart, which enables 42 preliminary selection of column spacing and encasement stiffness to achieve the desired 43 settlement reduction for the selected set of the soil/column parameters. 44 45

This paper presents extensive test results of linear elastic mechanical properties of Nomex paper and Nomex honeycomb structures. The fundamental mechanical properties of the Nomex paper are then used in the finite element modeling and analysis of Nomex honeycomb structures. The finite element results are then compared with the experimental results and with the results using the well known theory from Gibson and Ashby [Gibson LJ, Ashby MF. Cellular solids: structures & properties. Pergamon Press; 1988]. Size effects are observed for the moduli of Nomex honeycombs.

We consider the two and three-dimensional system of linear thermoelasticity in a bounded smooth domain with Dirichlet boundary conditions. We analyze whether the energy of solutions decays exponentially uniformly to zero as t->∞ . First of all, by a decoupling method, we reduce the problem to an observability inequality for the Lamé system in linear elasticity and more precisely to whether the total energy of the solutions can be estimated in terms of the energy concentrated on its longitudinal component. We show that when the domain is convex, the decay rate is never uniform. In fact, the lack of uniform decay holds in a more general class of domains in which there exist rays of geometric optics of arbitrarily large length that are always reflected perpendicularly or almost tangentially on the boundary. We also show that, in three space dimensions, the lack of uniform decay may also be due to a critical polarization of the energy on the transversal component of the displacement. In two space dimensions we prove a sufficient (and almost necessary) condition for the uniform decay to hold in terms of the propagation of the transversal characteristic rays, under the further assumption that the boundary of the domain does not have contacts of infinite order with its tangents. We also give an example, due to D. Hulin, in which these geometric properties hold. In three space dimensions we indicate (without proof) how a careful analysis of the polarization of singularities may lead to sharp sufficient conditions for the uniform decay to hold. In two space dimensions we prove that smooth solutions decay polynomially in the energy space to a finite-dimensional subspace of solutions except when the domain is a ball or an annulus. Finally we discuss some closely related controllability and spectral issues.

This article is devoted to some inverse problems arising in the context of linear elasticity, namely the identification of distributions of elastic moduli, model parameters, or buried objects such as cracks. These inverse problems are considered mainly for threedimensional elastic media under equilibrium or dynamical conditions, and also for thin elastic plates. The main goal is to overview some recent results, in an effort to bridge the gap between studies of a mathematical nature and problems defined from engineering practice. Accordingly, emphasis is given to formulations and solution techniques which are well suited to general-purpose numerical methods for solving elasticity problems on complex configurations, in particular the finite element method and the boundary element method. An underlying thread of the discussion is the fact that useful tools for the formulation, analysis and solution of inverse problems arising in linear elasticity, namely the reciprocity gap and the error in constitutive equation, stem from variational and virtual work principles, i.e. fundamental principles governing the mechanics of deformable solid continua. In addition, the virtual work principle is shown to be instrumental for establishing computationally efficient formulae for parameter or geometrical sensitivity, based on the adjoint solution method. Sensitivity formulae are presented for various situations, especially in connection with contact mechanics, cavity and crack shape perturbations, thus enriching the already extensive known repertoire of such results. Finally, the concept of topological derivative and its implementation for the identification of cavities or inclusions are expounded.

Usually the notion ''Newton-Raphson method'' is used in the context of non-linear finite element analysis based on quasi-static problems in solid mechanics. It is pointed out that this is only true in the case of non-linear elasticity. In the case of constitutive equations of evolutionary-type, like in viscoelasticity, viscoplasticity or elastoplasticity, the ''Multilevel-Newton algorithm'' is usually applied yielding the notions of global and local level (iteration), as well as the consistent tangent operator. In this paper, we investigate the effects of a consistent application of the classical Newton-Raphson method in connection with the finite element method, and compare it with the classical Multilevel-Newton algorithm. Furthermore, an improved version of the Multilevel-Newton method is applied.

In this paper shear correction factors for arbitrary shaped beam crosssections are calculated. Based on the equations of linear elasticity and further assumptions for the stress field the boundary value problem and a variational formulation are developed. The shear stresses are obtained from derivatives of the warping function. The developed element formulation can easily be implemented in a standard finite element program. Continuity conditions which occur for multiple connected domains are automatically fulfilled.

A computational methodology is proposed for fatigue damage assessment of metallic automotive components and its application is presented with numerical simulations of wheel radial fatigue tests. The technique is based on the local strain approach in conjunction with linear elastic FE stress analyses. The stress-strain response at a material point is computed with a cyclic plasticity model coupled with a notch stress-strain approximation scheme. Critical plane damage parameters are used in the characterization of fatigue damage under multiaxial loading conditions. All computational modules are implemented into a software tool and used in the simulation of radial fatigue tests of a disk-type truck wheel. In numerical models, the wheel rotation is included with a nonproportional cyclic loading history, and dynamic effects due to wheel-tire interaction are neglected. The fatigue lives and potential crack locations are predicted using effective strain, Smith-Watson-Topper and Fatemi-Socie parameters using computed stress-strain histories. Three-different test conditions are simulated, and both number of test cycles and crack initiation sites are estimated. Comparisons with the actual tests proved the applicability of the proposed approach.