Showing papers in "European Journal of Mechanics A-solids in 2007"

Mode coupling instability in friction-induced vibrations and its dependency on system parameters including damping

Abstract: Friction-induced vibrations due to coupling modes can cause severe damage and are recognized as one of the most serious problems in industry. In order to avoid these problems, engineers must find a design to reduce or to eliminate mode coupling instabilities in braking systems. Though many researchers have studied the problem of friction-induced vibrations with experimental, analytical and numerical approaches, the effects of system parameters, and more particularly damping, on changes in stable-unstable regions and limit cycle amplitudes are not yet fully understood. The goal of this study is to propose a simple non-linear two-degree-of-freedom system with friction in order to examine the effects of damping on mode coupling instability. By determining eigenvalues of the linearized system and by obtaining the analytical expressions of the Routh-Hurwitz criterion, we will study the stability of the mechanical system's static solution and the evolution of the Hopf bifurcation point as functions of the structural damping and system parameters. It will be demonstrated that the effects of damping on mode coupling instability must be taken into account to avoid design errors. The results indicate that there exists, in some cases, an optimal structural damping ratio between the stable and unstable modes which decreases the unstable region. We also compare the evolution of the limit cycle amplitudes with structural damping and demonstrate that the stable or unstable dynamic behaviour of the coupled modes are completely dependent on structural damping.

Two-dimensional sliding frictional contact of functionally graded materials

Abstract: A multi-layered model for sliding frictional contact analysis of functionally graded materials (FGMs) with arbitrarily varying shear modulus under plane strain-state deformation has been developed. Based on the fact that an arbitrary curve can be approached by a series of continuous but piecewise linear curves, the FGM is divided into several sub-layers and in each sub-layers the shear modulus is assumed to be a linear function while the Poisson's ratio is assumed to be a constant. In the contact area, it is assumed that the friction is one of Coulomb type. With this model the fundamental solutions for concentrated forces acting perpendicular and parallel to the FGMs layer surface are obtained. Then the sliding frictional contact problem of a functionally graded coated half-space is investigated. The transfer matrix method and Fourier integral transform technique are employed to cast the problem to a Cauchy singular integral equation. The contact stresses and contact area are calculated for various moving stamps by solving the equations numerically. The results show that appropriate gradual variation of the shear modulus can significantly alter the stresses in the contact zone.

A non-linear study of a cracked rotor

Abstract: The influence of the presence of transverse cracks in a rotating shaft is analyzed. The paper addresses the influence of crack opening and closing on dynamic response during operation. The evolution of the orbit of the cracked rotor near half and one-third of the first critical speed is investigated. The dynamic response of the rotor with a breathing crack is evaluated by expanding the changing stiffness of the crack as a truncated Fourier series and then using the Harmonic Balance Method. This method is applied to compute various parametric studies including the effects of the crack depth and location on the dynamic of a crack rotor. The evolution of the first critical speed, associated amplitudes at the critical speed and half of the critical speed, and the resulting orbits during transient operation are presented and some distinguishing features of a cracked rotor are examined.

Qualitative analysis of forced response of blisks with friction ring dampers

Abstract: A damping strategy for blisks (integrally bladed disks) of turbomachinery involving a friction ring is investigated. These rings, located in grooves underside the wheel of the blisks, are held in contact by centrifugal loads and the energy is dissipated when relative motions between the ring and the disk occur. A representative lumped parameter model of the system is introduced and the steady-state nonlinear response is derived using a multi-harmonic balance method combined with an AFT procedure where the friction force is calculated in the time domain. Numerical simulations are presented for several damper characteristics and several excitation configurations. From these results, the performance of this damping strategy is discussed and some design guidelines are given.

Structural synthesis of fully-isotropic parallel robots with Schönflies motions via theory of linear transformations and evolutionary morphology

Abstract: The paper presents structural synthesis of fully-isotropic parallel robotic manipulators (PMs) with Schonflies motions. The moving platform of a parallel manipulator with Schonflies motions (PMSM) has four degrees of freedom, which are three independent translations and one rotation about an axis of fixed direction. A method is proposed for structural synthesis of fully-isotropic PMSMs based on the theory of linear transformations and the evolutionary morphology. A one-to-one correspondence exists between the actuated joint velocity space and the external velocity space of the moving platform. The Jacobian matrix mapping the two vector spaces of fully-isotropic PMSMs presented in this paper is the identity 4 × 4 matrix throughout the entire workspace. The condition number and the determinant of the Jacobian matrix being equal to one, the manipulator performs very well with regard to force and motion transmission capabilities. The synthesis method proposed in this paper allows us to obtain structural solutions of PMSMs with decoupled and uncoupled motions, along with the fully-isotropic solutions in a systematic manner. Overconstrained/isostatic solutions with elementary/complex and identical/different legs are obtained. Uncoupled and fully-isotropic PMSMs have the advantage of simple command and important energy-saving due to the fact that, for a unidirectional motion, only one motor works as in a serial translational manipulator.

Euler-Bernoulli beams with multiple singularities in the flexural stiffness

Abstract: Euler–Bernoulli beams under static loads in presence of discontinuities in the curvature and in the slope functions are the object of this study. Both types of discontinuities are modelled as singularities, superimposed to a uniform flexural stiffness, by making use of distributions such as unit step and Dirac's delta functions. A non-trivial generalisation to multiple different singularities of an integration procedure recently proposed by the authors for a single singularity is presented in this paper. The proposed integration procedure leads to closed form solutions, dependent on boundary conditions only, which do not require enforcement of continuity conditions along the beam span. It is however shown how, from the solution of the clamped-clamped beam, by considering suitable singularities at boundaries in the flexural stiffness model, responses concerning several boundary conditions can be recovered. Furthermore, solutions in terms of deflection of the beam are obtained for imposed displacements at boundaries providing the so called shape functions. The above mentioned shape functions can be adopted to insert beams with singularities as frame elements in a finite element discretisation of a frame structure. Explicit expressions of the element stiffness matrix are provided for beam elements with multiple singularities and the reduction of degrees of freedom with respect to classical finite element procedures is shown. Extension of the proposed procedure to beams with axial displacement and vertical deflection discontinuities is also presented.

A cohesive zone model with a large displacement formulation accounting for interfacial fibrilation

Abstract: Interfacial fibrilation is a typical mechanism that frequently occurs during delamination of a polymer coating from a steel substrate. It involves large displacements at the interface as well as large deformations in the bulk material. Classical small displacement cohesive zone formulations fail to describe such large deformations correctly. Therefore, a generic cohesive zone model is introduced that is suitable to describe both uniform and non-uniform fracture at an interface with large deformations in the delaminating bulk and large displacements at the crack tip.

A strain gradient crystal plasticity analysis of grain size effects in polycrystals

Abstract: The influence of grain size on yield and flow stress in polycrystalline metals is analyzed using a strain gradient crystal plasticity theory with an internal material length scale. The numerical solutions are obtained with the finite element method considering a polycrystal modeled by 40 individually oriented grains in a unit cell, each having three planar slip systems. An energy potential that penalizes crystallographic slip at grain boundaries is included in the analyzes. The polycrystal is subjected to plane strain tension for various grain sizes and higher order boundary conditions at the grain boundaries. An increase in flow stress with decreasing grain size, d, was obtained on the form d−n, with n in the range 0.82 to 1.25 at initial yield and in the range 0.77 to 1.09 after 0.1 logarithmic strain.

Contact analysis of a flexible bladed-rotor

Abstract: This paper presents a model of fully flexible bladed rotor developed in the rotating frame. An energetic method is used to obtain the matrix equations of the dynamic behaviour of the system. The gyroscopic effects as well as the spin softening effects and the centrifugal stiffening effects, taken into account through a pre-stressed potential, are included in the model. In the rotating frame, the eigenvalues' imaginary parts of the latter matrix equation give the Campbell diagram of the system and its stability can be analysed through its associated eigenvalues' real parts. The turbo machine casing is also modelled by an elastic ring in the rotating frame through an energetic method. Thus, in some rotational speed ranges the contact problem between the rotor and the stator can be treated as a static problem since both structures are stationary to each other. Prior to the study of the complete problem of contact between the flexible blades of the rotor and the flexible casing, a simple model of an elastic ring having only one mode shape, excited by rotating loads is developed in the rotating frame too, in order to underline divergence instabilities and mode couplings. Then, the complete problem of frictionless sliding contact between the blades and the casing, without rubbing, is studied. The stable balanced static contact configurations of the structure are found as function of the rotational speed of the rotor. Finally, the results are compared to these of the simple model of rotating spring-masses on an elastic ring, showing good adequacy. The present model of rotor appears thus particularly adapted to the study of blades-casing contacts and highlighted an unstable phenomenon near the stator critical speed even in case of frictionless sliding.

The effect of the interface conditions on the dynamic response of a beam on a half-space to a moving load

Abstract: The classical model of a beam on elastic half-space is adopted as a benchmark model to study the response of a slab–track railway system to dynamic train loading. The focus of the investigation is placed on the effect of the description of the interface between the beam and the half-space on the dynamic response of the track and surrounding soil. Three conventional approaches to this description are addressed, the first two of which are simplified. According to the first approach, tractions are assumed to be uniformly distributed beneath the beam cross-section, whereas the continuity of the beam and half-space displacements is required only along the centre line of the beam. In the second approach, the stresses are still considered to be uniformly distributed across the beam, whereas the continuity is required between the beam displacement and the average displacement of the half-space under the beam. The third approach is the classical approach of contact mechanics, according to which a traction variation across the beam interface is accounted for, whereas the displacements of the half-space are assumed constant under the beam (no torsion is considered). A comparative analysis is carried out of the equivalent dynamic stiffness of the half-space under the beam and the steady-state track and soil response to moving constant and harmonic loads. On the basis of this comparison, applicability domains are established of the three respective interface descriptions.

Two scale damage model and related numerical issues for thermo-mechanical High Cycle Fatigue

Abstract: On the idea that fatigue damage is localized at the microscopic scale, a scale smaller than the mesoscopic one of the Representative Volume Element (RVE), a three-dimensional two scale damage model has been proposed for High Cycle Fatigue applications. It is extended here to anisothermal cases and then to thermo-mechanical fatigue. The modeling consists in the micromechanics analysis of a weak micro-inclusion subjected to plasticity and damage embedded in an elastic meso-element (the RVE of continuum mechanics). The consideration of plasticity coupled with damage equations at microscale, altogether with Eshelby–Kroner localization law, allows to compute the value of microscopic damage up to failure for any kind of loading, 1D or 3D, cyclic or random, isothermal or anisothermal, mechanical, thermal or thermo-mechanical. A robust numerical scheme is proposed in order to make the computations fast. A post-processor for damage and fatigue (DAMAGE_2005) has been developed. It applies to complex thermo-mechanical loadings. Examples of the representation by the two scale damage model of physical phenomena related to High Cycle Fatigue are given such as the mean stress effect, the non-linear accumulation of damage. Examples of thermal and thermo-mechanical fatigue as well as complex applications on real size testing structure subjected to thermo-mechanical fatigue are detailed.

The effect of temperature and moisture content on the mechanical behaviour of wood: a comprehensive model applied to drying and bending

Abstract: This paper proposes a model able to simulate heat and mass transfer and mechanical behaviour of a wooden board during processing. The coupled heat and mass transfer equations are solved using an existing computational model named TransPore. From the moisture content and temperature profiles, a rigorous one-dimensional formulation and a relevant constitutive model are used to calculate the stress and strain evolution within the board due to shrinkage or external loading. This allows a fast, comprehensive and realistic model to be implemented. Used as a tool, it allowed us to gain new insights into industrial operations: – the post-drying storage stage instead of the drying operation by itself is responsible for the high risk of checking encountered when drying thick boards; – the hydro-thermal activation is of utmost importance in wood bending and subsequent shape freezing.

Strain-gradient elastic-plastic material models and assessment of the higher order boundary conditions

Abstract: A gradient elastic material model exhibiting gradient kinematic and isotropic hardening is addressed within a thermodynamic framework suitable to cope with nonlocal-type continua. The Clausius–Duhem inequality is used, in conjunction with the concepts of energy residual, insulation condition and locality recovery condition, to derive all the pertinent restrictions upon the constitutive equations, including the PDEs and the related higher order (HO) boundary conditions that govern the gradient material behaviour. Through a suitable limiting procedure, the HO boundary conditions are shown to interpret the action, upon the body's boundary surface, of idealized extra HO constraints capable to impede the onset of strain as a nonlocality source and to react with a double traction (of dimension moment/area), work-conjugate of the impeded strain. The HO boundary conditions for the internal moving elastic/plastic boundary are also provided. A number of variational principles are proved. A few simple illustrative numerical examples are worked out.

A random-profile approach for trajectory planning of wheeled mobile robots

Abstract: We present a random-profile approach to treat the optimal free-trajectory planning problem for nonholonomic wheeled mobile robots subjected to move in a constrained workspace. This versatile method is based on a simultaneous search for the robot path and for the time evolution on this path. It handles obstacle avoidance issues while considering kinodynamic constraints (bounded velocities, accelerations and torques). It may be applied to treat problems with various forms of optimization criteria involving travel time, efforts and power. Numerical results, obtained via the simulated-annealing technique of optimization, are presented for two- and three-wheel mobile robots and are compared to those available in the literature.

Magnetoelectroelastic analysis for an opening crack in a piezoelectromagnetic solid

Abstract: Magnetoelectroelastic analysis of a cracked piezoelectromagnetic solid is made within the framework of the theory of linear magnetoelectroelasticity. The associated mixed boundary-value problem is solved by the Fourier integral transform. For general electromagnetic crack-face boundary conditions, a full magnetoelectroelastic field in the entire plane induced by a crack is obtained explicitly, and field intensity factors and energy release rate are given. The influences of applied electric and magnetic loadings on the energy release rate, the strain intensity factor, and the stress distribution are presented graphically.

Bounds and estimates for the effective yield surface of porous media with a uniform or a nonuniform distribution of voids

Abstract: This paper aims at studying the effects of a nonuniform distribution of voids on the macroscopic yield response of porous media with a rigid-perfectly plastic matrix. For this purpose, a semi-analytical model, recently proposed by Bilger et al. [Bilger, N., Auslender, F., Bornert, M., Masson, R., 2002. New bounds and estimates for porous media with rigid perfectly plastic matrix. C. R. Mecanique 330, 127–132], is extended to more general situations where the local porosity can fluctuate. The microstructure is described by a generalized Hashin-type assemblage of hollow spheres and the distribution of the local porosity is obtained from a three-dimensional simulated microstructure. The matrix layer around the voids is discretized into concentric sub-layers so as to take better into account the plasticity gradient along the radial direction. Classical homogenization techniques then provide new self-consistent estimates and upper bounds for the macroscopic yield surface. These results are compared first to the predictions of the Gurson model and its extensions and then to numerical results derived from three-dimensional Fast Fourier Transform (FFT) calculations carried out with the same material porosity distribution. A good agreement is obtained with the three-dimensional FFT calculations and with Gurson–Tvergaard's predictions even for high triaxiality and without fitting any parameter. Nevertheless, when the heterogeneous distribution of voids tends to form clusters, the proposed model fails to capture the properties of the macroscopic yield surface for large triaxiality factors.

Distributed piezoelectric actuation of a bistable buckled beam

Abstract: Bistable structures, such as buckled beams or plates, are characterized by a two-well potential. Their nonlinear properties are currently exploited in actuators design (e.g. MEMS micropumps, switches, memory cells) to produce relatively high displacements and forces with low actuation energies. We investigate the use of distributed multiparameter actuation to control the buckling and postbuckling behavior of a three-layer piezoelectric beam pinned at either end. A two-parameter bending actuation controls the transversal motion, whilst an axial actuation and a beam end-shortening modulate the tangent bending stiffness. The postbuckling behavior is studied by reducing to a 2 dof system a nonlinear extensible elastica model. When the bending actuation is spatially symmetric, the postbuckling phenomena are analogue to those obtained for a transversal midspan force, being characterized by a snap-through instability. The use of a two-parameter actuation opens new transition scenarios, where it is possible to get true quasi-static transitions between the two specular equilibria of the buckled beam, without any instability phenomenon. The efficiencies of these different transition paths are discussed in terms of energetic requirements and stability properties. A numerical example shows the technical feasibility of the proposed actuation technique.

A numerical model for non-linear dynamic analysis of slender masonry structures

Abstract: A numerical model is presented to enable performing non-linear dynamic analysis of slender masonry structures and elements, such as towers and columns or masonry walls in out-of-plane flexure Such structures are represented via a continuous one-dimensional model The main mechanical characteristics of the material in all sections along the height of such structures are taken into account by means of a non-linear elastic constitutive law formulated in terms of generalized stress and strain, under the assumption that the material has no resistance to tension and limited compressive strength The relations defined herein for the general case of hollow rectangular cross-sections are also aimed at enabling study of towers, bell-towers and similar slender structures

Dynamic fracture behaviors of cracks in a functionally graded magneto-electro-elastic plate

Abstract: In this paper the dynamic anti-plane problem for a functionally graded magneto-electro-elastic plate containing an internal or an edge crack parallel to the graded direction is investigated. The crack is assumed to be magneto-electrically impermeable. Integral transforms and dislocation density functions are employed to reduce the problem to Cauchy singular integral equations. Field intensity factors and energy release rate are derived, analyzed and partially calculated numerically. The effects of material graded index, loading combination parameter (including size and direction) and geometry criterion of the plate on the dynamic energy release rate are shown graphically. Numerical results indicate that increasing the graded index can all retard the crack extension, and that both the applied magnetic field loadings and electric field loadings play a dominant role in the dynamic fracture behaviors of crack tips.

On the direct interactions between heat transfer, mass transport and chemical processes within gradient elasticity

Abstract: The behaviour of complex material systems often results from the combined effects of several multi-scale mechanisms and simultaneously occurring coupled physical processes. In this paper, we focus on such complex response of a class of geomaterials in which heat conduction, mass diffusion, chemical reactions and gradient-type elastic strain mechanisms interact. Our purpose is to develop within a formal thermodynamic framework a complete set of constitutive equations which account for most of the possible aforementioned direct couplings and the associated relevant size effects in a unified phenomenological way. For the sake of simplicity, the volume element is described at the macroscopic scale as a classical homogeneous continuous mixture of chemically active species. Based on theories of second-gradient elasticity endowed with the concepts of both nonlocality residual and constitutive insulation condition, a thermo-diffuso-chemo-elastic formulation is proposed in the restricted case of small perturbations. Coupling terms entering the relevant constitutive relations are discussed throughout the paper. Then, the model is applied to a simple one-dimensional situation, in which only the mechanical response is reported. The implementation of such modelling in a finite element code should enable us to address more specific problems, such as the stress solution phenomenon in hollow cylinders subjected to external loading.

Thermoelastic interaction with energy dissipation in a transversely isotropic thin circular disc

Abstract: The distribution of stresses due to step input of temperature on the boundaries of a homogeneous transversely isotropic circular disc is investigated by applying Laplace transform technique in the context of generalized theories of thermo-elasticity. The inverse of the transformed solution is carried out by applying a method of Bellman et al. The stresses are computed numerically and presented graphically in a number of figures. A comparison of the results for different theories (CTE, CCTE, TRDTE(GL), TEWED(GN)) and the effect of anisotropy on the stresses are also presented. When the material is isotropic and outer radius of the disc tends to infinity, the corresponding result agrees with that of existing literature.

Cylindrical cavity expansion in compressible Mises and Tresca solids

Abstract: The elastoplastic field induced by quasi-static expansion in steady-state plane-strain conditions of a pressurized cylindrical cavity (cylindrical cavitation) is investigated. Material behavior is modeled by Mises and Tresca large strain flow theories formulated as hypoelastic. Both models account for elastic-compressibility and allow for arbitrary strain-hardening (or softening). For the Mises solid analysis centers on the axially-hydrostatic assumption (axial stress coincides with hydrostatic stress) in conjunction with a controlled error method. Introducing an error control parameter we arrive at a single-parameter-dependent quadrature expression for cavitation pressure. Available results are recovered with particular values of that parameter, and an optimal value is defined such that the cavitation pressure is predicted with high accuracy. For the Tresca solid we obtain an elegant solution with the standard model when no corner develops in the yield surface. Under certain conditions however a corner zone exists near the cavity and the solution is accordingly modified revealing a slight difference in cavitation pressure. Comparison with numerical solutions suggests that the present study establishes cylindrical cavitation analysis on equal footing with existing studies for spherical cavitation.

On the cumulative microslip phenomenon

Abstract: The cumulative microslip phenomenon is the accumulation of relative slips in a tangential direction on the contact interface of two solids under cyclic loadings. This leads to significant global relative displacement between components and can account for the failure of some assembly parts in mechanical structures. Practical examples from the automotive industry are presented in this paper to describe cumulative microslip effects in real situations. The phenomenon is then characterized from a theoretical point of view as an asymptotic behaviour for the contact interface under cyclic loads, by analogy with Ratcheting effects in elasto-plasticity. Accommodation and slip-shakedown are introduced in the same light. These various behaviours are illustrated with a reference discrete example that includes an original friction dissymmetry. Then we investigate the phenomenon's occurrence in various models. The existence of a dissymmetry in the assembly turns out to be a necessary condition for the phenomenon to occur. However, this condition proves not sufficient and the additional characteristics required to reproduce it are analysed. As dissymmetries are bound to exist in some assemblies because of the prescribed environment at work, a theoretical analysis of the phenomenon is performed and a slip-shakedown theorem is proposed. It leads to the introduction of a safety coefficient with respect to slips when a standard friction law is assumed. The safety coefficient can be computed from two static and kinematic approaches in min–max duality, which are illustrated on the reference discrete example.

A sweeping process approach to inelastic contact problems with general inertia operators

Abstract: The dynamics of systems with a finite number of degrees of freedom and nontrivial inertia matrix which are submitted to a single perfect purely inelastic unilateral constraint is studied. By adopting the measure differential formulation of J.J. Moreau, a velocity-based time-stepping method is developed, reminiscent of the catching-up algorithm for sweeping processes. It is shown that the numerical solutions converge to a solution of the problem, under a weaker assumption on the constraint as compared to position-based methods.

Electromechanical impact of an impermeable parallel crack in a functionally graded piezoelectric strip

Abstract: The dynamic fracture problem for a functionally graded piezoelectric material (FGPM) strip containing a crack parallel to the free boundaries is considered in this study. It is assumed that the electroelastic properties of the strip vary continuously along the thickness direction of the strip, and that the strip is under the in-plane mechanical and electric impact. Integral transform techniques and dislocation density functions are employed to reduce the problem to the solutions of a system of singular integral equations. The dynamic stress and electric displacement intensity factors versus time are presented for various values of dimensionless parameters representing the crack size, the crack location, the material nonhomogeneity and the loading combination.

Numerical modelling of the plasticity induced during diffusive transformation. Case of a cubic array of nuclei

Abstract: The experimental work of Taleb and Petit-Grostabussiat [Taleb, L., Petit-Grostabussiat, S., 2002. Elastoplasticity and phase transformations in ferrous alloys: some discrepancies between experiments and modeling. J. Phys. IV 12 (11), 187–194; Taleb, L., Petit, S., 2006. New investigations on transformation induced plasticity and its interaction with classical plasticity. Int. J. Plasticity 22 (1), 110–130] has shown evidence that the evolution of TRansformation Induced Plasticity (TRIP) in a low carbon steel (16MND5) could be significantly influenced by the loading history of the parent phase, for a martensitic as well as a bainitic transformation. Furthermore, estimates from the Leblond model – one of the few micromechanical models currently found in different Finite Element (FE) softwares – have appeared to be in disagreement with experiments in these cases where the parent phase has been strain hardened. This has motivated the development of alternative approaches based on FE computations. This paper presents our first investigations about simulations of diffusive transformations with FE in an idealized case: the parent and the product phase are considered as two homogeneous materials with given elastoplastic properties and density; the transformation takes place at the same instant at predefined elements constituting the nuclei; then it progresses at a uniform rate by changing the material properties of the layer of elements surrounding the nuclei. In the basic configuration of modelling, the volume of discretization stands for a unit cell of a periodic cellular array, with a single central nucleus. In a more complex configuration, which is introduced shortly here and to be presented in details in the paper under preparation [Barbe, F., Quey, R., Taleb, L., Souza de Cursi, E., 2006. Numerical modelling of the plasticity induced during diffusive transformation. Case of a random instantaneous array of nuclei, in preparation], the volume of computation contains few to several nuclei at random locations. For both configurations, results in terms of effective (mean) TRIP as a function of the volume fraction of product phase are in correct quantitative and qualitative agreement with experimental results.

An elastoplastic homogenization procedure for predicting the settlement of a foundation on a soil reinforced by columns

Abstract: This paper presents an elastoplastic homogenization method applied to a soil reinforced by regularly distributed columns. According to this method, the composite reinforced soil is regarded, from a macroscopic point of view, as a homogeneous anisotropic continuous medium, the elastic as well as plastic properties of which can be obtained from the solution to an auxiliary problem attached to the reinforced soil representative cell. Based upon an approximate solution to this problem, in which piecewise constant stress fields are used, the homogenized behavior of the reinforced soil subject to vertical oedometric conditions is investigated. A first application to the evaluation of the settlement of a reinforced soil foundation is then presented, taking into account the initial stress field generated by the reinforced soil own weight. A particular emphasis is put on the situation of a purely cohesive soft clay reinforced by purely frictional inclusions (“stone column” reinforcement technique), for which a simplified calculation procedure, in which the soil remains elastic, is proposed, leading to an analytical closed-form expression for the load–settlement curve.

Modelling of the internal stress in dislocation cell structures

Abstract: The nonuniform distribution of dislocations in metals gives rise to material anisotropy and internal stresses that determine the mechanical response. This paper proposes a micromechanical model of a dislocation cell structure that accounts for the material inhomogeneity and incorporates the internal stresses in a physically-based manner. A composite model is employed to describe the material with its dislocation cell structure. The internal stress is obtained as a natural result of plastic deformation incompatibility and incorporated in the composite model. Applications of this model enable the prediction of the mechanical behavior of metals under various nonuniform deformations. The implementation of the model is relatively straightforward, allowing easy use in macroscopic engineering computations.

Dynamic stress intensity factor for cracked functionally graded orthotropic medium under time-harmonic loading

Abstract: Dynamic stress intensity factor for a Griffith crack in functionally graded orthotropic materials under time-harmonic loading is investigated in the present paper. By using the Fourier transform and defining the jumps of displacement components across the crack surface as the unknown functions, two pairs of dual integral equations are derived. To solve the dual integral equations, the jumps of the displacement components across the crack surface are expanded in a series of Jacobi polynomial. Numerical examples are provided to show the effects of material properties and the crack configuration on the dynamic stress intensity factors of the functionally graded orthotropic materials with a Griffith crack.

The thermal effect on axially compressed buckling of a double-walled carbon nanotube

Abstract: The thermal effect on axially compressed buckling of a double-walled carbon nanotube is studied in this paper. The effects of temperature change, surrounding elastic medium and van der Waals forces between the inner and outer nanotubes are taken into account. Using continuum mechanics, an elastic double-shell model with thermal effect is presented for axially compressed buckling of a double-walled carbon nanotube embedded in an elastic matrix under thermal environment. Based on the model, an explicit formula for the critical axial stress is derived in terms of the buckling modes of the shell and the parameters that indicate the effects of temperature change, surrounding elastic medium and the van der Waals forces. Based on that, some simplified analysis is carried out to estimate the critical axial stress for axially compressed buckling of the double-walled carbon nanotube. Numerical results for the general case are obtained for the thermal effect on axially compressed buckling of a double-walled carbon nanotube. It is shown that the axial buckling load of double-walled carbon nanotube under thermal loads is dependent on the wave number of axially buckling modes. And a conclusion is drawn that at low and room temperature the critical axial stress for infinitesimal buckling of a double-walled carbon nanotube increase as the value of temperature change increases, while at high temperature the critical axial stress for infinitesimal buckling of a double-walled carbon nanotube decrease as the value of temperature change increases.