On the dynamic behavior of agricultural tires

The dynamic behavior of vehicles which are equipped with pneumatic tires depends, to a degree, on the properties of the tire. Therefore, road handling and comfort are also affected by tire characteristics. When the inflation pressure is reduced one obtains a softer “spring”. The dynamic spring coefficient C_dyn increases with increasing rolling speed. Damping coefficient k is related to the excitation frequency by a power function. This function shows a sharp negative slope for low velocities. These conclusions apply to the tire types and test conditions described in this paper.     

Thermodynamical functions for a gas of point vortices

We formulate nonlinear integro-differential equation for the averaged collective Hamiltonian of a gas of interacting two-dimensional vortices, derive its analytical solution, and discuss the equilibrium, axially-symmetrical, probability distributions that are possible for such a model. We also theoretically prove that the probability distribution for a system of 2D point vortices takes a form similar to the Gibbs distribution, but point out that the physical fundamentals of such a system differ from the standard theory of interacting particles. Furthermore, we find thermodynamical functions for positive and negative “temperature” of the system, and point out that the states with positive “temperature” correspond to stationary bell-shape vortex distributions, while the states with negative “temperature” correspond to distributions localized near container walls. To cite this article: E. Bécu et al., C. R. Mecanique 336 (2008).     

Asymptotic analysis of an end-loaded, transversely isotropic, elastic, semi-infinite strip weak in shear

We use linear elasticity to study a transversely isotropic (or specially orthotropic), semiinfinite slab in plane strain, free of traction on its faces and at infinity and subject to edge loads or displacements that produce stresses and displacements that decay in the axial direction. The governing equations (which are identical to those for a strip in plane stress, free of traction on its long sides and at infinity, and subject to tractions or displacements on its short side) are reduced, in the standard way. to a fourth-order partial differential equation with boundary conditions for a dimensionless Airy stress function ƒ. We study the asymptotic solutions to this equation for four sets of end conditions—traction, mixed (two), displacement—as g3, the ratio of the shear modulus to the geometric mean of the axial and transverse extensional moduli, approaches zero. In all cases, the solutions for ƒ consist of a “wide” boundary layer that decays slowly in the axial direction (over a distance that is long compared to the width of the strip) plus a “narrow” boundary layer that decays rapidly in the axial direction (over a distance that is short compared to the width of the strip). Moreover, we find that the narrow boundary layer has a “sinuous” part that varies rapidly in the transverse direction, but which, to lowest order, does not enter the boundary conditions nor affect the transverse normal stress or the displacements. Because the exact biorthogonality condition for the cigenfunctions associated with ƒ can be replaced by simpler orthogonality conditions in the limit as →b 0, we are able to obtain, to lowest order, explicit formulae for the coeflicients in the eigenfunction expansions of ƒ for the four different end conditions.     

Relativistic electron transport and confinement within charge-insulated, mass-limited targets

We present experimental results on the interaction of short-pulse ultra-high-intensity laser beams with small size (“mass-limited”) targets. Several diagnostics (X-ray spectroscopy, K_α and optical imaging of target rear side) have been simultaneously used in order to characterize the laser-generated fast electron transport and energy deposition into the target material. Our results show that fast electrons are effectively confined inside the target by the induced space charge. This electrostatic confinement opens new opportunities to create “Warm Dense Matter” states characterized by solid-state density and temperatures of the order of a few tens of eV.     

Mechanics of granular materials: The discrete and the continuum descriptions juxtaposed

In recent years a discussion could be followed where the pros and cons of the applicability of the Cosserat continuum model to granular materials were debated [Bardet, J.P., Vardoulakis, I., 2001. The asymmetry of stress in granular media. Int. J. Solids Struct. 38, 353–367; Kruyt, N.P., 2003. Static and kinematics of discrete Cosserat-type granular materials. Int. J. Solids Struct. 40, 511–534; Bagi, K., 2003. Discussion on “The asymmetry of stress in granular media”. Int. J. Solids Struct. 40, 1329–1331; Bardet, J.P., Vardoulakis, I. 2003a. Reply to discussion by Dr. Katalin Bagi. Int. J. Solids Struct. 40, 1035; Kuhn, M., 2003. Discussion on “The asymmetry of stress in granular media”. Int. J. Solids Struct. 40, 1805–1807; Bardet, J.P., Vardoulakis, I., 2003b. Reply to Dr. Kuhn’s discussion. Int. J. Solids Struct. 40, 1809; Ehlers, W., Ramm, E., Diebels, S., D’Addetta, G.A., 2003. From particle ensembles to Cosserat continua: homogenization of contact forces towards stresses and couple stresses. Int. J. Solids Struct. 40, 6681–6702; Chang, C.S., Kuhn, M.R., 2005. On virtual work and stress in granular media. Int. J. Solids Struct. 42, 3773–3793]. The authors follow closely this debate and try, with this paper, to provide a platform where the various viewpoints could find their position. We consider an ensemble of rigid, arbitrarily shaped grains as a set with structure. We establish a basic mathematical framework which allows to express the balance laws and the action–reaction laws for the discrete system in a “global” form, through the concepts of “part”, “granular surface”, “separately additive function” and “flux”. The independent variable in the balance laws is then the arbitrary part of the assembly rather than the single grain. A parallel framework is constructed for Cosserat continua, by applying the axiomatics established by [Noll, W., 1959. The foundation of classical mechanics in the light of recent advances in continuum mechanics. In: The axiomatic method, with special reference to Geometry and Physics, North-Holland Publishing Co., Amsterdam pp. 266–281, Gurtin, M.E., Williams, W.O., 1967. An axiomatic foundation of continuum thermodynamics. Arch. Rat. Mech. Anal. 26, 83–117, Gurtin, M.E., Martins, L.C., 1976. Cauchy’s theorem in classical physics. Arch. Rat. Mech. Anal. 60, 305–324]. The comparison between the two realisations suggests the microscopic interpretation for some features of Cosserat Mechanics, among which the asymmetry of the Cauchy-stress tensor and the couple-stress.     

On the use of Laplace transform inversion for reconstruction of relaxation spectra

We discuss the use of Fourier transforms to construct approximate inversion formulae for the Laplace transform and apply this technique to recover the relaxation spectrum from “data” for the relaxation modulus. We show that regularization by a Gaussian, as proposed by Davies and Anderssen [A.R. Davies, R.S. Anderssen, Sampling localization in determining the relaxation spectrum, J. Non-Newt. Fluid Mech. 73 (1997) 163–179] yields reasonable results even for data with significant noise. We also show that, in principle, other choices of regularization allow the relaxation spectrum to be reconstructed from data which are taken in any interval of time or frequency, however short and wherever located. We construct formulae which would do this, based on polynomial approximation of a function in an exponentially weighted space. This algorithm, however, turns out not to be practical, and we elucidate the reasons for that.     

On complex potentials for finite plane deformation of a transversely isotropic material

We consider the finite deformation of plane equilibrium problem for a transversely isotropic layer, using the complex variable approach. We give the general expression for the pertinent complex potentials and state the corresponding fundamental problems. We discuss in detail the boundary value problem for fundamental problem-one. As an application of the espoused method, an analytical solution of “Lame's problem” for an infinite layer is obtained. The nonlinear effect of this is highlighted in the obtained figure.     

Kinematics and dynamics of small-scale vorticity and strain-rate structures in the transition from isotropic to shear turbulence

We applied a technique that defines and extracts “structures” from a DNS dataset of a turbulence variable in a way that allows concurrent quantitative and visual analysis. Local topological and statistical measures of enstrophy and strain-rate structures were compared with global statistics to determine the role of mean shear in the dynamical interactions between fluctuating vorticity and strain-rate during transition from isotropic to shear-dominated turbulence. We find that mean shear adjusts the alignment of fluctuating vorticity, fluctuating strain-rate in principal axes, and mean strain-rate in a way that (1) enhances both global and local alignments between vorticity and the second eigenvector of fluctuating strain-rate, (2) two-dimensionalizes fluctuating strain-rate, and (3) aligns the compressional components of fluctuating and mean strain-rate. Shear causes amalgamation of enstrophy and strain-rate structures, and suppresses the existence of strain-rate structures in low-vorticity regions between enstrophy structures. A primary effect of shear is to enhance “passive” strain-rate fluctuations, strain-rate kinematically induced by local vorticity concentrations with negligible enstrophy production, relative to “active,” or vorticity-generating strain-rate fluctuations. Enstrophy structures separate into “active” and “passive” based on the level of the second eigenvalue of fluctuating strain-rate. We embedded the structure-extraction algorithm into an interactive visualization-based analysis system from which the time evolution of a shear-induced hairpin enstrophy structure was visually and quantitatively analyzed. The structure originated in the initial isotropic state as a vortex sheet, evolved into a vortex tube during a transitional period, and developed into a well-defined horseshoe vortex in the shear-dominated asymptotic state.     

On an attempt to simplify the Quartapelle–Napolitano approach to computation of hydrodynamic forces in open flows

In this paper we are interested in the Quartapelle–Napolitano approach to calculation of forces in viscous incompressible flows in exterior domains. We study the possibility of deriving a simpler formulation of this approach which might lead to a more convenient expression for the hydrodynamic force, but conclude that such a simplification is, within the family of approaches considered, impossible. This shows that the original Quartapelle–Napolitano formula is in fact “optimal” within this class of approaches.     

Fatigue crack growth in high and low strength steel under torsional loading

During loading of a crack in mode III the crack surfaces in contact slide against each other giving rise to friction, abrasion and mutual support, thereby reducing the effective stress at the crack tip (“sliding mode crack closure”). This phenomenon was investigated in a high strength steel (AISI 4340) and in a low strength steel (AISI C1018) in circumferentially notched specimens under pure cyclic torsion and combined loading (cyclic torsion plus static axial load). The influence of sliding mode crack closure on fatigue crack propagation is shown and “true” crack growth values (without the sliding mode crack closure influence) are determined on the basis of an extrapolation procedure. Explanations are given for causes of the various fracture modes observed, such as “factory roof” fracture, macroscopically flat mode III fracture and “lamella” fracture. Finally the scientific and technical importance of sliding mode crack closure is demonstrated.     

Bounds for the effective properties of heterogeneous plates

This paper presents new bounds for heterogeneous plates which are similar to the well-known Hashin–Shtrikman bounds, but take into account plate boundary conditions. The Hashin–Shtrikman variational principle is used with a self-adjoint Green-operator with traction-free boundary conditions proposed by the authors. This variational formulation enables to derive lower and upper bounds for the effective in-plane and out-of-plane elastic properties of the plate. Two applications of the general theory are considered: first, in-plane invariant polarization fields are used to recover the “first-order” bounds proposed by Kolpakov [Kolpakov, A.G., 1999. Variational principles for stiffnesses of a non-homogeneous plate. J. Meth. Phys. Solids 47, 2075–2092] for general heterogeneous plates; next, “second-order bounds” for n-phase plates whose constituents are statistically homogeneous in the in-plane directions are obtained. The results related to a two-phase material made of elastic isotropic materials are shown. The “second-order” bounds for the plate elastic properties are compared with the plate properties of homogeneous plates made of materials having an elasticity tensor computed from “second-order” Hashin–Shtrikman bounds in an infinite domain.     

A “quasi-elastic” affine formulation for the homogenised behaviour of nonlinear viscoelastic polycrystals and composites

The derivation of the overall behaviour of nonlinear viscoelastic (or rate-dependent elastoplastic) heterogeneous materials requires a linearisation of the constitutive equations around uniform per phase stress (or strain) histories. The resulting Linear Comparison Material (LCM) has to be linear thermoviscoelastic to fully retain the viscoelastic nature of phase interactions. Instead of the exact treatment of this LCM (i.e., correspondence principle and inverse Laplace transforms) as proposed by the “classical” affine formulation, an approximate treatment is proposed here. First considering Maxwellian behaviour, comparisons for a single phase as well as for two-phase materials (with “parallel” and disordered morphologies) show that the “direct inversion method” of Laplace transforms, initially proposed by Schapery (1962), has to be adapted to fit correctly exact responses to creep loading while a more general method is proposed for other loading paths. When applied to nonlinear viscoelastic heterogeneous materials, this approximate inversion method gives rise to a new formulation which is consistent with the classical affine one for the steady-state regimes. In the transient regime, it leads to a significantly more efficient numerical resolution, the LCM associated to the step by step procedure being no more thermoviscoelastic but thermoelastic. Various comparisons for nonlinear viscoelastic polycrystals responses to creep as well as relaxation loadings show that this “quasi-elastic” formulation yields results very close to classical affine ones, even for high contrasts.     

Effect of gravity on the vibration of vertical cantilevers

The free vibration of a vertically-oriented, thin, prismatic cantilever is influenced by weight. That is, the natural frequencies (and to a lesser extent, mode shapes) are affected by the application of a linearly varying axial load. A beam with an “upward” orientation, i.e., with the free end above the clamped end, will experience a de-stiffening effect, up to the point of self-weight buckling (at zero effective stiffness). A beam in a “downward” orientation will be stiffened by the weight of the beam. This technical note describes some simple experiments on very slender strips and their (vertical) orientation and shows a close correlation with theory.     

Sources of variability in traction data

A 18.4R38 tyre was tested at 124 kPa inflation pressure, approximately 24 kN axle load in a firm and in a tilled Yolo-loam soil using (i) constant slip, (ii) constant draught, (iii) varying slip and (iv) varying draught tyre testing procedures. The results indicated that the constant slip test procedure leads to repeatable and consistent results whereas a variable slip test procedure leads to considerable scatter in the data. The constant draught test procedure yielded acceptable results. Varying slip appeared to influence the system dynamics much more than varying draught during tyre testing. An accurate method of predicting “true rolling radius” and “true slip” for an assumed zero condition is presented. The concept of motion resistance, its variability due to assumed zero conditions, and possible interpretations are discussed. The traction test data indicates that the motion resistance is not constant but varies with slip.     

Steady shear banding in complex fluids

Shear banding (SB) is manifested by the abrupt “demixing” of the flow into regions of high and low shear rate. In this paper, we first relate analytically the rheological parameters of the fluid with the range of shear rates and stresses of SB occurrence. For this, we accept that the origin of shear banding is constitutive, and adopt a non-linear viscoelastic expression able to accommodate the double-valuedness of the stress with flow intensity, under certain conditions. We then implement the model for the case of pressure driven flow through a cylindrical pipe; we derive approximate expressions for the velocity profile in the two-banded regions (core and outer annular), the overall throughput in the presence or absence of “spurt”, and the radial location limits of the shear rate discontinuity.     

Molecular dynamics study of size, temperature and rate dependent thermomechanical properties of copper nanofilms

Molecular dynamics simulations are performed to study the thermomechanical properties of copper nanofilms at different temperatures and extremely-high loading rates. The results show a drastic temperature softening effect on the film strength and modulus. The increase of strain rate could result in a much higher strength while the modulus is relatively less affected. It is shown, based on the stress results, that the observed “smaller is softer” and “smaller is stronger” behaviors of nanofilms might be due to the surface plasticity and the volumetric dislocations, respectively. It is also found that the thinner a nanofilm, the smaller the thermal expansion coefficient. The present work reveals that the quasistatic thermomechanical properties of bulk copper at room temperature might be inadequate for the continuum-based study of thermomechanical response of copper nanofilms due to ultrafast laser heating.     

Geomechatronics – Interaction between ground and construction machinery and its application to construction robotics

“Geomechatronics” is a technical field in which “Geotechniques” is fused with “Mechatronics” that is the technical field to promote the automatic control of machines by using the electronics. In the field of “Geomechatronics”, a construction machine, which treats geotechnical materials such as soil and rock, automatically evaluates the properties and conditions of the ground and determines the optimum controlling method of itself for the ground with the base of the machine–ground interaction. Some researches for practical use in the field of geomechatronics are introduced, and then the progressing view of this research and technical filed is explained in this paper.     

DYNAMICS AND STABILITY OF PINNED–CLAMPED AND CLAMPED–PINNED CYLINDRICAL SHELLS CONVEYING FLUID

The paper examines the dynamics and stability of fluid-conveying cylindrical shells having pinned–clamped or clamped–pinned boundary conditions, where “pinned” is an abbreviation for “simply supported”. Flügge's equations are used to describe the shell motion, while the fluid-dynamic perturbation pressure is obtained utilizing the linearized potential flow theory. The solution is obtained using two methods — the travelling wave method and the Fourier-transform approach. The results obtained by both methods suggest that the negative damping of the clamped–pinned systems and positive damping of the pinned–clamped systems, observed by previous investigators for any arbitrarily small flow velocity, are simply numerical artefacts; this is reinforced by energy considerations, in which the work done by the fluid on the shell is shown to be zero. Hence, it is concluded that both systems are conservative.