The comparison of two approaches to numerical modelling of gas-particles turbulent flow and heat transfer in a pipe

The comparison of two theoretical approaches for the numerical investigation of turbulent gas–solid flows with heat transfer in a pipe are presented in this paper. The first approach is based on Eulerian–Eulerian modelling of investigated phenomena, the second one is formulated within the framework of the Eulerian–Lagrangian approach. The verification of numerical models under consideration. Their testing against available experimental data show good prognostic properties of the elaborated theoretical tool for research activities to study new physical fundamentals of turbulent gas-suspended particles flows in pipes and channels.     

Energy approach to crack growth in a fiber-reinforced brittle material modeled by an inclusion

Brittle materials randomly reinforced with a low volume fraction of strong, stiff and ductile fibers are considered, with specific reference to fiber-reinforced cements and concrete. Visible cracks in such materials are accompanied by a surrounding damage zone – together these constitute a very complex “crack system”. Enormous effort has been put into trying to understand the micromechanics of such systems. Almost all of these efforts do not deal with the “crack system” propagation behavior as a whole. The propagation process of such a “crack system” includes propagation of the visible crack and the growth of the damage zone. Propagation may take place by lengthening of the visible crack together with the concomitant lengthening of the surrounding damage zone, or simply by broadening of the damage zone while the visible crack length remains unchanged – or simultaneously by growth of both types. A phenomenological completely theoretical model (for an ideal material) is here proposed which can serve to examine the propagation process by means of energy principles, without recourse to the microscopic details of the process. An application of this theoretical approach is presented for the case of a damage zone evolving with a rectangular shape. This shape is chosen because it is expected that it will illustrate the nature of damage evolution and because the computational procedure necessary to follow the growth is the most straightforward.     

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.     

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.     

Fatigue strength of welded joints based on local, semi-local and nominal approaches

Analysis based on the so-called “local approach” is made to estimate the fatigue strength of welded joints. Numerical analyses or strain gauges are employed for finding the stress and/or strain state in the vicinity of the weld toe. The notch stress intensity factor (NSIF) approach applied to fillet welded joints, as far as the opening angle between the weld and the main plate surface is constant (e.g. 135°, typical for many fillet welds), is able to rationalise the fatigue strength data both for different joint geometries and absolute dimensions. The NSIF approach has been previously developed as an extension of the Linear Elastic Fracture Mechanics (LEFM) to open V-notches and is based on the exponential local stress field around the V-notch tip. Several different “local approaches”, although simpler and more practical than the NSIF, are based on the stress (or strain) values determined beyond the exponential local one. To distinguish such approaches from the NSIF based one, we define the former as semi-local or nominal approaches while the latter is a local approach. The paper underlines that the local approaches, differently from the other ones, are able to unify in a single scatter band the fatigue strength data obtained from welded joints having different geometry and absolute dimensions.     

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.     

The Lanczos method applied to quasi-static stark broadening of spectral lines

The quasi-static ion approximation of Stark broadened spectral lines involves an average of the field-dependent line shape over the microfield probability distribution. In the conventional approach, this can become computationally expensive since the calculation at each field point requires inverting a possibly large matrix. It is shown that these calculations are well suited to the “Padé Via Lanczos” approach, which allows for an efficient and accurate numerical integration over the quasi-static field. In turn, the integration forms the basis for determining convergence with Lanczos iterations. Simple examples are used to demonstrate improved performance over conventional methods.     

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.     

Thermal dissociation of diatomic molecules in a nonisothermal two-temperature boundary layer

Nonequilibrium thermal dissociation in a nonisothermal boundary layer in a mixture of Morse anharmonic oscillators — molecules of a diatomic gas and its atoms — is considered within the framework of the ladder mechanism. The local nonlinear nonequilibrium corrections to the two-temperature macroscopic dissociation rate, which depend, in particular, on the translational and vibrational temperature gradients and the degree of dissociation, are determined.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 191–201, March–April, 1996.     

Orthotropic bone remodeling: case of plane stresses

Cancellous bone is constituted by a porous solid matrix filled with fluid. Matrix microstructure gives bone most of its mechanical strength properties. In our macroscopic approach, bone is seen as a continuous medium with a local (at our scale) time-dependent linearly elastic orthotropic behavior. Remodeling consists, by matrix material apposition or resorption, in microstructure modifications in order to optimize its mechanical characteristics. The proposed model is built on a time iterative procedure where the compliance tensor evolves such that, depending on the applied stresses, principal strains tend to fall within an admissible domain. The suggested remodeling laws in this work modify the elasticity “constants” as well as the orthotropy directions. The first results presented here correspond to the plane stresses case.     

Finite deformation of incompressible fiber-reinforced elastomers: A computational micromechanics approach

The in-plane finite deformation of incompressible fiber-reinforced elastomers was studied using computational micromechanics. Composite microstructure was made up of a random and homogeneous dispersion of aligned rigid fibers within a hyperelastic matrix. Different matrices (Neo-Hookean and Gent), fibers (monodisperse or polydisperse, circular or elliptical section) and reinforcement volume fractions (10–40%) were analyzed through the finite element simulation of a representative volume element of the microstructure. A successive remeshing strategy was employed when necessary to reach the large deformation regime in which the evolution of the microstructure influences the effective properties. The simulations provided for the first time “quasi-exact” results of the in-plane finite deformation for this class of composites, which were used to assess the accuracy of the available homogenization estimates for incompressible hyperelastic composites.     

A tentative approach to the direct simulation of drag reduction by polymers

An efficient technique for drag reduction uses dilute solutions of a few p.p.m. of polymers. A possible reduction in drag of up to 80% is achieved. Several experimental observations have been made which tend to indicate that the polymers modify the turbulence structures within the buffer layer. Flow visualisations have shown that the changes consist of a weakening of the strength of the streamwise vortices. Existing literature reveals no attempts of numerical simulation of this phenomenon. In this paper an approach is pursued by using a constitutive equation which relates the elongation viscosity to the local properties of the flow. According to this model this viscosity is large in zones where the amount of strain rate is greater than the amount of vorticity, and is zero when the vorticity exceeds the strain rate. Simulations have been performed in a “minimal channel” to give good resolution with a limited number of grid points. The accuracy of the method is tested by comparison with the results of other techniques. For simulations with polymers, quantitative comparisons cannot be made, but the results reproduce the qualitative outputs of the experiments. The mean streamwise velocity is modified in the buffer layer; the peak of the streamwise turbulent intensity, in wall units, increases and its maximum moves far from the wall; and the vertical turbulent intensity is largely reduced in the wall region. An interesting outcome from both the simulation and the experiments is that the strength of the longitudinal vortices is reduced when the polymers are present.     

On perfectly plastic flow in porous material

Experimental observations suggest that for perfectly-plastic materials containing pores, the (small) strain at which significant macroscopic yielding occurs is relatively insensitive to porosity, for volume fractions below approximately 15–20% (although the yield stress drops significantly with increasing porosity). Another observation is that, at these porosity levels, the stress–strain curve remains approximately linear almost up to the yield point. Based on these observations, Sevostianov and Kachanov constructed yield surfaces that explicitly reflect the shapes of the pores and their orientation. The underlying microscale mechanism is that local plastic “pockets” near pores blunt the stress concentrations; as a result, they remain limited in size and well contained in the elastic field until they connect and almost the entire matrix plasticizes within a narrow interval of stresses that can be idealized as the yield point. The present paper provides direct insight into the micromechanics of poroplasticity through direct microscale numerical simulation. Besides confirming the basic microscale mechanism, these simulations reveal that the reduction of the macroscopic poroplastic yield stress is approximated quite closely by 1−v₂ times the dense nonporous yield stress, where v₂ is the volume fraction of the pores.     

The use of Padé approximation to eliminate nonuniformities of asymptotic expansions

Nonuniformities of asymptotic expansions seriously restrict their applicability [1–4]. The various methods used to overcome this difficulty (Lighthill [1], renormalizations [2, 3], generalized summation [2]) do not always succeed. In addition, it is helpful to have alternative approaches. It is shown in the present paper by some examples that Padé rearrangement of the perturbation series can eliminate the nonuniformities of asymptotic expansions.Translated from Izvestlya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, 166–167, May–June, 1984.     

Spectral Properties of Dynamical Systems, Model Reduction and Decompositions

In this paper we discuss two issues related to model reduction of deterministic or stochastic processes. The first is the relationship of the spectral properties of the dynamics on the attractor of the original, high-dimensional dynamical system with the properties and possibilities for model reduction. We review some elements of the spectral theory of dynamical systems. We apply this theory to obtain a decomposition of the process that utilizes spectral properties of the linear Koopman operator associated with the asymptotic dynamics on the attractor. This allows us to extract the almost periodic part of the evolving process. The remainder of the process has continuous spectrum. The second topic we discuss is that of model validation, where the original, possibly high-dimensional dynamics and the dynamics of the reduced model – that can be deterministic or stochastic – are compared in some norm. Using the “statistical Takens theorem” proven in (Mezić, I. and Banaszuk, A. Physica D, 2004) we argue that comparison of average energy contained in the finite-dimensional projection is one in the hierarchy of functionals of the field that need to be checked in order to assess the accuracy of the projection.     

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.     

Re-examined principles of thrust generation by a track on soft ground

Dr. Bekker’s first book Theory of land locomotion offers in fact two different concepts of thrust generation on soft ground with respect to the slip: (a) as the push of grousers causing horizontal soil “distortion” and (b) as the shear force in the failure plane linked with the shear deformation. Bekker preferred the second concept and backed it up by the unique shear-ring measuring technique. To clear up the matter, the author decided to re-examine the thrust generation by a track plate experimentally in field conditions. The tests have shown that the initial stage of thrust generation in compressible ground is always horizontal soil compression by grousers, which divides the soil under a track into separate blocks initially at rest. This compression increases at least to the transition point, when a block is sheared off simultaneously at the bottom and in both lateral planes and starts sliding along the channel formed by the preceding grouser. The analysis of these measurements enabled to define the compressive displacement of the face of the soil block (travel of the grouser) appurtenant to the mentioned transition point, useful to define the thrust–slip curve. The case may also be described by the conventional shear stress–shear displacement relationship, imagined to take place in the bottom failure plane, however, namely the “shear displacement” is rather an unusual quantity.     

Evolution of subsequent yield surfaces and elastic constants with finite plastic deformation. Part-I: A very low work hardening aluminum alloy (Al6061-T6511)

In the present study, the initial and subsequent yield surfaces in Al 6061-T6511, based on 10 με deviation from linearity definition of yield, are presented. The subsequent yield surfaces are determined during tension, free end torsion, and combined tension–torsion proportional loading paths after reaching different levels of strains. The yield surfaces are also obtained after linear, bi-linear and non-linear unloading paths after finite plastic deformation. The initial yield surface is very close to the von-Mises yield surface and the subsequent yield surfaces undergo translation and distortion. In the case of this low work hardening material, the size of the yield surfaces is smaller and negative cross-effect is observed with finite plastic deformation. The subsequent yield have a usual “nose” in the loading direction and flattened shape in the reverse loading direction; the observed nose is more dominant in the case of tension and combined tension–torsion loading than in torsional loading. The size of the yield surfaces after unloading is smaller than the initial yield surface but larger than subsequent yield surfaces obtained during prior loading, show much smaller cross-effect, and the shape of these yield surfaces depends strongly on the loading and unloading paths. Elastic constants (Young’s and shear moduli) are also measured within each subsequent yield surfaces. Evolution of these constants with finite deformation is also presented. The decrease of the two moduli is found to be much smaller than reported earlier in tension by Cleveland and Ghosh [Cleveland, R.M., Ghosh, A.K., 2002. Inelastic effects on springback in metals. Int. J. Plast. 18, 769–785]. Part-II and III [(Khan et al., 2009a) and (Khan et al., 2009b)] of the papers will include experimental results on annealed 1100 Al (a very high work hardening material) and on both Al alloys (Al6061-T6511 and annealed 1100 Al) in tension- tension stress space, respectively. The results for both cases are quite different than the ones that are presented in this paper.