The BKZ as an alternative to the Wagner model for fitting shear and elongational flow data of an LDPE melt

For the low density polyethylene Melt I, which is the melt for which the most complete set of shear and elongational data exists, the semi-empirical single integral Wagner model gives an excellent data-fit, but suffers the drawback of having no entropic constitutive equation, that is a relationship between strain history and elastic free energy from which viscous heating and cohesive failure can be predicted. We show here that the BKZ model, which does possess an entropic constitutive equation, gives as good a fit as does the Wagner model to both the shear and elongational data.     

Modifications for an explicit algebraic stress model

An extension of the explicit algebraic stress model, developed by Gatski and Speziale [Gatski TB, Speziale CG. On the explicit algebraic stress models for complex turbulent flows. Journal of Fluid Mechanics 1993; 254: 59–78] is proposed. The extension implicates some essential characteristics of second‐order closure models. The strain‐dependent coefficients are modified, resulting in an alleviation of the numerical instabilities involved in the model. A new near‐wall damping function f_μ in the eddy viscosity relation is introduced. To enhance dissipation in near‐wall regions, the model constant C_ϵ1 is modified and an extra positive source term is included in the dissipation equation. In addition, a realizable time scale is incorporated to remove the wall singularity. Computed results show that the modified Gatski–Speziale (MGS) model predictions are in better agreement with the direct numerical simulation (DNS) and experimental data than those of the original Gatski–Speziale (OGS) model. Copyright © 2001 John Wiley & Sons, Ltd.     

A model for the effect of physical ageing on the stress relaxation behavior of high density polyethylene

The stress relaxation behavior of high density polyethylene (HDPE) can be affected by ageing processes; e.g., with increasing storage time at a low temperature following a quench from a high temperature (close to the melting point) the relaxation curves change shape. More specifically, the stress level approached after very long loading times in a stress relaxation experiment increases with the ageing time. Here this stress level is denoted the internal stress _i. Struik has pointed out that physical ageing may also occur in semicrystalline polymers like HDPE. The physical ageing should then be associated with that part of the amorphous phase which is closest to the surfaces of the crystallites. This part of the amorphous phase of HDPE can be assumed to have a restricted mobility at room temperature and may have a partially glassy character. In this paper a model for explaining the increase in _i for HDPE with increasing ageing time is proposed and discussed. It is based on the separation of the amorphous phase into two parts as suggested by Struik. The glassy part of the amorphous phase ages in a way similar to that of an entirely amorphous polymer quenched to a temperature below its glass transition, while the more rubbery phase is assumed not to undergo any physical ageing.     

A possible alternative to the FENE dumbbell model of dilute polymer solutions

The dumbbell model of dilute polymer solutions is simple and successful, and its FENE version has progressively become a paradigm. In some transient extensional flows however, an increased dissipation was observed which could not be understood within the FENE model. This prompted us to look for a new dumbbell-like model in which the finite extensibility of the polymer is taken more thoroughly into account, i.e. not only through the Warner potential. The main lines of this alternative model are presented.     

Dynamic coefficient evaluation for an algebraic subgrid stress model

Static model coefficients for an algebraic subgrid stress (SGS) model are determined using a dynamic approach, based on results from simulations of isotropic decaying turbulence. The study was motivated by the discrepancies in energy transfer predictions using the previously documented coefficients (Bhushan and Warsi, Int. J. Numer. Meth. Fluids 2005; 49 : 489–519). The discrepancies are identified to be due to inconsistent filter functions used in the analytic estimates and the simulations. The study emphasizes that SGS model development should use filter functions compatible with those inherent in CFD application solvers. The dynamic approach predicts consistent model and transfer coefficients for different grid resolutions and is judged to be a reliable basis for model coefficient adjustments. The predicted Leonard's stress coefficient and associated energy transfer coefficients agree very well with the analytic estimates using a Gaussian/cutoff combination filter. This suggests that the modeling of Leonard's stress term using a truncated Taylor series expansion is robust and may not benefit significantly from dynamic modeling. Validation simulations were performed for turbulent channel flow at Re_τ = 180 and 590. The dynamic approach was found to be reliable only for the lower log‐layer of the Re_τ = 590 case, where the scale invariance condition was satisfied. Nonetheless, in this narrow range, the model and transfer coefficients compare well with the isotropic case. The static coefficient algebraic model with new adjusted coefficients shows improved predictions compared with the previous coefficients, for both isotropic decaying turbulence and channel flow cases. Copyright © 2013 John Wiley & Sons, Ltd.     

The stress on an elastic half-space due to sectionally smooth-ended punch

The axisymmetric contact problem for an elastic half-space and a rigid punch is considered using integral transform methods. The end of the punch is sectionally smooth and there is incomplete penetration. The normal stress under the punch is calculated and found to have an elliptic integral type of singularity.     

A stress point algorithm for an elastoplastic model in unsaturated soils

Two stress fields, combination of total stresses, liquid pressure and gas pressure have to be considered to explain the deformational behaviour of unsaturated media. Elastoplastic models developed for these materials consider generally two yield surfaces, each one associated to a stress field, and whose intersection produces a corner in the space of generalised stress components. In this paper, a stress point algorithm is proposed to cope with the integration of such constitutive laws, which can be seen as non smooth multisurface plastic models in the space of the two stress fields. The basic model developed by Alonso et al. (Alonso, E.E., Gens, A., 1990. A constitutive model for partially saturated soils. Géotechnique 40 (3), 405–430), which will be used to test the algorithm, is first described. Generalised stress and strain variables are then defined. Implementation of the return mapping algorithm, based on an implicit integration scheme, is presented with special attention devoted to the problem of mixed control imposed by the F.E. formulation generally used to analyse the hydromechanical behaviour of unsaturated media. Validation results on distinct generalised stress paths are given at the end.     

A two-level system with induced transitions as a model of stress relaxation

This paper outlines the basic features of a two-level cooperative model of the stress relaxation in solids. In contrast to similar models presented earlier, the transitions between the two energy levels can take place in both directions, the relaxation process thus assuming a quasi-equilibrium character. The kinetics of this model are the same as obtained in the model where the transitions take place from the higher to the lower level only.Dedicated to Prof. Dr. F. R. Schwarzl on the occasion of his 60th birthday     

Numerical simulations of counter-current two-phase flow experiments in a PWR hot leg model using an interfacial area density model

In order to improve the understanding of counter-current two-phase flows and to validate new physical models, CFD simulations of 1/3rd scale model of the hot leg of a German Konvoi PWR with rectangular cross section was performed. Selected counter-current flow limitation (CCFL) experiments at the Helmholtz–Zentrum Dresden–Rossendorf (HZDR) were calculated with ANSYS CFX 12.1 using the multi-fluid Euler–Euler modeling approach. The transient calculations were carried out using a gas/liquid inhomogeneous multiphase flow model coupled with a k-ω turbulence model for each phase. In the simulation, the surface drag was approached by a new correlation inside the Algebraic Interfacial Area Density (AIAD) model. The AIAD model allows the detection of the morphological form of the two phase flow and the corresponding switching via a blending function of each correlation from one object pair to another. As a result this model can distinguish between bubbles, droplets and the free surface using the local liquid phase volume fraction value. A comparison with the high-speed video observations shows a good qualitative agreement. The results indicated that quantitative agreement of the CCFL characteristics between calculation and experimental data was obtained. The goal is to provide an easy usable AIAD framework for all Code users, with the possibility of the implementation of their own correlations.     

A prediction of the pressure field in a plane turbulent jet using an algebraic stress model

A numerical prediction is obtained for the mean pressure field in the similarity region of a plane turbulent jet. An algebraic stress model, which introduces non-isotropic relations for the Reynolds stress components, is used to close the mean momentum equation. The full two-dimensional form of the transport equations is retained and the resultant equation set solved elliptically. The numerical prediction simulates many of the characteristics of the pressure field measured by experimental studies. However, the overall level of the predicted field is lower than the experimental values. The level obtained for the mean pressure field depends strongly on the prediction for the transverse normal Reynolds stress component 〈u₂u₂〉. The pressure field is shown to represent a small negative contribution to the net strearnwise momentum balance.     

Force prediction equation using distorted model as an analog device

The force versus speed response of a distorted model of a soil-engaging tool operating in a soil and at a depth where the performance evaluation of the prototype is required to be determined, is used to compute analog values. A prediction equation relating draft force with tool width, depth of cut, soil specific weight, tool velocity and analog values has been developed. A comparison between the forces predicted by the equation and that measured on flat rectangular blades and angled tools operating at a speed of 2–8.5 km/hr is presented. The closeness in prediction accuracies points that the distorted model itself can be used as a fairly good analog device.     

Micro-mechanical approximation to the stress field around an inclined fiber of FRCC

Matrix spalling or crushing is one of the important mechanisms of fiber-matrix interaction of fiber reinforced cementitious composites (FRCC). The fiber pullout mechanisms have been extensively studied for an aligned fiber but matrix failure is rarely investigated since it is thought not to be a major affect. However, for an inclined fiber, the matrix failure should not be neglected. Due to the complex process of matrix spalling, experimental investigation and analytical study of this mechanism are rarely found in literature. In this paper, it is assumed that the load transfer is concentrated within the short length of the inclined fiber from the exit point towards anchored end and follows the exponential law. The Mindlin formulation is employed to calculate the 3D stress field. The simulation gives much information about this field. The 3D approximation of the stress state around an inclined fiber helps to qualitatively understand the mechanism of matrix failure. Finally, a spalling criterion is proposed by which matrix spalling occurs only when the stress in a certain volume, rather than the stress at a small point, exceeds the material strength. This implies some local stress redistribution after first yield. The stress redistribution results in more energy input and higher load bearing capacity of the matrix. In accordance with this hypothesis, the evolution of matrix spalling is demonstrated. The accurate prediction of matrix spalling needs the careful determination of the parameters in this model. This is the work of further study.     

Numerical-analytical method to determine the stress state of an elastic rectangular plate

A numerical-analytical method for solving the plane problem of elasticity is proposed. Systems of nonorthogonal functions are used. The method involves the minimization of a quadratic form that is equal to the integral of the sum of squared residuals of the solution and given forces. An explicit expression for stresses is derived. Bessel's inequality and the convergence of the solution are proved. The accuracy of the boundary conditions is estimated. The stress and strain distribution in the plate depending on the maximum magnitude of distributed forces and the size of their localization area is analyzed numerically. New quantitative and qualitative features of the stress distribution in the plate are established __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 1, pp. 90–98, January 2008.     

An alternative approach to the heat equation

The technique of conformal transformations of the metric, widely used in general relativity and in cosmology, is applied to the analysis of heat conduction in an anisotropic medium, in which the thermal conductivity is described by a tensor instead of a scalar. The anisotropic medium is reduced to an effective equivalent one, which is isotropic. The simplification is achieved for a particular conformal factor of the transformation, uniquely determined under physically reasonable assumptions on the thermal conductivity, density, and specific heat of the medium. Another application consists in the formal elimination of source or sink terms from the heat equation by using a suitable conformal transformation.

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