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Constitutive Equations (constitutive + equation)
Kinds of Constitutive Equations Selected AbstractsTheory and numerics of geometrically non-linear open system mechanicsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2003E. Kuhl Abstract The present contribution aims at deriving a general theoretical and numerical framework for open system thermodynamics. The balance equations for open systems differ from the classical balance equations by additional terms arising from possible local changes in mass. In contrast to existing formulations, these changes not only originate from additional mass sources or sinks but also from a possible in- or outflux of matter. Constitutive equations for the mass source and the mass flux are discussed for the particular model problem of bone remodelling in hard tissue mechanics. Particular emphasis is dedicated to the spatial discretization of the coupled system of the balance of mass and momentum. To this end we suggest a geometrically non-linear monolithic finite element based solution technique introducing the density and the deformation map as primary unknowns. It is supplemented by the consistent linearization of the governing equations. The resulting algorithm is validated qualitatively for classical examples from structural mechanics as well as for biomechanical applications with particular focus on the functional adaption of bones. It turns out that, owing to the additional incorporation of the mass flux, the proposed model is able to simulate size effects typically encountered in microstructural materials such as open-pored cellular solids, e.g. bones. Copyright © 2003 John Wiley & Sons, Ltd. [source] Momentum and heat transfer over a continuously moving surface with a parallel free stream in a viscoelastic fluidNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 2 2010T. Hayat Abstract The flow and heat transfer characteristics for a continuous moving surface in a viscoelastic fluid are investigated. Constitutive equations of viscoelastic fluid obey the second-grade model. Analytic expressions to velocity and temperature have been developed by employing homotopy analysis method. The criterion to the convergence of the solution is properly discussed. Furthermore, the values of skin friction coefficient and the local Nusselt number have been computed and discussed. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010 [source] The effect of annealing on the nonlinear viscoelastic response of isotactic polypropylenePOLYMER ENGINEERING & SCIENCE, Issue 4 2003Aleksey D. Drozdov Three series of tensile relaxation tests are performed on isotactic polypropylene at room temperature in the vicinity of the yield point. In the first series of experiments, injection-molded samples are used without thermal pre-treatment. In the second and third series, the specimens are annealed at 130°C for 4 and 24 hours, respectively. Constitutive equations are derived for the time-dependent response of semicrystalline polymers at isothermal loading with small strains. A polymer is treated as an equivalent temporary network of macromolecules bridged by junctions (physical cross-links, entanglements and crystalline lamellae). Under loading, junctions slide with respect to their positions in the bulk material (which reflects the viscoplastic behavior), whereas active strands separate from their junctions and dangling strands merge with the network at random times (which reflects the viscoelastic response). The network is thought of as an ensemble of meso-regions (MRs) with various activation energies for detachment of chains from temporary nodes. Adjustable parameters in the stress-strain relations are found by fitting the observations. The experimental data demonstrate that the relaxation spectrum (characterized by the distribution of MRs with various potential energies) is independent of mechanical factors, but is altered at annealing. For specimens not subjected to thermal treatment, the growth of longitudinal strain does not affect the volume fraction of active MRs and the attempt rate for detachment of chains from their junctions. For annealed samples, the concentration of active MRs increases and the attempt rate decreases with strain. These changes in the time-dependent response are attributed to broadening of the distribution of strengths of lamellae at annealing. [source] An electromagnetic modelling tool for the detection of hydrocarbons in the subsoilGEOPHYSICAL PROSPECTING, Issue 2 2000Carcione Electromagnetic geophysical methods, such as ground-penetrating radar (GPR), have proved to be optimal tools for detecting and mapping near-surface contaminants. GPR has the capability of mapping the location of hydrocarbon pools on the basis of contrasts in the effective permittivity and conductivity of the subsoil. At radar frequencies (50 MHz to 1 GHz), hydrocarbons have a relative permittivity ranging from 2 to 30, compared with a permittivity for water of 80. Moreover, their conductivity ranges from zero to 10 mS/m, against values of 200 mS/m and more for salt water. These differences indicate that water/hydrocarbon interfaces in a porous medium are electromagnetically ,visible'. In order to quantify the hydrocarbon saturation we developed a model for the electromagnetic properties of a subsoil composed of sand and clay/silt, and partially saturated with air, water and hydrocarbon. A self-similar theory is used for the sandy component and a transversely isotropic constitutive equation for the shaly component, which is assumed to possess a laminated structure. The model is first verified with experimental data and then used to obtain the properties of soils partially saturated with methanol and aviation gasoline. Finally, a GPR forward-modelling method computes the radargrams of a typical hydrocarbon spill, illustrating the sensitivity of the technique to the type of pore-fluid. The model and the simulation algorithm provide an interpretation methodology to distinguish different pore-fluids and to quantify their degree of saturation. [source] Analysis of the steady-state flow of a compressible viscoplastic medium over a wedgeINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 6 2006Oana Cazacu Abstract A new model for calculating the resistance to penetration into geological or geologically derived materials is proposed. We assume steady-state flow of the target material over the penetrator. The target medium is described by a rate dependent constitutive equation that accounts for combined effects of strain rate and compaction on yielding. The wedge-shaped penetrator is considered to be rigid. The influence of the characteristics of the penetrator/target interface, impact velocity, target mechanical properties and nose geometry on the resistance to penetration is investigated. It is found that for low to intermediate impact velocities, accounting for friction results in a blunter optimal wedge geometry for optimal penetration performance. Copyright © 2005 John Wiley & Sons, Ltd. [source] Shear band evolution and accumulated microstructural development in Cosserat mediaINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 10 2004A. Tordesillas Abstract This paper prepares the ground for the continuum analysis of shear band evolution using a Cosserat/micropolar constitutive equation derived from micromechanical considerations. The nature of the constitutive response offers two key advantages over other existing models. Firstly, its non-local character obviates the mathematical difficulties of traditional analyses, and facilitates an investigation of the shear band evolution (i.e. the regime beyond the onset of localization). Secondly, the constitutive model parameters are physical properties of particles and their interactions (e.g. particle stiffness coefficients, coefficients of inter-particle rolling friction and sliding friction), as opposed to poorly understood fitting parameters. In this regard, the model is based on the same material properties used as model inputs to a discrete element (DEM) analysis, therefore, the micromechanics approach provides the vehicle for incorporating results not only from physical experiments but also from DEM simulations. Although the capabilities of such constitutive models are still limited, much can be discerned from their general rate form. In this paper, an attempt is made to distinguish between those aspects of the continuum theory of localization that are independent of the constitutive model, and those that require significant advances in the understanding of micromechanics. Copyright © 2004 John Wiley & Sons, Ltd. [source] Gradient plasticity modelling of strain localization in granular materialsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 6 2004O. Al Hattamleh Abstract The flow stress in the yield surface of plastic constitutive equation is modified with a higher order gradient term of the effective plastic strain to model the effect of inhomogeneous deformation in granular materials. The gradient constitutive model has been incorporated into the finite element code ABAQUS and used to simulate biaxial shear tests on dry sand. It is shown that the shape of the post-peak segment of the load displacement curve predicted by the numerical analysis is dependent on the mesh size when gradient term is not used. Use of an appropriate gradient coefficient is shown to correct this and predict a unique shape of the load displacement curve regardless of the mesh size. The gradient coefficient required turns out to be approximately inversely proportional to the mesh elemental area. Use of the strain gradient term is found to diffuse the concentration of plastic strains within shear band resulting in its consistent width. The coefficient of the higher gradient term appears as a function of the grain size, the mean confining stress, and the plastic softening modulus. Copyright © 2004 John Wiley & Sons, Ltd. [source] A large time incremental finite element method for finite deformation problem,INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 11 2001Y. Liu Abstract Based on the process optimal control variational principle, some new ideas for finite deformation analysis using large increment are proposed. Combined with hyperelastic,plastic constitutive equation, the governing equations and the corresponding numerical algorithm are formulated. The proposed approaches are validated with the application to the analysis for finite deformation involving contact and friction. Copyright © 2001 John Wiley & Sons, Ltd. [source] Lagrangian finite element treatment of transient vibration/acoustics of biosolids immersed in fluidsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2008P. Krysl Abstract Superposition principle is used to separate the incident acoustic wave from the scattered and radiated waves in a displacement-based finite element model. An absorbing boundary condition is applied to the perturbation part of the displacement. Linear constitutive equation allows for inhomogeneous, anisotropic materials, both fluids and solids. Displacement-based finite elements are used for all materials in the computational volume. Robust performance for materials with limited compressibility is achieved using assumed-strain nodally integrated simplex elements or incompatible-mode brick elements. A centered-difference time-stepping algorithm is formulated to handle general damping accurately and efficiently. Verification problems (response of empty steel cylinder immersed in water to a step plane wave, and scattering of harmonic plane waves from an elastic sphere) are discussed for assumed-strain simplex and for voxel-based brick finite element models. A voxel-based modeling scheme for complex biological geometries is described, and two illustrative results are presented from the bioacoustics application domain: reception of sound by the human ear and simulation of biosonar in beaked whales. Copyright © 2007 John Wiley & Sons, Ltd. [source] The least-squares meshfree method for elasto-plasticity and its application to metal forming analysisINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2005Kie-Chan Kwon Abstract A new meshfree method for the analysis of elasto-plastic deformation is presented. The method is based on the proposed first-order least-squares formulation for elasto-plasticity and the moving least-squares approximation. The least-squares formulation for classical elasto-plasticity and its extension to an incrementally objective formulation for finite deformation are proposed. In the formulation, equilibrium equation and flow rule are enforced in least-squares sense, i.e. their squared residuals are minimized, and hardening law and loading/unloading condition are enforced pointwise at each integration point. The closest point projection method for the integration of rate-form constitutive equation is inherently involved in the formulation, and thus the radial-return mapping algorithm is not performed explicitly. The proposed formulation is a mixed-type method since the residuals are represented in a form of first-order differential system using displacement and stress components as nodal unknowns. Also the penalty schemes for the enforcement of boundary and frictional contact conditions are devised and the reshaping of nodal supports is introduced to avoid the difficulties due to the severe local deformation near contact interface. The proposed method does not employ structure of extrinsic cells for any purpose. Through some numerical examples of metal forming processes, the validity and effectiveness of the method are discussed. Copyright © 2005 John Wiley & Sons, Ltd. [source] Computational issues in large strain elasto-plasticity: an algorithm for mixed hardening and plastic spinINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2005Francisco Javier Montáns Abstract In this paper an algorithm for large strain elasto-plasticity with isotropic hyperelasticity based on the multiplicative decomposition is formulated. The algorithm includes a (possible) constitutive equation for the plastic spin and mixed hardening in which the principal stress and principal backstress directions are not necessarily preserved. It is shown that if the principal trial stress directions are preserved during the plastic flow (as assumed in some algorithms) a plastic spin is inadvertently introduced for the kinematic/mixed hardening case. If the formulation is performed in the principal stress space, a rotation of the backstress is inadvertently introduced as well. The consistent linearization of the algorithm is also addressed in detail. Copyright © 2005 John Wiley & Sons, Ltd. [source] Computability in non-linear solid mechanicsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1-2 2001T. Belytschko Abstract The computability of non-linear problems in solid and structural mechanics problems is examined. Several factors which contribute to the level of difficulty of a simulation are discussed: the smoothness and stability of the response, the required resolution, the uncertainties in the load, boundary conditions and initial conditions and inadequacies and uncertainties in the constitutive equation. An abstract measure of the level of difficulty is proposed, and some examples of typical engineering simulations are classified by this measure. We have put particular emphasis on engineering calculations, where many of the factors that diminish computability play a prominent role. Copyright © 2001 John Wiley & Sons, Ltd. [source] Transient free-surface flow of a viscoelastic fluid in a narrow channelINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2004Roger E. Khayat Abstract The interplay between inertia and elasticity is examined for transient free-surface flow inside a narrow channel. The lubrication theory is extended for the flow of viscoelastic fluids of the Oldroyd-B type (consisting of a Newtonian solvent and a polymeric solute). While the general formulation accounts for non-linearities stemming from inertia effects in the momentum conservation equation, and the upper-convected terms in the constitutive equation, only the front movement contributes to non-linear coupling for a flow inside a straight channel. In this case, it is possible to implement a spectral representation in the depthwise direction for the velocity and stress. The evolution of the flow field is obtained locally, but the front movement is captured only in the mean sense. The influence of inertia, elasticity and viscosity ratio is examined for pressure-induced flow. The front appears to progress monotonically with time. However, the velocity and stress exhibit typically a strong overshoot upon inception, accompanied by a plug-flow behaviour in the channel core. The flow intensity eventually diminishes with time, tending asymptotically to Poiseuille conditions. For highly elastic liquids the front movement becomes oscillatory, experiencing strong deceleration periodically. A multiple-scale solution is obtained for fluids with no inertia and small elasticity. Comparison with the exact (numerical) solution indicates a wide range of validity for the analytical result. Copyright © 2004 John Wiley & Sons, Ltd. [source] Development of an optimal hybrid finite volume/element method for viscoelastic flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2003M. Aboubacar Abstract A cell-vertex hybrid finite volume/element method is investigated that is implemented on triangles and applied to the numerical solution of Oldroyd model fluids in contraction flows. Particular attention is paid to establishing high-order accuracy, whilst retaining favourable stability properties. Elevated levels of elasticity are sought. The main impact of this study reveals that switching from quadratic to linear finite volume stress representation with discontinuous stress gradients, and incorporating local reduced quadrature at the re-entrant corner, provide enhance stability properties. Solution smoothness is achieved by adopting the non-conservative flux form with area integration, by appealing to quadratic recovered velocity-gradients, and through consistency considerations in the treatment of the time term in the constitutive equation. In this manner, high-order accuracy is maintained, stability is ensured, and the finer features of the flow are confirmed via mesh refinement. Lip vortices are observed for We>1, and a trailing-edge vortex is also apparent. Loss of evolution and solution asymptotic behaviour towards the re-entrant corner are also discussed. Copyright © 2003 John Wiley & Sons, Ltd. [source] Simulation of dry-spinning process of polyimide fibersJOURNAL OF APPLIED POLYMER SCIENCE, Issue 5 2009Gang Deng Abstract As one type of high-performance fibers, the polyimide fibers can be prepared from the precursor polyamic acid via dry-spinning technology. Unlike the dry-spinning process of cellulose acetate fiber or polyurethane fiber, thermal cyclization reaction of the precursor in spinline with high temperature results in the relative complex in the dry-spinning process. However, the spinning process is considered as a steady state due to a slight degree of the imidization reaction from polyamic acid to polyimide, and therefore a one-dimensional model based on White-Metzer viscoelastic constitutive equation is adopted to simulate the formation of the fibers. The changes of solvent mass fraction, temperature, axial velocity, tensile stress, imidization degree, and glass transition temperature of the filament along the spinline were predicted. The effects of spinning parameters on glass transition temperature and imidization degree were thus discussed. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009 [source] Three-Dimensional Solar Cell Finite-Element Sintering SimulationJOURNAL OF THE AMERICAN CERAMIC SOCIETY, Issue 7 2009Gordon R. Brown The sintering process is ubiquitous in manufacturing, but the design-oriented modeling of sintering has presented considerable challenges. This type of modeling is necessary to be able to predict deformation and thus design appropriate powder compacts so that after they are sintered, the desired dimensions will be achieved. Currently this is done through a costly and time-consuming trial and error process. In our research, an application of the Skorohod,Olevsky viscous sintering constitutive equation in a finite-element (FE) model is developed and used to model solar cell manufacturing. Experimental measurements are used to determine the properties of the solar cell materials, and these are used to calculate the parameters for the FE model. Simulation results are compared with experimental data and analysis has been made to evaluate the adequacy and usefulness of this approach. [source] The minimum free energy for incompressible viscoelastic fluidsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 18 2006Giovambattista Amendola Abstract A general closed expression is given in the frequency domain for the isothermal minimum free energy of an incompressible viscoelastic fluid, whose constitutive equation is expressed by a linear functional of the history of strain. Another equivalent form of the minimum free energy is also derived and used to study the particular case of a discrete model material response. Copyright © 2006 John Wiley & Sons, Ltd. [source] Approximation of time-dependent, viscoelastic fluid flow: Crank-Nicolson, finite element approximation,NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 2 2004Vincent J. Ervin Abstract In this article we analyze a fully discrete approximation to the time dependent viscoelasticity equations with an Oldroyd B constitutive equation in ,, = 2, 3. We use a Crank-Nicolson discretization for the time derivatives. At each time level a linear system of equations is solved. To resolve the nonlinearities we use a three-step extrapolation for the prediction of the velocity and stress at the new time level. The approximation is stabilized by using a discontinuous Galerkin approximation for the constitutive equation. For the mesh parameter, h, and the temporal step size, ,t, sufficiently small and satisfying ,t , Ch, existence of the approximate solution is proven. A priori error estimates for the approximation in terms of ,t and h are also derived. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 248,283, 2004 [source] Constitutive modeling for intercalated PMMA/clay nanocomposite foamsPOLYMER ENGINEERING & SCIENCE, Issue 12 2006Choonghee Jo A constitutive model for tensile behavior of PMMA/clay nanocomposite foams was developed in this study. The elastic modulus of the nanocomposites is affected by the form of clays embedded in the polymer matrix. The reinforcing effect by intercalation of the clays and the detrimental effect by clay agglomeration were considered for the determination of the elastic modulus of the nanocomposites. A viscoelastic model was adapted for the tensile behavior of the material. The developed constitutive equation is expressed in terms of clay morphology and material properties. The aspect ratio of clays and the expansion of clay layer spacing in the intercalated clay clusters were proved to play a vital role in the reinforcing mechanism. For the verification of the constitutive model, Poly(methyl-methacrylate) (PMMA)/clay nanocomposite foams were manufactured by batch process method and their uniaxial tensile test results were compared with theoretical predictions. Compared with the experimental results, the proposed constitutive equation showed agreement with the experimental test results. POLYM. ENG. SCI. 46:1787,1796, 2006. © 2006 Society of Plastics Engineers. [source] Theoretical and experimental studies of anisotropic shrinkage in injection moldings of semicrystalline polymersPOLYMER ENGINEERING & SCIENCE, Issue 6 2006Keehae Kwon A novel approach to predict anisotropic shrinkage of semicrystalline polymers in injection moldings was proposed using flow-induced crystallization, frozen-in molecular orientation, elastic recovery, and PVT equation of state. The anisotropic thermal expansion and compressibility affected by the frozen-in orientation function and the elastic recovery that was not frozen during moldings were introduced to obtain the in-plane anisotropic shrinkages. The frozen-in orientation function was calculated from amorphous and crystalline contributions. The amorphous contribution was based on the frozen-in and intrinsic amorphous birefringence, whereas the crystalline contribution was based on the crystalline orientation function, which was determined from the elastic recovery and intrinsic crystalline birefringence. To model the elastic recovery and frozen-in stresses related to birefringence during molding process, a nonlinear viscoelastic constitutive equation was used with temperature- and crystallinity-dependent viscosity and relaxation time. Occurrence of the flow-induced crystallization was introduced through the elevation of melting temperature affected by entropy production during flow of the viscoelastic melt. Kinetics of the crystallization was modeled using Nakamura and Hoffman-Lauritzen equations with the rate constant affected by the elevated melting temperature. Numerous injection molding runs on polypropylene of various molecular weights were carried out by varying the packing time, flow rate, melt temperature, and mold temperature. The anisotropic shrinkage of the moldings was measured. Comparison of the experimental and simulated results indicated a good predictive capability of the proposed approach. POLYM. ENG. SCI., 46:712,728, 2006. © 2006 Society of Plastics Engineers [source] The draw ratio,Deborah number diagram: A useful tool for coating applicationsPOLYMER ENGINEERING & SCIENCE, Issue 3 2006S. Bourrigaud The understanding of the basic physical effects of viscoelasticity on drawing performances in the coating process leads to a useful approach to link the rupture of the polymer melt to critical processing conditions. In particular, we show that when solving the drawing problem in the air gap with a simple constitutive equation,like the upper convected Maxwell model,a mathematical inconsistency appears for some drawing parameters. This mathematical instability may be experimentally correlated to the occurrence of melt-rupture, giving rise to a discussion on the effect of viscoelastic properties on drawing performances. Results are given in terms of a diagram representing the maximum drawing ratio Dr with respect to the Deborah number De. A master curve, obtained form experimental results, accounts for the temperature, melt-index, air-gap height, and extrusion output dependences. The limitations of the "universality" of the concept are discussed later. POLYM. ENG. SCI. 46:372,380, 2006. © 2006 Society of Plastics Engineers [source] Study of particle trajectories, residence times and flow behavior in kneading discs of intermeshing co-rotating twin-screw extrudersPOLYMER ENGINEERING & SCIENCE, Issue 4 2004V. L. Bravo A three-dimensional finite element model was implemented for the solution of mass and momentum conservation equations in the kneading disc section of an intermeshing co-rotating twin-screw extruder. The polymer melt was modeled with a Carreau constitutive equation. The particle tracking technique was used to obtain residence times and analyze distributive mixing for different length to diameter ratios (L/D) of kneading discs. Previous studies from Kalyon et al. (1) and Cheng and Manas-Zloczower (2) have shown that the mixing performance of intermeshing co-rotating twin-screw extruders is highly dependent on the combination of screw configuration and operating conditions. The complexity of the geometry and the transient character of the flow demand powerful computational tools to characterize the flow and to develop a prediction tool for the analysis of relative performance between different configurations. Difficulties arise in the particle tracking technique because of the time discretization and the presence of moving boundaries. Results show the importance of particle history on the evaluation of the relative performance of different configurations of kneading blocks and suggest a reevaluation of the use of average flow characteristics for the analysis of mixing. Results also confirm the importance of an accurate description of the geometry and clearances in order to obtain information about relative mixing performance. Polym. Eng. Sci. 44:779,793, 2004. © 2004 Society of Plastics Engineers. [source] Generalized slit flow of an ellis fluidPOLYMER ENGINEERING & SCIENCE, Issue 11 2001Ryszard T. Steller Isothermal, steady-state and fully developed flows of Ellis fluids in planar and annular slits are discussed. The flow equations derived for Ellis fluids describe also the flows of Newtonian and power law fluids as specific cases. The most important flows resulting from thp general theory, i.e., the pressure flows in flat and annular slits for stationary channel walls and at transverse and longitudinal movements of a wall, are analyzed in detail. Numerical verification of the results leads to the conclusion that the planar and annular flows of Ellis and power law fluids are qualitatively similar The quantitative differences resulting from the slit curvature and the type of constitutive equation are relatively large only for flows of strongly non-New-tonian liquids. [source] Effect of non-isothermal oriented crystallization on the velocity and elongational viscosity profiles during the melt spinning of high density polyethylene fibersPOLYMER ENGINEERING & SCIENCE, Issue 7 2001A. Makradi Based on the experimental data of spine line temperature and percent crystallization, a time-integral constitutive equation has been used together with the degree of phase transformation theory to predict the velocity and elongational viscosity profiles. For the velocity profile, our predicted results are compared to experimental data and good agreement is found. Under a drawing force, the elongational viscosity profile shows a stress softening due to the molecular alignment; then the fiber hardens close to the take-up point, owing to filament crystallization. [source] On helical flows of polymer fluidsPOLYMER ENGINEERING & SCIENCE, Issue 6 2001Jae-Hyeuk Jeong Isothermal and non-isothermal steady helical flows are theoretically investigated under the assumption that the flow is fully developed in both the thermal and hydrodynamic senses. It is well known that the basic gross characteristics of steady isothermal helical flows of non-Newtonian liquids can be found relatively easily if the flow curve (or non-Newtonian viscosity) in simple shearing is known. Nevertheless, evaluation of more detailed viscoelastic properties in this type of flow is also sometimes desirable. These properties are shown to be exactly determined in both the isothermal and non-isothermal cases as soon as a nonlinear viscoelatic constitutive equation is specified. Shear thinning due to fluid rotation and strong temperature dependence of Newtonian viscosity highly increase dissipative heat. This can produce significant non-isothermal effects in intense helical flows, even when the wall temperature is kept uniform and constant. It is shown that the energy consumption in isothermal and non-isothermal helical flows is always higher than in respective annular flows with the same flow rate. Comparisons between our calculations and available experimental data are also discussed. [source] Overall numerical simulation of extrusion blow molding processPOLYMER ENGINEERING & SCIENCE, Issue 8 2000Shin-Ichiro Tanifuji This paper focuses on the overall numerical simulation of the parison formation and inflation process of extrusion blow molding. The competing effects due to swell and drawdown in the parison formation process were analyzed by a Lagrangian Eulerian (LE) finite element method (FEM) using an automatic remeshing technique. The parison extruded through an annular die was modeled as an axisymmetric unsteady nonisothermal flow with free surfaces and its viscoelastic properties were described by a K-BKZ integral constitutive equation. An unsteady die-swell simulation was performed to predict the time course of the extrudate parison shape under the influence of gravity and the parison controller. In addition, an unsteady large deformation analysis of the parison inflation process was also carried out using a three-dimensional membrane FEM for viscoelastic material. The inflation sequence for the parison molded into a complex-shaped mold cavity was analyzed. The numerical results were verified using experimental data from each of the sub-processes. The greatest advantage of the overall simulation is that the variation in the parison dimension caused by the swell and drawdown effect can be incorporated into the inflation analysis, and consequently, the accuracy of the numerical prediction can be enhanced. The overall simulation technique provides a rational means to assist the mold design and the determination of the optimal process conditions. [source] Effective Dynamic Material Properties of Foam-like MicrostructuresPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2005S. Alvermann The effective material parameters of a microstructured material can be found using homogenization procedures based on calculations of a Representative Volume Element (RVE) of the material. In our approach the RVE is calculated in frequency domain and inertia is taken into account, leading to a frequency dependent behavior of the RVE. With the frequency response of the RVE, effective dynamic properties of the material are calculated using an optimization procedure. Due to the frequency dependent material behavior on the microscale a viscoelastic constitutive equation is applied on the macroscale. An example calculation is presented for an auxetic 2-D foam-like microstructure which is modelled as a plane frame structure. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Short fibers suspension in steady recirculating flowsTHE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, Issue 3 2002Francisco Chinesta Abstract Numerical modeling of short fiber suspensions flows involves the coupling between motion equations, which definean elliptic problem, and the fluid constitutive equation, which introduces a non-linear advection problem related to the fiber orientation (induced anisotropy). In a previous work these authors have proposed a numerical procedure to determine a steady solution of the fibers orientation in steady recirculating flows, taking into account that neither initial nor boundary conditions are given. This procedure may be used in the numerical simulation of SFRT flows involving recirculating parts as encountered in the simulationof industrial processes, as well as in inverse rheological identification using, for example, rotative rheometric devices. La modélisation numérique des suspensions de fibres courtes implique le couplage entre les équations de mouvement (qui définissent un problème élliptique) et l'equation constitutive qui introduit un problème de transport non linéaire asocié à l'orientation des fibres. Les auteurs ont proposé, dans des travaux précédents, une technique numérique pour le calcul de l'orientation des fibres dans un écoulement stationnaire recirculant pour lequel les conditions aux limites et les conditions initiates ne sont pas connues. Cette technique peut être utilisée dans la simulation d'écoulements de fibres courtes présentant des recirculations, comme c'est le cas dans les écoulements industrielles en contraction ainsi que dans les instruments rhéométriques rotatifs. [source] A variable order constitutive relation for viscoelasticityANNALEN DER PHYSIK, Issue 7-8 2007L.E.S. Ramirez Abstract A constitutive relation for linear viscoelasticity of composite materials is formulated using the novel concept of Variable Order (VO) differintegrals. In the model proposed in this work, the order of the derivative is allowed to be a function of the independent variable (time), rather than a constant of arbitrary order. We generalize previous works that used fractional derivatives for the stress and strain relationship by allowing a continuous spectrum of non-integer dynamics to describe the physical problem. Starting with the assumption that the order of the derivative is a measure of the rate of change of disorder within the material, we develop a statistical mechanical model that is in agreement with experimental results for strain rates varying more than eight orders of magnitude in value. We use experimental data for an epoxy resin and a carbon/epoxy composite undergoing constant compression rates in order to derive a VO constitutive equation that accurately models the linear viscoelastic deformation in time. The resulting dimensionless constitutive equation agrees well with all the normalized data while using a much smaller number of empirical coefficients when compared to available models in the literature. [source] An Overview of the Anatomy of Crystal Plasticity ModelsADVANCED ENGINEERING MATERIALS, Issue 9 2009Georges Cailletaud Abstract Single crystals, polycrystals, and DS alloys can be modeled in the same framework by means of crystal plasticity. This paper wants to show the common features of the different approaches on the grain level, and the additional assumptions that are needed to derive polycrystal or DS models. Phenomenological rules are introduced for representing the hardening in the single crystal constitutive equations. Series of examples are given to illustrate the capabilities of the various approaches that are mainly related to the crystallographic character, and to the fact that the macroscopic yield locus is not predefined, but built from a collection of linear yield conditions. [source] | ||||||||||||||||||||||