An implicit BEM formulation to model strong discontinuities in solids

A boundary element method (BEM) formulation to predict the behavior of solids exhibiting displacement (strong) discontinuity is presented. In this formulation, the effects of the displacement jump of a discontinuity interface embedded in an internal cell are reproduced by an equivalent strain field over the cell. To compute the stresses, this equivalent strain field is assumed as the inelastic part of the total strain. As a consequence, the non-linear BEM integral equations that result from the proposed approach are similar to those of the implicit BEM based on initial strains. Since discontinuity interfaces can be introduced inside the cell independently on the cell boundaries, the proposed BEM formulation, combined with a tracking scheme to trace the discontinuity path during the analysis, allows for arbitrary discontinuity propagation using a fixed mesh. A simple technique to track the crack path is outlined. This technique is based on the construction of a polygonal line formed by segments inside the cells, in which the assumed failure criterion is reached. Two experimental concrete fracture tests were analyzed to assess the performance of the proposed formulation.

Gelation of siloxane-poly(oxypropylene) composites

The viscoelastic properties of siloxane-poly(oxypropylene) (PPO) nanocomposites prepared by the sol-gel process has been analyzed during gelation by dynamic rheological measurements. The changes of storage and loss moduli, complex viscosity and phase angle has been measured as a function of time showing the newtonian viscosity of the sol in the initial step of gelation, and its progressive transformation to a viscoelastic gel. The rheologic properties have been correlated to mass fractal, nearly linear growth models and percolation theory. This study, completed by quasi-elastic light scattering and Si-29 solid state nuclear magnetic resonance measurements, shows that the mechanisms of gelation of siloxane-PPO hybrids depend on the molecular weight of the polymer and on the pH of the hybrid sol. For hybrids prepared in acid medium, a polymerization involving silicon reactive species located at the extremity of the polymer chains and presenting a functionality f = 2 occurs, forming a fractal structure during the first stage of sol-gel transition. For samples prepared under neutral pH, the fractal growth is only observed for hybrids containing short polymer chains (M-w similar to 130 gmol(-1)). The fractal dimensionality determined from the change in the rheological properties, indicates that the fractal growth mechanism changes from reaction-limited to diffusion-limited aggregation when the molecular weight of the PPO increases from 130 to 4000 gmol(-1) and as catalyst conditions change from acidic to neutral. Near the gel point, these hybrid gels have the typical scaling behavior expected from percolation theory. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Rheological study of the thermoreversible sol-gel transition of sulfate modified zirconyl chloride aqueous sol

The sols prepared by mixing a ZrOCl2 acidified solution to a hot H2SO4 aqueous solutions were studied in order to clarify the mechanism of thermoreversible sol-gel transition observed in this system. The viscoelastic properties of these suspensions were analyzed during the sol-gel transition by dynamic rheological measurements and quasi-elastic light scattering. The rheological properties were correlated to mass fractal and nearly linear growth models, and percolation theory. The results evidence that the thermoreversible sol-gel transition in this system is due to the formation of a network of physically linked aggregates having fractal structure. The decrease of the SO42- contents in the initial solution leads to the decrease of the fractal dimensionality from 2.3 to 1.8, indicating a change of the kinetic mechanism of aggregate growth. Near the gel point these samples have the typical scaling expected from percolation theory. (C) 2004 Elsevier B.V. All rights reserved.

Viscoelastic behavior of persimmons dried at constant air temperature

The viscoelastic behavior of dried persimmons at different air-drying temperatures and velocities was evaluated. Air temperatures and velocities were varied according to a second-order central composite design, with temperature ranging from 40degreesC to 70degreesC and air velocity from 0.8 to 2.0 m/s. After drying, persimmons were equilibrated at four different water activities: 0.432, 0.576, 0.625 and 0.751. The rheological behavior of dried and conditioned persimmons was studied under uniaxial compression-relaxation tests. Three different rheological models were fitted to the experimental relaxation curves: Maxwell, Generalized Maxwell and Peleg and Normand. Based on the root mean square of residuals, the Generalized Maxwell model showed the best fit and a regression analysis was applied to obtain response surfaces for the model parameters. The dependence of the rheological properties on water activity was also analysed. Results showed that only the linear effect of air temperature was significant at a 5% level on the equilibrium stress and relaxation times. In a general way, these parameters increased with increasing air temperature and decreasing water activity. (C) 2004 Swiss Society of Food Science and Technology. Published by Elsevier Ltd. All rights reserved.

Influence of viscoelastic characteristics of the colloidal suspensions on the formation of SnO2 supported membranes

SnO2 supported membranes have been prepared by sol-casting on alumina tubular substrate, using aqueous colloidal suspensions prepared by sol-gel route. The viscoelastic behaviour during sol ageing was analyzed by dinamic rheologial measurements. The complex viscosity and the storage and loss moduli have been followed during the sol-gel transition and the results have been correlated with the linear aggregates growth and the scalar percolation models. The scanning electron microscopy has evidenced that the homogeneity and thickness of the membrane depend on the sol ageing time. Crack-free and homogeneous membranes have been obtained for coated layers of 0.5μm thickness. © 1997 Trans Tech Publications.

Giant non-linear absorption in Er3+-doped fluoroindate glass

Non-linear absorption is observed in Er3+-doped fluoroindate glass (in mol% 37InF2:20ZnF2:20SrF2:16BaF2:2GdF2: 2NaF:1GaF3:2ErF3) when the sample is irradiated with a CW laser emitting at 650 nm. An intensity dependence of the optical transmittance is detected. Saturation and sequential absorption of two photons are responsible for the decrease of 50% in the transmittance. The results are explained by simple models which are solved based on rate-equations for the populations of energy levels.

Evolution of the viscoelastic properties of SnO2 colloidal suspensions during the sol-gel transition

This paper describes the effect of the concentration of electrolyte and pH on the kinetics of aggregation and gelation processes of SnO2 colloidal suspensions. Creep, creep-recovery, and oscillatory rheological experiments have been done in situ during aggregation and gelation. A phenomenological description of the structure of the colloidal system is given from the time evolution of rheological parameters. The dependence of the equilibrium steady-state shear compliance on the terminal region of clusters or aggregates seems to be a way to determine the beginning of interconnection of aggregates and the gel point. We propose that at this point the equilibrium steady-state compliance is a minimum. The steady-state viscosity determined from creep experiment can be fit with a power law with the extent of the transformation, giving critical exponent s = 0.7 ± 0.1. The value of the critical exponent Δ = 0.78 ± 0.05 was determined from oscillatory experiment. These results indicate that gelation of SnO2 colloidal suspension exhibits the typical scale expected from the scalar percolation theory. © 2000 Elsevier Science B.V. All rights reserved.

Dielectric and viscoelastic properties of cross-linked polyethylene aged under multi stressing conditions

Different measurements were performed in cross-linked polyethylene (XLPE) employed as insulating material in coaxial cables that were field-aged and laboratory-aged under multi-stressing conditions at room temperature. Samples were peeled from the XLPE cable insulation in three different positions: just below the external semiconductor layer (outer layer), in the middle (middle layer) and just above the internal semiconductor layer of the cable (inner layer). The imaginary part of the electric susceptibility showed three peaks that obey the Dissado-Hill model. For laboratory-aged XLPE samples peeled from the inner and from the middle positions the peak at very low frequency region increased while in samples from the outer position a quasi-DC conduction process was observed. In medium frequency range a broadening of the peak was observed for all samples. Viscoelastic properties determined through dynamic mechanical analysis suggested that the aging generates processes that promoted changes of the crystallinity and the cross-linking degrees of the polymer. Fourier transform infrared spectroscopy (FTIR) measurements revealed an increase of oxidation products (esters), evidence of polar residues of the bow-tie tree and the presence of cross-linking by-products (acetophenone). Optical and scanning electronic microscope (SEM) measurements in aged samples revealed the existence of voids and bow-tie trees that were formed during aging in the middle region of the cable.

Numerical assessment of mass conservation on a MAC-type method for viscoelastic free surface flows

A numerical study of mass conservation of MAC-type methods is presented, for viscoelastic free-surface flows. We use an implicit formulation which allows for greater time steps, and therefore time marching schemes for advecting the free surface marker particles have to be accurate in order to preserve the good mass conservation properties of this methodology. We then present an improvement by using a Runge-Kutta scheme coupled with a local linear extrapolation on the free surface. A thorough study of the viscoelastic impacting drop problem, for both Oldroyd-B and XPP fluid models, is presented, investigating the influence of timestep, grid spacing and other model parameters to the overall mass conservation of the method. Furthermore, an unsteady fountain flow is also simulated to illustrate the low mass conservation error obtained.

Modelagem da produção acumulada de biogás em biodigestores tipo batelada segundo a porcentagem de inóculo adicionada utilizando os modelos de regressão não-linear de Gompertz e expoencial

Pós-graduação em Agronomia (Energia na Agricultura) - FCA

Análise linear e espacial entre alguns atributos produtivos e tecnológicos da cana- de-açúcar com o pH de um argissolo vermelho de Suzanápolis (SP)

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Dynamic analysis for different finite element models of beams with viscoelastic damping layer

Many new viscoelastic materials have been developed recently to help improve noise and vibration levels in mechanical structures for applications in automobile and aeronautical industry. The viscoelastic layer treatment applied to solid metal structures modifies two main properties which are related to the mass distribution and the damping mechanism. The other property controlling the dynamics of a mechanical system is the stiffness that does not change much with the viscoelastic material. The model of such system is usually complex, because the viscoelastic material can exhibit nonlinear behavior, in contrast with the many available tools for linear dynamics. In this work, the dynamic behavior of sandwich beam is modeled by finite element method using different element types which are then compared with experimental results developed in the laboratory for various beams with different viscoelastic layer materials. The finite element model is them updated to help understand the effects in the damping for various natural frequencies and the trade-off between attenuation and the mass add to the structure.

MECHANICAL TESTING DEVICE FOR VISCOELASTIC BIOMATERIALS

Nearly all biologic tissues exhibit viscoelastic behavior. This behavior is characterized by hysteresis in the response of the material to load or strain. This information can be utilized in extrapolation of life expectancy of vascular implant materials including native tissues and synthetic materials. This behavior is exhibited in many engineering materials as well such as the polymers PTFE, polyamide, polyethylene, etc. While procedures have been developed for evaluating the engineering polymers the techniques for biologic tissues are not as mature. There are multiple reasons for this. A major one is a cultural divide between the medical and engineering communities. Biomedical engineers are beginning to fill that void. A digitally controlled drivetrain designed to evaluate both elastic and viscoelastic characteristics of biologic tissues has been developed. The initial impetus for the development of this device was to evaluate the potential for human umbilical tissue to serve as a vascular graft material. The consequence is that the load frame is configured for membrane type specimens with rectangular dimensions of no more than 25mm per side. The designed load capacity of the drivetrain is to impose an axial load of 40N on the specimen. This drivetrain is capable of assessing the viscoelastic response of the specimens by four different test modes: stress relaxation, creep, harmonic induced oscillations, and controlled strain rate tests. The fluorocarbon PTFE has mechanical properties commensurate with vascular tissue. In fact, it has been used for vascular grafts in patients who have been victims of various traumas. Hardware and software validation of the device was accomplished by testing PTFE and comparing the results to properties that have been published by both researchers and manufacturers.

Numerical simulation of some viscoelastic fluids

Numerical simulation of the Oldroyd-B type viscoelastic fluids is a very challenging problem. rnThe well-known High Weissenberg Number Problem" has haunted the mathematicians, computer scientists, and rnengineers for more than 40 years. rnWhen the Weissenberg number, which represents the ratio of elasticity to viscosity, rnexceeds some limits, simulations done by standard methods break down exponentially fast in time. rnHowever, some approaches, such as the logarithm transformation technique can significantly improve rnthe limits of the Weissenberg number until which the simulations stay stable. rnrnWe should point out that the global existence of weak solutions for the Oldroyd-B model is still open. rnLet us note that in the evolution equation of the elastic stress tensor the terms describing diffusive rneffects are typically neglected in the modelling due to their smallness. However, when keeping rnthese diffusive terms in the constitutive law the global existence of weak solutions in two-space dimension rncan been shown. rnrnThis main part of the thesis is devoted to the stability study of the Oldroyd-B viscoelastic model. rnFirstly, we show that the free energy of the diffusive Oldroyd-B model as well as its rnlogarithm transformation are dissipative in time. rnFurther, we have developed free energy dissipative schemes based on the characteristic finite element and finite difference framework. rnIn addition, the global linear stability analysis of the diffusive Oldroyd-B model has also be discussed. rnThe next part of the thesis deals with the error estimates of the combined finite element rnand finite volume discretization of a special Oldroyd-B model which covers the limiting rncase of Weissenberg number going to infinity. Theoretical results are confirmed by a series of numerical rnexperiments, which are presented in the thesis, too.

Analysis and numerical solution of the Peterlin viscoelastic model

Liquids and gasses form a vital part of nature. Many of these are complex fluids with non-Newtonian behaviour. We introduce a mathematical model describing the unsteady motion of an incompressible polymeric fluid. Each polymer molecule is treated as two beads connected by a spring. For the nonlinear spring force it is not possible to obtain a closed system of equations, unless we approximate the force law. The Peterlin approximation replaces the length of the spring by the length of the average spring. Consequently, the macroscopic dumbbell-based model for dilute polymer solutions is obtained. The model consists of the conservation of mass and momentum and time evolution of the symmetric positive definite conformation tensor, where the diffusive effects are taken into account. In two space dimensions we prove global in time existence of weak solutions. Assuming more regular data we show higher regularity and consequently uniqueness of the weak solution. For the Oseen-type Peterlin model we propose a linear pressure-stabilized characteristics finite element scheme. We derive the corresponding error estimates and we prove, for linear finite elements, the optimal first order accuracy. Theoretical error of the pressure-stabilized characteristic finite element scheme is confirmed by a series of numerical experiments.