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EN
In this paper, we consider a weakly dissipative viscoelastic equation with a nonlinear damping. A general decay rate is proved for a wide class of relaxation functions. To support our theoretical findings, some numerical results are provided.
2
Content available Effects of X-ray on fibroblast mechanical properties
EN
Concerning the widespread use of X-rays to detect various diseases, such as oral and dental ones, it is essential to study the effects of this radiation on living cells. From the past, genetic effects and cell death because of X-rays have been studied. In addition, the effect of this ionizing radiation on the mechanical properties of the cell and cytoskeleton has been studied, but different results have been obtained based on different models. In this study, post-culture gingival fibroblast cells were classified into two groups of control and radiation with Nano Magnetic Particles functionalized by folic acid. The cells of the radiation group were exposed to X-rays of 3 mGy·cm2 . The specimens were undergone static creep test by a magnetic tweezer. Spring and damper coefficients were obtained based on the viscoelastic solid modeling. The static and dynamic stiffness of the groups was also calculated. The maximum deformation was decreased after radiation from 0.049 ± 0.01 µm to 0.029 ± 0.01 µm and the static stiffness of the model was 1.6 times decreased. Also, the gel point frequency for the control group was 27 Hz and for the radiation group was 7.5 Hz. The results show that the static and dynamic stiffness of the cells decreases after radiation, and less deformation appears in the cells after irradiation. These changes can be due to the breakdown of membrane chemical bonds and activation of actin fibers after radiation.
EN
The example studies a forced response of plate with viscoelastic auxetic damper located at the free end of the plate. Damping elements consist of the cover layer and layer of viscoelastic material with positive or negative Poisson's ratio. Viscoelastic materials are often used for reduction of vibration (seismic or wind induced vibrations in building structures or other structures). The common feature is that the frequency of the forced vibrations is low. Calculations are made using finite element method with Comsol Multiphysics software.
EN
The article is presented to enhance our knowledge about the propagation of Lamb waves in the layer of a viscoelastic transversely isotropic medium in the context of thermoelasticity with GN theory of type-II and III. Secular equations for symmetric and skew-symmetric modes of wave propagation in completely separate terms are derived. The amplitudes of displacements and temperature distribution were also obtained. Finally, the numerical solution was carried out for cobalt and the dispersion curves, amplitudes of displacements and temperature distribution for symmetric and skew-symmetric wave modes are presented to evince the effect of anisotropy. Some particular cases are also deduced.
5
Content available remote Models Based on Mechanical Properties of Biological Cells in Microfluidics
EN
The paper is devoted to the modeling deformation of biological cell in microfluidic microchannel devices. The background and purpos of actual research is developing mechanical model of the biological cell shell for improving simulation and design of microfluidic lab-chip diagnostic devices.
EN
We consider a mathematical model which describes the equilibrium between a viscoelastic body in frictionless contact with an obstacle. The contact is modelled with normal compliance, associated with Signorini's conditions and adhesion. The adhesion is modelled with a surface variable, the bonding field, whose evolution is described by a first-order differential equation. We establish a variational formulation of the mechanical problem and prove the existence and uniqueness of the weak solution. The proof is based on arguments of evolution equations with multivalued maximal monotone operators, differential equations and the Banach fixed point theorem.
EN
Purpose: The aim of this study is to propose a method to construct corneal biomechanical model which is the foundation for simulation of corneal microsurgery. Methods: Corneal material has two significant characteristics: hyperelastic and viscoelastic. Firstly, Mooney–Rivlin hyperelastic model of cornea obtained based on stored-energy function can be simplified as a linear equation with two unknown parameters. Then, modified Maxwell viscoelastic model of the cornea, whose analytical form is consistent with the generalized Prony-series model, is proposed from the perspective of material mechanics. Results: Parameters of the model are determined by the uniaxial tensile tests and the stress-relaxation tests. Corneal material properties are simulated to verify the hyper-viscoelastic model and measure the effectiveness of the model in the finite element simulation. On this basis, an in vivo model of the corneal is built. And the simulation of extrusion in vivo cornea shows that the force is roughly nonlinearly increasing with displacement, and it is consistent with the results obtained by extrusion experiment of in vivo cornea. Conlusions: This paper derives a corneal hyper-viscoelastic model to describe the material properties more accurately, and explains the mathematical method for determination of the model parameters. The model is an effective biomechanical model, which can be directly used for simulation of trephine and suture in keratoplasty. Although the corneal hyper-viscoelastic model is taken as the object of study, the method has certain adaptability in biomechanical research of ophthalmology.
EN
To add damping to the system, viscoelastic materials (VEM) are added to structures, in order to enhance damping effects of the VEM, a constraining layer is attached. Due to the addition of the material on the system the fundamental characteristics of the systems are altered much. This paper analyzes the damping effect of the constraining layer on plate type structures numerically using the FEM software ANSYS. Experiments are conducted to validate the analytical results. The use of weightless composite materials as constraining layers has been analyzed. Results are compared with the conventional constraining layer materials. The results showed that composite materials give a better damping effect without much altering the fundamental characteristics.
EN
This paper presents the ground motion amplification scenario along with fundamental frequency (F0) of sedimentary deposit for the seismic microzonation of Kolkata City, situated on the world’s largest delta island with very soft soil deposit. A 4th order accurate SH-wave viscoelastic finite-difference algorithm is used for computation of response of 1D model for each borehole location. Different maps, such as for F0, amplification at F0, average spectral amplification (ASA) in the different frequency bandwidth of earthquake engineering interest are developed for a variety of end-users communities. The obtained ASA of the order of 3-6 at most of the borehole locations in a frequency range of 0.2510.0 Hz reveals that Kolkata City may suffer severe damage even during a moderate earthquake. Further, unexpected severe damage to collapse of multi-storey buildings may occur in localities near Hoogly River and Salt Lake area due to double resonance effects during distant large earthquakes.
EN
Energy stability of a horizontal layer of a two-component Maxwell fluid in a porous medium heated and salted from below is studied under the Oberbeck-Boussinesq-Darcy approximation using the Lyapunov direct method. The effect of stress relaxation on the linear and non-linear critical stability parameters is clearly brought out with coincidence between the two when the solute concentration is dilute. Qualitatively, the result of porous and clear fluid cases is shown to be similar. In spite of lack of symmetry in the problem it is shown that non linear exponential stability can be handled.
EN
In this paper an oscillatory flow of a viscoelastic, incompressible and electrically conducting fluid through a porous medium bounded by two infinite vertical parallel plates is discussed. One of these plates is subjected to a slip-flow condition and the other to a no-slip condition. The pressure gradient in the channel oscillates with time. A magnetic field of uniform strength is applied in the direction perpendicular to the plates. The induced magnetic field is neglected due to the assumption of a small magnetic Reynolds number. The temperature difference of the two plates is also assumed high enough to induce heat transfer due to radiation. A closed form analytical solution to the problem is obtained. The analytical results are evaluated numerically and then presented graphically to discuss in detail the effects of different parameters entering into the problem. A number of particular cases have been shown by dotted curves in the figures. During the analysis it is found that the physical and the mathematical formulations of the problems by Makinde and Mhone (2005), Mehmood and Ali (2007), Kumar et al. (2010) and Choudhury and Das (2012) are not correct. The correct solutions to all these important oscillatory flow problems are deduced.
EN
In this study, a nonlinear poroelastic model of intervertebral disc as an infrastructure was developed. Moreover, a new element was defined consisting a disc (Viscoelastic Euler Beam Element) and a vertebra (Rigid Link) as a unit element. Using the new element, three different viscoelastic finite element models were prepared for lumbar motion segment (L4/L5). Prolonged loading (short-term and longterm creep) and cyclic loading were applied to the models and the results were compared with results of in vivo tests. Simplification of the models by using the new element leads to reduction of the runtime of the models in dynamic analyses to few minutes without losing the accuracy in the results.
PL
W artykule przedstawiono wyniki numerycznego modelowania procesu walcowania blach M1E z zastosowaniem rozwiązań dla ciał lepkosprężystych. Przedstawione w artykule wyniki modelowania numerycznego mają na celu uwidocznienie problemu wpływu rozprężenia walcowanego materiału po wyjściu z kotliny walcowniczej na stan odkształceń. Uwzględnienie opóźnionych efektów lepkosprężystych jest niezbędne przy opracowaniu nowych technologii oraz podyktowane jest ciągłym dążeniem do zwiększenia dokładności obliczeń wymiarów walcowanych wyrobów płaskich. W pracy do badań numerycznych zastosowano model matematyczny opracowany w ramach pracy [1], który stosowany jest do analizy procesu walcowania ciał lepkosprężystych.
EN
The paper presents results of numerical modelling of the rolling process of plates M1 using solutions for viscoelastic bodies. The investigation numerical modelling results reported in the paper are intended to highlight the problem of the effect of rolled material expansion upon exit from the roll gap on the strain state. The need for taking into account the delayed viscoelastic effects in developing new technologies results from the constant attempts at achieving increasingly higher accuracy in the calculation of the dimensions of flat rolled products. In the paper mathematical model developed in the work [1] was used for the analysis of rolling process of viscoelastic bodies.
14
Content available remote Double - diffusive electro-convection in aqueous solutions of polymeric liquids
EN
The linear stability analysis of double-diffusive electroconvection in an aqueous- solution of a polymeric liquid is performed when a uniform DC electric field is applied. The polymeric liquid is assumed to be viscoelastic and the viscoelastic correction to the momentum equation is effected by considering the Jeffry constitutive equation. The eigenvalue at the onset of convection is obtained by employing the Rayleigh-Ritz technique for isothermal and isohaline boundary combination. The results of the study reveal that the strengths of the electric field and salinity delay the onset of convection. The classical results of the effect of the viscoelastic parameter on the onset of convection are found to be unaltered by the inducted electric field. The problem has industrial applications.
PL
W pracy przedstawiono i omówiono proces walcowania blach z zastosowaniem rozwiązań lepkosprężystych. Celem badań numerycznych było określenie wpływu opóźnionych efektów lepkosprężystych na przebieg procesu walcowania blach na zimno. W pracy określono wartości odkształceń walcowanej blachy w kotlinie walcowniczej oraz w strefie opóźnionych efektów lepkosprężystych metodą zatrzymanego obrazu.
EN
In the work was presented and discussed the problem of rolling plate using solutions for viscoelastic bodies. The aim of the numerical researches was the determination of the phenomena of delayed viscoelastic effects influence at the cold rolling plate. The values of deformations of rolled metal were defined with use digital analysis of freezing picture method in frames of work plates and were qualified in rolling gap and the zone of delayed viscoelastic.
16
Content available remote Lepkosprężystość tworzyw adhezyjnych
PL
W pracy przedstawiono problematykę modelowania lepkospreżystych właściwości tworzyw adhezyjnych. Do modelowania lepkosprężystych właściwości spoiny klejowej wykorzystano ciało Burgersa. Współczynniki elementów składowych ciała Burgersa wyznaczono na podstawie krzywych pełzania kleju. Stwierdzono, że istnieje możliwość badania zagadnień lepkospreżystosci tworzyw adhezyjnych metodami numerycznymi.
EN
Modeling viscoelastic properties of an adhesive materials issues are presented in the article. Modeling the properties of the adhesive layer using the Burgers body. The coefficients of the Burgers body components were determined on the basis of the creep curves of the epoxy adhesive. It was ascertained that it is possible to examine the problems viscoelastic properties of adhesive bonds using numerical analysis.
EN
Standard constitutive equations governing the HWKK/H, HWK/H and HW/H rheological models for hardening plastics are presented. Short/moderate/long-term deformations are simulated by the HWKK/H model described by 6 constants of viscoelasticity, i.e. 3 long-term creep coefficients and 3 retardation times. A computer aided algorithm for univocal identification of viscoelasticity constants of hardening plastics has been developed. The algorithm employs only time-histories of directional strains in the creep experiment of unidirectionally tensioned bar specimens. The elasticity and viscoelasticity constants have been identified for three important structural hardening plastics. The validation test of the HWKK/H rheological model has been also performed.
PL
W pracy sformułowano standardowe równania konstytutywne opisujące modele reologiczne HWKK/H, HWK/H oraz HW/H duroplastów. Model HWKK/H symulujący krótkotrwałe, średniotrwałe i długotrwałe deformacje, jest opisany przez 6 stałych lepkosprężystości, tj. 3 współczynniki pełzania długotrwałego i 3 czasy retardacji. Rozwinięto komputerowo wspomagany algorytm jednoznacznej identyfikacji stałych lepkosprężystości duroplastów. W algorytmie wykorzystuje się tylko eksperymentalnie zmierzone odkształcenia kierunkowe w procesie pełzania próbki prętowej rozciąganej osiowo. Stałe sprężystości i lepkosprężystości zidentyfikowano w odniesieniu do trzech duroplastów konstrukcyjnych o symbolach A590, E53 i P109. Wykonano również test walidacyjny modelu HWKK/H.
18
Content available remote On the implementation of viscoelastic models in commercial CFD programs
EN
Although finite-volume methods have significant advantages in terms of memory usage and computational speed, traditionally finite-element based programs are used to solve complex viscoelastic fluid dynamic problems. This work presents the successful extension of the commercial, finite volume based, state-of-the-art CFD software package FLUENTŽ to viscoelastic fluid flow problems, a feature which is not supported by the standard version of the program. Differential viscoelastic models of Maxwell-Type are implemented utilizing two principle capabilities of the software, i.e. the possibilities to define additional transport equations for each component of the viscoelastic stress tensor and to modify this equations using the programming interface, respectively. Results of an illustrative benchmark problem are presented, demonstrating the capability and accuracy of the proposed method to perform viscoelastic flow simulations up to a Deborah number of 100.
EN
The aim of the present problem is to investigate the efficiency of the method of Adomian for the solution of non-linear and complicated differential equation in a random medium. Here the problem is connected with the investigation of the mean and variance of the displacement distribution in a thin linear random non-homogeneous Biot type viscoelastic semi-infinite rod, due to general time-dependent displacement input at the rod. A truncated series solution of the wave problem following the method of Adomian after using the Laplace transform is obtained for small random variations in viscoelastic properties. Three specific cases concerning the probability measure as a function of the continuous type of random variable have been discussed.
EN
This paper is an analysis of an incompressible unsteady pulsatile laminar flow of electrically conducting non-Newtonian fluid through a channel bounded by two permeable plates taking into account the induced magnetic field and the effect of couple stresses on the flow. Solutions of the equations of motion are obtained by using Mathematica program and the effects of the various parameters entering the problem are discussed with the help of graphs. The main results show that the effect of couple stresses is to decrease the flow velocity and it is to increase (or decrease) the induced magnetic field near one of the boundaries and decrease (or increase) it near the other according to the time variation.
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