Retardation time spectra computed from complex compliance functions

2008 ◽  
Vol 129 (10) ◽  
pp. 104513 ◽  
Author(s):  
Gustavo Domínguez-Espinosa ◽  
Damian Ginestar ◽  
Maria J. Sanchis ◽  
Ricardo Díaz-Calleja ◽  
Evaristo Riande
Keyword(s):  
Retardation Time ◽  
Complex Compliance

scholarly journals Influence of Retardation Time on Viscoelastic Behavior of Plane Beams Modeled by the Nonlinear Positional Formulation of the Finite Element Method

2021 ◽  
Vol 2021 ◽  
pp. 1-22
Author(s):  
Juliano dos Santos Becho ◽  
Marcelo Greco
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Rheological Model ◽  
Iterative Process ◽  
Numerical Procedure ◽  
Viscoelastic Behavior ◽  
Retardation Time ◽  
The Finite Element Method ◽  
Divergence Problem ◽  
Element Method

A numerical procedure is presented to avoid the divergence problem during the iterative process in viscoelastic analyses. This problem is observed when the positional formulation of the finite element method is adopted in association with the finite difference method. To do this, the nonlinear positional formulation is presented considering plane frame elements with Bernoulli–Euler kinematics and viscoelastic behavior. The considered geometrical nonlinearity refers to the structural equilibrium analysis in the deformed position using the Newton–Raphson iterative method. However, the considered physical nonlinearity refers to the description of the viscoelastic behavior through the adoption of the stress-strain relation based on the Kelvin–Voigt rheological model. After the presentation of the formulation, a detailed analysis of the divergence problem in the iterative process is performed. Then, an original numerical procedure is presented to avoid the divergence problem based on the retardation time of the adopted rheological model and the penalization of the nodal position correction vector. Based on the developments and the obtained results, it is possible to conclude that the presented formulation is consistent and that the proposed procedure allows for obtaining the equilibrium positions for any time step value adopted without presenting divergence problems during the iterative process and without changing the analysis of the final results.

Viso-Elastic Properties of the Body-Wall of Sea Anemones

1962 ◽  
Vol 39 (3) ◽  
pp. 373-386
Author(s):  
R. MCN. ALEXANDER
Keyword(s):  
Tensile Stress ◽  
Elastic Properties ◽  
Body Wall ◽  
The Body ◽  
Polymeric System ◽  
Retardation Time ◽  
Sea Anemones

1. Creep of narcotized Metridium and Calliactis body-wall at constant tensile stress has been studied quantitatively. 2. It was found to be reversible, and seemed to be controlled by the mesogloea. Its course could be represented by equations of the formε(t)= εo+ευ(I-e-t/τ),where the retardation time τ was about 1 hr. for Metridium and many hours for Calliactis. 3. The results can most simply be explained in terms of a cross-linked and a noncross-linked polymeric system, acting in parallel. An explanation in terms of a lattice of inextensible fibres is not satisfactory. 4. The results are discussed in relation to the behaviour of the animals.

Dynamic viscoelastic behaviour of low-molecular-mass polystyrene melts

1977 ◽  
Vol 356 (1684) ◽  
pp. 77-102 ◽  
Keyword(s):  
Molecular Mass ◽  
Molecular Mass Distribution ◽  
Low Frequency ◽  
Single Equation ◽  
Supercooled Liquids ◽  
Alternative Analysis ◽  
Complex Compliance ◽  
Complex Shear ◽  
Observed Behaviour ◽  
Good Agreement

Measurements have been made of the viscoelastic properties of a range of low-molecular-mass polystyrenes each having a narrow molecular mass distribution. Several experimental techniques using alternating shear have been employed covering the frequency range 10 -2 Hz to 450 MHz and at temperatures from the glass transition temperature to T g + 80 K. The equilibrium (limiting low-frequency) compliance, J e , and the limiting high-frequency compliance, », have each been determined as a function of temperature. Jw is found to be independent of molecular mass at any given value of T— T g . The sample of molecular mass 580 shows a behaviour closely similar to that of non-polymeric supercooled liquids. Samples of molecular mass above 1100 show distinct polymeric behaviour as an additional lowfrequency contribution to the complex shear modulus which can be accounted for by summation over a limited number of Rouse modes of the unentangled polymer molecule. This, combined with the ‘liquid-like’ behaviour of short elements of the polymer chain, gives calculated curves which are in good agreement with experimental results. An alternative analysis describes the complete behaviour by a single equation for the complex compliance of the form J*(jw) = J∞+1/1wn+Jr/(1+jwTr)B, where J r is the retardational compliance. It is not possible to distinguish between these two approaches on the basis of the present data. At temperatures above T g + 40 K measured values of J e are in agreement with calculations based upon the Rouse equations, which can therefore be used as a basis for predicting the observed behaviour both as regards the equilibrium properties and over the relaxation region.

UNSTEADY MODEL OF TRANSPORTATION OF JEFFREY-FLUID BY PERISTALSIS

2010 ◽  
Vol 03 (04) ◽  
pp. 473-491 ◽  
Author(s):  
S. K. PANDEY ◽  
DHARMENDRA TRIPATHI
Keyword(s):  
Relaxation Time ◽  
Flow Rate ◽  
Volume Flow Rate ◽  
Cylindrical Tube ◽  
Maximum Flow ◽  
Mechanical Efficiency ◽  
Volume Flow ◽  
Jeffrey Fluid ◽  
Retardation Time ◽  
Circular Cylindrical Tube

The investigation is to explore the transportation of a viscoelastic fluid by peristalsis in a channel as well as in a circular cylindrical tube by considering Jeffrey-model. In order to apply the model to the swallowing of food-bolus through the oesophagus, the wave equation assumed to propagate along the walls is such that the walls contract in the transverse/radial direction and relax but do not expand further. Solutions have been presented in the closed form by using small Reynolds number and long wavelength approximations. The expressions of pressure gradient, volume flow rate and average volume flow rate have been derived. It is revealed on the basis of computational investigation that for a fixed flow rate, pressure decreases when the ratio of relaxation time to retardation time is increased. In both the channel and tubular flows, the pressure decreases on increasing the ratio of relaxation time to retardation time if the averaged flow rate is less than the maximum flow rate. It is also revealed that the maximum tubular flow rate is higher than that of the channel-flow. It is further found through the theoretical analysis that mechanical efficiency, reflux and local wall shear stress remain unaffected by viscoelastic property of the fluid modelled as Jeffrey-fluid.

scholarly journals USE OF ATANGANA–BALEANU FRACTIONAL DERIVATIVE IN HELICAL FLOW OF A CIRCULAR PIPE

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040049 ◽  
Author(s):  
KASHIF ALI ABRO ◽  
ILYAS KHAN ◽  
KOTTAKKARAN SOOPPY NISAR
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Rheological Parameters ◽  
Shear Stresses ◽  
Fractional Differentiation ◽  
Retardation Time ◽  
Governing Equations ◽  
Partial Differential ◽  
Gamma Functions ◽  
Helical Pipe

There is no denying fact that helically moving pipe/cylinder has versatile utilization in industries; as it has multi-purposes, such as foundation helical piers, drilling of rigs, hydraulic simultaneous lift system, foundation helical brackets and many others. This paper incorporates the new analysis based on modern fractional differentiation on infinite helically moving pipe. The mathematical modeling of infinite helically moving pipe results in governing equations involving partial differential equations of integer order. In order to highlight the effects of fractional differentiation, namely, Atangana–Baleanu on the governing partial differential equations, the Laplace and Hankel transforms are invoked for finding the angular and oscillating velocities corresponding to applied shear stresses. Our investigated general solutions involve the gamma functions of linear expressions. For eliminating the gamma functions of linear expressions, the solutions of angular and oscillating velocities corresponding to applied shear stresses are communicated in terms of Fox- H function. At last, various embedded rheological parameters such as friction and viscous factor, curvature diameter of the helical pipe, dynamic analogies of relaxation and retardation time and comparison of viscoelastic fluid models (Burger, Oldroyd-B, Maxwell and Newtonian) have significant discrepancies and semblances based on helically moving pipe.

On the foundations of linear isotropic visco-elasticity

1959 ◽  
Vol 250 (1263) ◽  
pp. 524-549 ◽  
Keyword(s):  
Elastic Material ◽  
Relaxation Function ◽  
Creep Function ◽  
Stored Energy ◽  
Stress Strain ◽  
Complex Compliance ◽  
In Series ◽  
Constant Coefficients ◽  
Material Element ◽  
Rate Of Dissipation

The properties of a linear visco-elastic material are developed from the hypothesis that the microscopic structure of such a material is mechanically equivalent to a network of elastic and viscous elements. The stored energy and the rate of dissipation of energy can be found for any material element at any time. For an isotropic material, each deviatoric component of strain is related solely to the corresponding deviatoric component of stress and the dilatational part of the strain solely to the dilatational part of the stress; the energies are the sum of the respective energies for the deviatoric components and for the dilatation. It is shown both that the strain can be expressed in terms of the stress increments and the creep function, and that the stress can be expressed in terms of the strain increments and the relaxation function. The complex compliances and moduli have alternating zeros and poles on the positive imaginary axis and no zeros or poles elsewhere. The stress-strain law can be expressed in operational form, Pσ = Qϵ , where P and Q are polynomials in d/d t with constant coefficients. The zeros of P and Q are all real and non-positive and they alternate. The energies can be expressed in terms of either the creep function and the stress at previous times, or the relaxation function and the strain at previous times, or the stress, strain and their time derivatives at a given time or, for a sinusoidal oscillation, in terms of the complex compliance and its derivative with respect to frequency. It is shown that models consisting of Voigt element in series, or of Maxwell elements in parallel, can represent the mechanical properties and the stored and dissipated energies of any visco-elastic material. The analysis can be extended to networks containing an infinite number of elements. Two examples, one of each of two different cases, are given.

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