Viscoelasticity quasi-linear

The set of relations (8.27) determines the fluxes as quasi-linear functions of forces. The coefficients in (8.27) are unknown functions of the thermodynamic variables and internal variables. We should pay special attention to the fourth relation in (8.27) which is a relaxation equation for variable The viscoelastic behaviour of the system is determined essentially by the relaxation processes. If the relaxation processes are absent (all the =0), equations (8.27) turn into constitutive equations for a viscous fluid. 

Kumar B, Das A, Alagirusamy R. An approach to determine pressure profile generated by compression bandage using quasi-linear viscoelastic model. J Biomech Eng Trans Asme 2012 134(9). 

In the context of nonlinear viscoelasticity, one of the simplest model is the Quasi-Linear viscoelastic model proposed by Fung [164]. In one dimension, he... 

The Quasi-Linear Viscoelastic (QLV) model has proven to be a successful phenomenological model for describing the nonlinear viscoelastic behavior of solids [186-188]. 

Rajagopal K, Wineman A (2008) A quasi-correspondence principle for Quasi-Linear viscoelastic solids. Mech Time-Depend Mater 12 1-14... 

Typical for the spectroscopic character of the measurement is the rapid development of a quasi-steady state stress. In the actual experiment, the sample is at rest (equilibrated) until, at t = 0, oscillatory shear flow is started. The shear stress response may be calculated with the general equation of linear viscoelasticity [10] (introducing Eqs. 4-3 and 4-9 into Eq. 3-2)... 

Petrie and Ito (84) used numerical methods to analyze the dynamic deformation of axisymmetric cylindrical HDPE parisons and estimate final thickness. One of the early and important contributions to parison inflation simulation came from DeLorenzi et al. (85-89), who studied thermoforming and isothermal and nonisothermal parison inflation with both two- and three-dimensional formulation, using FEM with a hyperelastic, solidlike constitutive model. Hyperelastic constitutive models (i.e., models that account for the strains that go beyond the linear elastic into the nonlinear elastic region) were also used, among others, by Charrier (90) and by Marckmann et al. (91), who developed a three-dimensional dynamic FEM procedure using a nonlinear hyperelastic Mooney-Rivlin membrane, and who also used a viscoelastic model (92). However, as was pointed out by Laroche et al. (93), hyperelastic constitutive equations do not allow for time dependence and strain-rate dependence. Thus, their assumption of quasi-static equilibrium during parison inflation, and overpredicts stresses because they cannot account for stress relaxation furthermore, the solutions are prone to numerical instabilities. Hyperelastic models like viscoplastic models do allow for strain hardening, however, which is a very important element of the actual inflation process. 

Although bone is a viscoelastic material, at the quasi-static strain rates in mechanical testing and even at the ultrasonic frequencies used experimentally, it is a reasonable first approximation to model cortical bone as an anisotropic, linear elastic solid with Hooke s law as the appropriate constitutive equation. Tensor notation for the equation is written as ... 

With the development of TMDSC it has become possible to study the kinetics of the freezing and unfreezing in the glass transition region. As one would expect, limitations exist in the generation of quantitative information. Quasi-isothermal data extrapolated to zero temperature-modulation amplitude need to be generated to characterize a sample, as illustrated in Figures 1-3. This extrapolation to make the kinetic expression of Equation (6) linear, corresponds to the limits of the description of DMA to linear viscoelasticity. 

Abstract This chapter deals with capillary instability of straight free liquid jets moving in air. It begins with linear stability theory for small perturbations of Newtonian liquid jets and discusses the unstable modes, characteristic growth rates, temporal and spatial instabilities and their underlying physical mechanisms. The linear theory also provides an estimate of the main droplet size emerging from capillary breakup. Formation of satellite modes is treated in the framework of either asymptotic methods or direct numerical simulations. Then, such additional effects like thermocapiUarity, or swirl are taken into account. In addition, quasi-one-dimensional approach for description of capillary breakup is introduced and illustrated in detail for Newtonian and rheologically complex liquid jets (pseudoplastic, dilatant, and viscoelastic polymeric liquids). 

Keywords Capillary instability of liquid jets Curvature Elongational rheology Free liquid jets Linear stability theory Nonlinear theory Quasi-one-dimensional equations Reynolds number Rheologically complex liquids (pseudoplastic, dilatant, and viscoelastic polymeric liquids) Satellite drops Small perturbations Spatial instability Surface tension Swirl Temporal instability Thermocapillarity Viscosity... 

The quasi-equilibrium adsorption layers (the formation time of60,000-70,000 sec) were subjected to compressive/tensile deformation sinusoidally in the field of linear viscoelasticity. The dependences of the complex viscoelastic modulus of adsorption layers (E), as well as its elastic (real part. 

Chazeau L, Cavaille JY, Canova G et al (1999a) Viscoelastic properties of plasticized PVC reinforced with cellulose whiskers. J Appl Polym Sci 71 1797-1808 Chazeau L, Cavaille JY, Terech P (1999b) Mechanical behaviour above Tg of a plasticised PVC reinforced with cellulose whiskers a SANS structural study. Polymer 40 5333-5344 Chazeau L, Paillet M, Cavaille JY (1999c) Plasticized PVC reinforced with cellulose whiskers. I. Linear viscoelastic behavior analyzed through the quasi-point defect theory. J Polym Sci Part B Polym Phys 37 2151-2164... 

An approximate method to analyze viscoelastic problems has been outlined by Schap-ery.(30) jn this method, the solution to a viscoelastic problem is approximated by a correspond ing elasticity solution wherein the elastic constants have been replaced by time-dependent creep or relaxation functions. The method may be applied to linear as well as nonlinear problems. Weitsman D used Schapery s quasi-elastic approximation to investigate the effects of nonlinear viscoelasticity on load transfer in a symmetric double lap joint. By introducing a stress-dependent shift factor, he observed that the enhanced creep causes shear stress relief near the edges of the adhesive joint. 

Analysis of crack growth in viscoelastic media is mainly limited to linear isotropic, homogeneous materials. Schapery(34) proposed the use of parameters similar to the J integral for quasi-static crack growth in a class of nonlinear viscoelastic materials subject to finite strains. 

The non linear viscoelasticity of various particles filled rubber is addressed in range of studies. It is found that the carbon black filled-elastomer exhibit quasi-static and dynamic response of nonlinearity. Hartmann reported a state of stress which is the superposition of a time independent, long-term, response (hyperelastic) and a time dependent, short-term, response in carbon black filled-rubber when loaded with time-dependent external forces. The short term stresses were larger than the long term hyperelastic ones. The authors had done a comparative study for the non linear viscoelastic models undergoing relaxation, creep and hysteresis tests [20-22]. For reproducible and accurate viscoelastic parameters an experimental procedure is developed using an ad hoc nonlinear optimization algorithm. 

To our knowledge, there is no comprehensive and predictive theory of polyurethane elastomer linear viscoelasticity. We believe that it should be possible to extend om- earlier model (Section 2.2) to describe not just quasi-static modulus, but also the time (or frequency) dependent moduli and overall effects of linear viscoelasticity. This is a subject of ongoing research. 

Nuismer, R. J. (1974) On the governing equation for quasi-static crack growth in linearly viscoelastic materials. J. Appl. Mech. 41, 631-634... 

Chazeau, L., PaiUet, M., CavaiUe, J.Y., 1999c. Plasticized PVC reinforced with ceUulose whiskers. I. Linear viscoelastic behavior analyzed through the quasi-point defect theory. Journal of Polymer Science Polymer Physics 37, 2151—2164. 

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