Viscoelastic models Zener

The Zener viscoelastic model is a modification of the Voigt model, in which a spring is placed in series with the dashpot. This causes the... 

Figure 5.14 Common viscoelastic models a) Voigt/Kelvin model b) Zener model/standard linear solid.

Smce the Zener model is a linear viscoelastic model, it obeys the Boltz-mann superposition principle. In this problem we are concerned with a strain history which is a smooth varying function of time, with y undergoing sinusoidal oscillations. Therefore the integral form of the BSP is the most straightforward one to apply ... 

Fig. 3. Visualization of the viscoelastic Zener model within the Huber/Vilgis approach...

The Zener model gives a lucid description of the origin of the large temperature dependence of the viscoelastic properties of polymers. Of the three parameters and Tg. the dominant parameter is r,. Both... 

A response closer to that of a real polymer is obtained by adding a second spring of modulus in parallel with a Maxwell unit (Figure 4.12). This model is known as the standard linear solid and is usually attributed to Zener [2]. It provides an approximate representation to the observed behaviour of polymers in their viscoelastic range. In creep, both springs extend, so that... 

The Zener model gives a lucid description of the origin of the large temperature dependence of the viscoelastic properties of polymers. Of the three parameters Jy, Jr, and the dominant parameter is t . Both J and Jr do vary with temperature, but the effect is small. For convenience, let the relaxation time at temperatures T and To be written r and tr,- Then the temperature dependence can be described by a parameter Oy... 

As understand from material properties test, both parenchyma and trachea show viscoelastic properties behavior. To model a mechanical property for calculation, Zener s Model of differential equation is used. 

A three-parameter model, the Zener element or standard linear solid (SLS), has been used to represent viscoelastic behavior in certain solids. Two equivalent forms of the SLS are ... 

A viscoelastic material shows a dynamic modulus under an external perturbation. It is initially hard but softens over time. The two elastic limits are Eg for the instantaneous modulus at the start of the external perturbation and E for the relaxed modulus (infinite time). For cross-linked polymers, the modulus relaxation is usually described by constitutive models for viscoelasticity in which springs and dashpots are combined in series or parallel and multiple characteristic time scan exist in one material. For instance, an extended Zener model is given in Figure 11, in which applied stress and , and //, are the modulus and the viscosity of the ith viscoelastic component, respectively. 

Figure 11 Extended Zener model. is the relaxed modulus over a long time, f, and ti, are the modulus and viscosity of the /th viscoelastic component, respectively, and r is the stress. Adapted from Sun, Y. Walker, G. Langrnuir2m, 21, 8694-8702. ...

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