Viscous material mechanical model

Tanaka et al. (1971) have used a two-element mechanical model (Figure 8-32) to represent fats as viscoplastic materials. The model consists of a dashpot representing the viscous element in parallel with a friction element that represents the yield value. 

The mechanical response of viscoelastic materials to mechanical excitation has traditionally been modeled in terms of elastic and viscous components such as springs and dashpots (1-3). The corresponding theory is analogous to the electric circuit theory, which is extensively described in engineering textbooks. In many respects the use of mechanical models plays a didactic role in interpreting the viscoelasticity of materials in the simplest cases. However, it must be emphasized that the representation of the viscoelastic behavior in terms of springs and dashpots does not imply that these elements reflect the molecular mechanisms causing the actual relaxation... 

Fig. 10 Dashpot as the mechanical model of an ideal viscous material the dashpot flows to similar extent but in a different time span depending on the force applied.

Finally, the material will flow as if it were a Newtonian body (C-D in Fig. 13A). Here, the ruptured links have no time to reform, and the linearity of this part of the curve indicates fully viscous behavior. In the mechanical model, this region refers to the deformation of dashpot 2 (Fig. 13B). The Newtonian compliance can be calculated from ... 

The creep and recovery of plastics can be simulated by an appropriate combination of elementary mechanical models for ideal elastic and ideal viscous deformations. Although there are no discrete molecular structures which behave like individual elements of the models, they nevertheless aid in understanding the response of plastic materials. 

The viscoelastic response of the rubbery material can be modeled using simple mechanical models representing combinations of Eq. 1 and the time derivative of Eq. 3. A simple Dashpot model represents the viscous component and the spring model represents the elastic component. Note that E and r represent the appropriate modulus and viscosity based on the state of stress being modeled. 

This model was proposed in the 19th century by Maxwell to explain the time-dependent mechanical behaviour of viscous materials, such as tar or pitch. It consists of a spring and dashpot in series as shown in Fig. 5.7(a). Under the action of an overall stress cr there will be an overall strain e in the system which is given by... 

In using nonlinear mechanical models, in addition to utilizing nonlinear elastic and shear thickening or thinning dashpot elements, a perturbation technique can also be used to incorporate nonlinear behavior. This is accomplished by adding small perturbation terms which are functions of the current level of elastic strain and strain rate to the elastic and viscous coefficients, respectively. This method was originally proposed by Davis (1964) and later applied by Renieri et al. (1976) in material characterization of bulk adhesives. 

James Clerk Maxwell (Niven 2003) proposed, in 1867, a simplified mechanical model consisting of a viscous dashpot in a serial connection to an elastic spring to describe viscoelastic material properties. 

Polymers differ from traditional construction materials by their viscoelastic deformation behavior [8, 9]. The time-, stress- and temperature-dependent deformation can be described by rheological-mechanical models, which base on a network of elastic (springs) and viscous (dash-pots) elements. Figure 2 [10]. 

Through the dashpot a viscous contribution was present in both the Maxwell and Voigt models and is essential to the entire picture of viscoelasticity. These have been the viscosities of mechanical units which produce equivalent behavior to that shown by polymers. While they help us understand and describe observed behavior, they do not give us the actual viscosity of the material itself. 

As the term implies, viscoelasticity is the response of a material to an applied stress that has both a viscous and an elastic component. In addition to a recoverable elastic response to an applied force, polymers can undergo permanent deformation at high strains, just as was the case for metals and some glasses, as described previously. The mechanism of permanent deformation is different in polymers, however, and can resemble liquid-like, or viscous flow, just like we described in Chapter 4. Let us first develop two important theoretical models to describe viscoelasticity, then describe how certain polymers exhibit this important property. 

The physical properties of barrier dressings were evaluated using the Seiko Model DMS 210 Dynamic Mechanical Analyzer Instrument (see Fig. 2.45). Referring to Fig. 2.46, dynamic mechanical analysis consists of oscillating (1 Hz) tensile force of a material in an environmentally (37°C) controlled chamber (see Fig. 2.47) to measure loss modulus (E") and stored modulus (E ). Many materials including polymers and tissue are viscoelastic, meaning that they deform (stretch or pull) with applied force and return to their original shape with time. The effect is a function of the viscous property (E") within the material that resists deformation and the elastic property (E )... 

Another approach that has physical merit is to model the behavior of viscoelastic materials as a series of springs (elastic elements) and dashpots (viscous elements) either in series or parallel (see Figure 8.1). If the spring and dashpot are in series, which is described as a Maxwell mechanical element, the stress in the element is constant and independent of the time and the strain increases with time. 

The use of monomers bearing more than two associating groups is a straightforward way to introduce a controlled amount of branches or crosshnks in a supramolecular polymer structure [6,58,121,123-127]. The improvement of the mechanical properties can be spectacular. For instance, trifunctional monomer 17 (Fig. 21) forms highly viscous solutions in chloroform, and is a viscoelastic material in the absence of solvent [124]. The reversibly cross-linked network displays a higher plateau modulus than a comparable covalently cross-linked model. This is explained by the fact that the reversibly cross-hnked network can reach the thermodynamically most stable conformation, whereas the covalent model, which has been cross-linked in solution and then dried, is kinetically trapped. 

---