**4.5. Viscoelastic and elastoviscos behaviours**

The unitary properties of matter at the microscopic scale are viscosity (*μ*) and elasticity (*E*). Viscosity as a property is associated to purely viscous fluids, while the elastic property is associated with purely elastic bodies.

Actually, matter is viscoelastic if viscosity prevails and it is elastoviscos if elasticity prevails. For a real physical body, which features the two properties in different ratios, based on PCE one can write that the total participation of specific energies is:

$$P\left(\mu\right) + P\left(E\right) = 1\tag{44}$$

where *P*(*μ*) is the contribution of the viscous component, whereas *P*(*E*) is the contribution of the elastic component.

If *P*(*μ*)=0, the body is perfectly elastic (*PT* = *P*(*E*)), whereas if *P*(*E*)=0, the body is perfectly viscous (*PT* = *P*(*μ*)).

If: *P*(*μ*)< *P*(*E*) —the body is elastoviscos;

*P*(*μ*)> *P*(*E*) —the body is viscoelastic.

The *purely elastic nonlinear* behaviour is mapped on the form of the general law (6),

$$
\sigma = M\_{\sigma} \cdot \varepsilon^{k} \tag{45}
$$

where σ is the normal stress, ε —strain, while *M*σ and *k* —constants of the elastic solid. The *purely viscous nonlinear* behaviour is given by Oswald—de Waele's law

$$
\tau = \mathbf{K} \cdot \dot{\mathbf{y}}^{\nu} \tag{46}
$$

where *τ* is the shear stress, *γ*˙ is the shear strain, *K* and ν are the constants of the viscous fluid. The participation of the specific energy corresponding to the elastic component is:

$$P(E) = \left(\frac{\sigma}{\sigma\_{cr}}\right)^{a+1} \tag{47}$$

where α=1 / *k*.

The participation of the specific energy corresponding to the viscous component is:

$$P\left(\mu\right) = \left(\frac{\pi}{\tau\_{\alpha}}\right)^{\beta+1} \tag{48}$$

where *β* =1 / *ν*.

Out of relations (43), (46) and (47), one gets:

$$\left(\frac{\sigma}{\sigma\_{\alpha}}\right)^{a+1} + \left(\frac{\tau}{\tau\_{\alpha}}\right)^{\beta+1} = 1\tag{49}$$

The graphical representation of the relationship (48) in Figure 5 separates the zone of elasto‐ viscos bodies from the zone of viscoelastic bodies.

**Figure 5.** Graphic representation of relation (48).

If: *P*(*μ*)< *P*(*E*) —the body is elastoviscos; *P*(*μ*)> *P*(*E*) —the body is viscoelastic.

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where α=1 / *k*.

where *β* =1 / *ν*.

Out of relations (43), (46) and (47), one gets:

viscos bodies from the zone of viscoelastic bodies.

The *purely elastic nonlinear* behaviour is mapped on the form of the general law (6),

s

The *purely viscous nonlinear* behaviour is given by Oswald—de Waele's law

t

*M <sup>k</sup>* s

where σ is the normal stress, ε —strain, while *M*σ and *k* —constants of the elastic solid.

*K* n

The participation of the specific energy corresponding to the elastic component is:

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where *τ* is the shear stress, *γ*˙ is the shear strain, *K* and ν are the constants of the viscous fluid.

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The participation of the specific energy corresponding to the viscous component is:

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The graphical representation of the relationship (48) in Figure 5 separates the zone of elasto‐

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Proceedings of the International Conference on Interdisciplinary Studies (ICIS 2016) - Interdisciplinarity and Creativity

= × (45)

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(48)

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