40 lines
1.6 KiB
Markdown
40 lines
1.6 KiB
Markdown
Viscous materials, like water, resist both shear flow and strain linearly with
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time when a stress is applied. Elastic materials strain when stretched and
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immediately return to their original state once the stress is removed. The study of such materials is covered by [[Rheology]].
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A viscoelastic substance dissipates energy when a load is applied, then removed.
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In most of the analyses, extensional/compressional strains of the viscoelastic layer are not taken into account since the damping comes mostly from the shear strain.
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The properties of a viscoelastic layer change with the frequency of excitation .
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# Models
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(see [[Rheology#Linear viscosity]] for the definition of $f$ and $g$, and for the sources)
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## Perfectly elastic solid
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Rheologic equation $$\varepsilon(t)=J\tau(t)$$
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Where $J$ is the elastic compliance. $G=\frac{1}{J}$ is called the elastic modulus
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the creep function $f(t)$ is then :
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$$f(t)=J$$
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## Newtonian viscous fluid
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Rheologic equation (see [[Rheology#Dynamic viscosity]])
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$$\frac{d\varepsilon(t)}{dt}=\frac{\tau(t)}{\eta}$$
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initial conditions : $t<0$ ; $\tau(t)=0$ ; $\varepsilon(t)=0$, so
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$$\varepsilon(t)=\frac{1}{\eta}\int_{0}^{t}\tau(t')dt'$$
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under a constant stress $\tau_0$ :
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$$\varepsilon(t)=\frac{\tau_0}{\eta}t$$
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the creep function is obtained with a constant unit stress, so with $\tau_0=1$
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$$f(t)=\frac{t}{\eta}$$
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## Associations
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### Parallel
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- stress to the whole is **the sum of** the stresses on each branch
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- strain to the whole is **equal to** the strains in each branch
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### Series
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- stress to the whole is **equal to** the stresses on each branch
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- strain to the whole is **the sum of** the strains in each branch |