Viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation. Viscous materials, like honey, resist shear flow and strain linearly with time when a stress is applied. Elastic materials strain instantaneously when stretched and just as quickly return to their original state once the stress is removed. Viscoelastic materials have elements of both of these properties and, as such, exhibit time dependent strain. Whereas elasticity is usually the result of bond stretching along crystallographic planes in an ordered solid, viscoelasticity is the result of the diffusion of atoms or molecules inside of an amorphous material
A basic viscoelastic material is modeled as a purely viscous damper and a purely elastic spring. The damper is modeled as as a Newtonian fluid and the spring with Hooke's law. If we connect these two elements in series we get a Maxwell material, and in parallel we get a Kelvin-Voigt material.
Spring and Dashpot Models:
| Viscoelastic fluids: Strain rates add.
| Viscoelastic solids: Strains add.
|And so on, with decreasing physical interpretation.|
The Maxwell model
|Maxwell mode: Add the strain rates:|
|For the elastic component:|
|For the viscous component:|
|The resulting differential equation is:|
Viscoelasticity - Creep test
For a creep test: A stress is applied instantaneously and maintained. The strain is measured as a function of time"
Viscoelasticity - Stress relaxation
For a stress relaxation, a rapid strain is applied and held. The problem is to determine the stress as a function of time:
Viscoelasticity - Molecular relaxations
- Osmotic pressure
- Force microscopy: scanning, tunneling, atomic
- Dynamic scattering over time scales
- Static scattering – x-rays, neutrons, back-scattering
- Typical energies are kT
- Fluctuations and Brownian motion
- Wide length scales – use coarse grain models
- Hierarchical structures
- Physics dominates over chemistry (so far)
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