Viscoelasticity combines viscous dissipation with elastic storage and relaxation of deformation.
The conformation tensor describes the average stretch and orientation of polymer molecules. Its equilibrium value is the identity tensor under a common normalization.
An objective time derivative transforms covariantly under time-dependent rigid changes of observer, so constitutive predictions do not depend on the observer's rotation.
The Oldroyd-B model combines a Newtonian solvent with infinitely extensible Hookean polymer dumbbells. It predicts constant shear viscosity, a positive first normal-stress difference, and an extensional catastrophe at a finite extension rate.
The FENE-P model replaces infinitely extensible Hookean polymers by finitely extensible nonlinear elastic springs with a mean-field closure. Finite extensibility regularizes the Oldroyd-B extensional catastrophe and produces shear thinning.
The Oldroyd-A model is the lower-convected counterpart of the Oldroyd-B model: its polymeric stress evolves using a lower-convected derivative.
The uniaxial extensional viscosity is the tensile normal-stress difference divided by the imposed extension rate.
The Trouton ratio is extensional viscosity divided by shear viscosity. It approaches three for an incompressible Newtonian fluid in uniaxial extension.
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Viscoelasticity is a property of materials that exhibit both viscous and elastic characteristics when undergoing deformation. This means that these materials can both flow like a fluid (viscous behavior) and deform elastically (return to their original shape) when stress is applied. ### Key Characteristics: 1. **Viscous Behavior**: When a force is applied to a viscous material, it deforms and flows continuously over time.