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Nonlinear viscoelasticity is when the function is not separable. It usually happens when the deformations are large or if the material changes its properties under deformations. Nonlinear viscoelasticity also elucidates observed phenomena such as normal stresses, shear thinning, and extensional thickening in viscoelastic fluids.
Viscoelasticity is studied using dynamic mechanical analysis where an oscillatory force (stress) is applied to a material and the resulting displacement (strain) is measured. [2] In purely elastic materials the stress and strain occur in phase, so that the response of one occurs simultaneously with the other.
The Maxwell model does not exhibit creep since it models strain as linear function of time. If a small stress is applied for a sufficiently long time, then the irreversible strains become large. Thus, Maxwell material is a type of liquid.
Viscoelasticity of bone can arise from multiple factors related to structures on multiple length scales. [1] Bone is a composite of the bio-polymer collagen and the bio-ceramic hydroxyapatite. Additionally the collagen is plied in various directions around the bone.
For this case only two components of the shear stress became non-zero: = ˙ and = ˙ where ˙ is the shear rate.. Thus, the upper-convected Maxwell model predicts for the simple shear that shear stress to be proportional to the shear rate and the first difference of normal stresses is proportional to the square of the shear rate, the second difference of normal stresses is always zero.
In physics and chemistry, a non-Newtonian fluid is a fluid that does not follow Newton's law of viscosity, that is, it has variable viscosity dependent on stress. In particular, the viscosity of non-Newtonian fluids can change when subjected to force. Ketchup, for example, becomes runnier when shaken and is thus a non-Newtonian fluid.
On the other hand, the Voigt model is good at predicting creep but rather poor at predicting stress relaxation (see viscoelasticity). The extracellular matrix and most tissues are stress relaxing, and the kinetics of stress relaxation have been recognized as an important mechanical cue that affects the migration, proliferation , and ...
This implies that a master curve at a given temperature can be used as the reference to predict curves at various temperatures by applying a shift operation. The time-temperature superposition principle of linear viscoelasticity is based on the above observation. [5] Moduli measured using a dynamic viscoelastic modulus analyzer.