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The generalized Maxwell model also known as the Maxwell–Wiechert model (after James Clerk Maxwell and E Wiechert [1] [2]) is the most general form of the linear model for viscoelasticity. In this model, several Maxwell elements are assembled in parallel. It takes into account that the relaxation does not occur at a single time, but in a set ...
In materials science and continuum mechanics, viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation. Viscous materials, like water, resist both shear flow and strain linearly with time when a stress is applied.
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.
The equation can be applied either to the shear stress or to the uniform tension in a material. In the former case, the viscosity corresponds to that for a Newtonian fluid . In the latter case, it has a slightly different meaning relating stress and rate of strain.
A Kelvin–Voigt material, also called a Voigt material, is the most simple model viscoelastic material showing typical rubbery properties. It is purely elastic on long timescales (slow deformation), but shows additional resistance to fast deformation.
The shape of the time-dependent strain curve is true to the type of equation that characterizes the behavior of the model over time, depending upon how the model is loaded. Although this model can be used to accurately predict the general shape of the strain curve, as well as behavior for long time and instantaneous loads, the model lacks the ...
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.
Schematic diagram of Burgers material, Kelvin representation. Given that the Kelvin material has an elasticity and viscosity , the spring has an elasticity and the dashpot has a viscosity , the Burgers model has the constitutive equation