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Nonlinear viscoelasticity also elucidates observed phenomena such as normal stresses, shear thinning, and extensional thickening in viscoelastic fluids. [ 3 ] An anelastic material is a special case of a viscoelastic material: an anelastic material will fully recover to its original state on the removal of load.
A Maxwell model is the most simple model viscoelastic material showing properties of a typical liquid. [1] It shows viscous flow on the long timescale, but additional elastic resistance to fast deformations. [2] It is named for James Clerk Maxwell who proposed the model in 1867. [3] [4] It is also known as a Maxwell fluid.
The yield function is often expressed as an equation consisting of some invariant of stress and a model for the yield stress (or plastic flow stress). An example is von Mises or J 2 {\displaystyle J_{2}} plasticity.
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 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 ...
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 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 ...
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