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A Maxwell material is the most simple model viscoelastic material showing properties of a typical liquid. It shows viscous flow on the long timescale, but additional elastic resistance to fast deformations. [1] It is named for James Clerk Maxwell who proposed the model in 1867. [2] [3] It is also known as a Maxwell fluid
The model was proposed by James G. Oldroyd. The concept is named after James Clerk Maxwell. It is the simplest observer independent constitutive equation for viscoelasticity and further is able to reproduce first normal stresses. Thus, it constitutes one of the most fundamental models for rheology. The model can be written as:
Schematic of Maxwell-Wiechert Model. The generalized Maxwell model, also known as the Wiechert model, is the most general form of the linear model for viscoelasticity. It takes into account that the relaxation does not occur at a single time, but at a distribution of times. Due to molecular segments of different lengths with shorter ones ...
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.
Schematic diagram of Burgers material, Maxwell representation. Given that one Maxwell material has an elasticity and viscosity , and the other Maxwell material has an elasticity and viscosity , the Burgers model has the constitutive equation
Schematic representation of Kelvin–Voigt model. The Kelvin–Voigt model, also called the Voigt model, is represented by a purely viscous damper and purely elastic spring connected in parallel as shown in the picture. If, instead, we connect these two elements in series we get a model of a Maxwell material.
One viscoelastic model, called the Maxwell model predicts behavior akin to a spring (elastic element) being in series with a dashpot (viscous element), while the Voigt model places these elements in parallel. Although the Maxwell model is good at predicting stress relaxation, it is fairly poor at predicting creep.
This model has the general form and the isotropic form respectively =: = +. where : is tensor contraction, is the second Piola–Kirchhoff stress, : is a fourth order stiffness tensor and is the Lagrangian Green strain given by = [() + + ()] and are the Lamé constants, and is the second order unit tensor.