Maxwell Material - Definition

Definition

The Maxwell model can be represented by a purely viscous damper and a purely elastic spring connected in series, as shown in the diagram. In this configuration, under an applied axial stress, the total stress, and the total strain, can be defined as follows:

where the subscript D indicates the stress/strain in the damper and the subscript S indicates the stress/strain in the spring. Taking the derivative of strain with respect to time, we obtain:

where E is the elastic modulus and η is the material coefficient of viscosity. This model describes the damper as a Newtonian fluid and models the spring with Hooke's law.

If we connect these two elements in parallel, we get a model of Kelvin–Voigt material.

In a Maxwell material, stress σ, strain ε and their rates of change with respect to time t are governed by equations of the form:

or, in dot notation:

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.

The model is usually applied to the case of small deformations. For the large deformations we should include some geometrical non-linearity. For the simplest way of generalizing the Maxwell model, refer to the upper-convected Maxwell model.