A Maxwell material is a viscoelastic material having the properties both of elasticity and viscosity. It is named for James Clerk Maxwell who proposed the model in 1867. A viscoelastic material is one in which: hysteresis is seen in the stress-strain curve. ... in Economics see elasticity (economics) in Materials Science the word elastomer refers to a material which is very elastic, like rubber. ... The pitch drop experiment at the University of Queensland. ... James Clerk Maxwell (June 13, 1831–November 5, 1879) was a Scottish mathematical physicist, born in Edinburgh. ... 1867 was a common year starting on Tuesday (see link for calendar). ...

Definition

The Maxwell model can be represented by a purely viscous damper and a purely elastic spring connected consecutively, as shown in the diagram.

If we connect these two elements in parallel, we get a model of Kelvin material. Image File history File links Maxwell_diagram. ... A Kelvin material is a viscoelastic material having the properties both of elasticity and viscosity. ...

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: Figure 1  Stress tensor In physics, stress is a measure of the internal distribution of force per unit area within a body that balances and reacts to the loads applied to it. ... In any branch of science dealing with materials and their behaviour, strain is the geometrical expression of deformation caused by the action of stress on a physical body. ...

or, in dot notation:

where E is a modulus of elasticity and c a "viscosity". 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. Shear stress is a stress state where the shape of a material tends to change (usually by sliding forces -- torque by transversely-acting forces) without particular volume change. ... The introduction to this article provides insufficient context for those unfamiliar with the subject matter. ...

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 generalization the Maxwell model see Upper Convected Maxwell Model. The Upper Convected Maxwell model (or UCM model) is a generalisation of the Maxwell material for the case of large deformations using the Upper convected time derivative. ...

Effect of a sudden deformation

If Maxwell material is suddenly deformed to strain of ε₀ and is kept under this deformation, then the stresses would exponentially decay: In any branch of science dealing with materials and their behaviour, strain is the geometrical expression of deformation caused by the action of stress on a physical body. ... A quantity is said to be subject to exponential decay if it decreases at a rate proportional to its value. ...

σ(t) = Eε₀exp( − λt),

where t is time and the rate of relaxation

The picture shows dependence of dimensionless stress upon dimensionless time λt:

Dependence of dimesionless stress upon dimensionless time under constant strain

If we would free the material at time t₁, then the elastic element would spring back by the value of Image File history File links Maxwell_deformation. ...

The viscous element would stay there it was, thus, the irreversible component of deformation is:

Effect of a sudden stress

If a Maxwell material is suddenly subjected to a stress σ₀, then the elastic element would suddenly deform and the viscous element would deform with a constant rate:

If at some time t₁ we would release the material, then the deformation of the elastic element would be the spring-back deformation and the deformation of the viscous element would spring back:

If even a small stress is applied for a sufficiently long time, then the irreversible stresses become large. Thus, Maxwell material is a type of liquid. A liquid will assume the shape of its container. ...

Dynamic modulus

The complex dynamic modulus of Maxwell material would be: To meet Wikipedias quality standards, this article or section may require cleanup. ...

Thus, the components of the dynamic modulus are :

and

Relaxational spectrum for Maxwell material

The picture shows relaxational spectrum for Maxwell material. Image File history File links Maxwell_relax_spectra. ...

See also

• Generalized Maxwell material
• Kelvin material
• Oldroid material