Upper Convected Maxwell Model

Upper Convected Maxwell Model

The upper-convected Maxwell (UCM) model is a generalisation of the Maxwell material for the case of large deformations using the upper-convected time derivative. The model was proposed by James G. Oldroyd. The concept is named after James Clerk Maxwell.

The model can be written as:

where:

• is the stress tensor;
• is the relaxation time;
• is the upper-convected time derivative of stress tensor:

• is the fluid velocity
• is material viscosity at steady simple shear;
• is the tensor of the deformation rate.