Choosing Shape Functions in Multiphysics Models
In problems where several physics fields participate, the accuracy can sometimes be improved by considering how the different fields interact. In structural mechanics, it is common that other physics fields directly affect the inelastic strains. This is the case in, for example, thermal expansion and hygroscopic swelling.
In thermal expansion, the elastic strain used in most constitutive relations is the difference between the total strain, which is computed from derivatives of the displacement field, and the thermal strain:
Since the thermal strain is directly proportional to the temperature, a consistent approximation would be to use one step lower discretization order for the temperature than for the displacements. When using built-in multiphysics couplings, such as Thermal Expansion, such a modification is not necessary. Any mismatch is automatically taken care of by reinterpolating the thermal strains to an order that matches the general strain field.
Another type of coupling appears on the boundary between two domains having different physics, as in fluid–structure interaction and acoustic–structure interaction. When, for example, Thermoviscous Acoustics is coupled to Solid Mechanics, then the time derivative of the displacement in the solid is set equal to the velocity in the acoustic medium on the shared boundary. In this case, it makes sense to have the same shape function order for these two fields.
For bidirectional multiphysics couplings, it is not always possible to select shape function orders for all fields that will give perfectly consistent representation of all terms.