[bigphil]

To publicly answer a question I received via email:

Question
Why can the d2dt2 and ddt be set to steady state and the boundary conditions be set with a time dependence?

Answer

In solid mechanics, we are often interested in quasi-static responses, where by quasi-static we mean than the solid is moving slow enough such that inertial effects are negligible and can be ignored.

If the governing equation (linear momentum) can be written in the form of Newton's second law (sum of F = ma) then for quasi-static analyses 'a' is zero and so we get (sum of F = 0). To achieve quasi-static in OpenFOAM, we set d2dt2 and ddt to "steadyState".

However, quasi-static analyses can still have time-varying boundary conditions e.g. a standard tensile test has time-varying boundary conditions but the inertial effects are negligible.

Hopefully, this makes sense.

Philip