What happens when DC is applied to a piezo crystal?
How do I do it with DC


For a very short period of time is the short answer.

Longer answer - a piezo is basically a capacitor in terms of equivalent circuit and, to push a constant current through that capacitor requires a ramp voltage applied to the terminals. This follows from the basic capacitance equation: -

$$ I = C\dfrac{dv}{dt}$$

In other words, to keep current at a constant value dv/dt needs to be constant and that means a voltage waveform that is a ramp. Pretty soon you will have raised the ramping voltage so high that you have thousands of volts across the piezo and it's going to breakdown due to over-stress voltage.


  so I would like to know theoretically what direction of DC will cause
  the crystal to compress or expand?


Assuming you can overcome the above difficulty by only applying the ramp for a short period of time, the data sheet for the piezo will tell you the answer.