I guess you want to model the diode as either fully off or fully on with a 0.6 V diode drop across it?
If so, then I would draw a "diode on" and "diode off" equivalent circuit, and analyse those separately.
Note that you can just add the the DC and AC signals to compute the voltage that the diode feels at any time, and from that you'll be able to see when the diode is forward or reverse biased. There is no current flow until the diode is forward biased by 0.6 V, so no voltage drop across the 100R until then. When the diode is on, the current through it does not affect the voltage drop across it (it's always 0.6 V in our assumption) so you can apply KVL in the usual way to find i(t), and hence V_R(t) and U_D(t).