The control board that I'm looking for should be able to sampling an input voltage sinusoidal wave with frequency f=85kHz
The ADC sampling frequency will be:
85KHz * Samples_number_per_period.
The maximum ADC sampling frequency of a DUE is 1Msps, That is to say a maximum of 11 samples per period. I doubt it would be the accuracy you are looking for, wouldn't it ?
You would need a bipolar ADC, it can be done with a DUE providing you add some hardware:
You could trigger an interrupt whenever you cross 3.3V / 2 with the ADC window feature.