As far as the law goes, any nonconcensual act of sex is rape, period.

But there ARE types of roleplay fantasy that involve rape, in which case it would be established BEFOREHAND that the act to follow was a consensual roleplay of a rapist and a rape victim.

Also, any serious BDSM activity requires the use of a "safe" word, something the receiver will say if the pain/activity/etc. is too much and no longer concentual, as often they will say no as a vocal reaction even if what they are receiving is wanted as part of the fetish. (ie, your example of saying no, but thinking yes on the inside)

In any actual rape situation- plain out nonconsensual sex, there would never (well, I suppose never say never, but it would not be something I could ever imagine happening more than extremely rarely) be a situation where someone could "ask" for rape, or be resisting sex vocally but inwardly wanting it.

The second situation would be the one I could plasuibly see happening, as there are cases already that could be seen as similar. For example, a girl becomes pregnant and claims it was rape to get an abortion or so her parents won't be mad at her; a couple has sex and one partner later regrets it or they break up/get into a fight and so rape is claimed as a method of "punishment/other"

Sorry that this is all a bit jumbled.

I suppose, to answer your question directly:

Legally, in the eyes of the law, there would (probably) not be a case that someone "asks" to be raped and then reports the "rapist" to the police. Also, in the eyes of the law, rape is whenever a sexual act is not consensual, either by a vocal or physical reistance (so even if the vitim was consenting to the sex internally but vocalizing "no" it would probably be considered rape, as there really is no way to prove that the victim was feeling one way or another inside his or her head. Though if the victim truely was thinking yes inside their head when saying no, this raises the question of whether or not they'd even report it as rape), or if the victim could not, due to an impaired state, truely consent to the act (ie, the victim was drunk).

If consent exists, throughout all of the activity by both parties, it is not rape. One cannot ask someone to rape them, because that request in and of itself means it is not rape: that's basically an oxymoron. One can ask someone to have sex with them under guise of a rape fantasy, but that is role play, not reality.

If a person wants the sex in question -- if sexual activity is wanted -- again, that is not rape.