"rigorous demands" is a perfectly correct and usable phrase in written English.
For example, you might say something like, "The job requires meeting rigorous demands for quality."
The coach had made rigorous demands on certain players.
Moreover, not all immigrant Sikhs hew to the rigorous demands of their faith.
The dancers seem driven as they set about fulfilling its rigorous demands, and so its challenges draw you in.
It has been good for its suppliers, as its rigorous demands have forced them to improve their own efficiency and quality.
Virtually nothing can induce boredom at this point more than a close-up of someone talking about the rigorous demands of her job in public relations.
While there are hundreds of breeds in existence, commercial facilities rely on only a select few that meet the rigorous demands of industrial production.
The resulting body of work is rigorous, demanding and concentrated.
Even so, Heizer has a rigorous, demanding view of patronage.
In particular, long-term residential treatment is a rigorous, demanding and life-changing experience.
It is a rigorous, demanding approach that lets students who apply themselves create more than a major.
But for most part the musicians took rigorous, demanding works and played them with an almost breezy ease.
