The phrase "assumed manner of" is correct and usable in written English.
It can be used when describing a way of behaving or conducting oneself that is taken on or adopted, often in a specific context.
Example: "In her presentation, she adopted an assumed manner of confidence that captivated the audience."
Alternatives: "adopted style of" or "taken approach of".
He assumed the manner of an interrogator, repeatedly accusing the women of having once been members of the underground resistance.
Our planet is a fascinating and diverse place, and the human race, ever pushy and inquisitive, has wriggled its way into all sorts of interesting corners and assumed all manner of heroic roles.
Which of course assume all manner of contradictory forms.
In photographs, Copperfield assumes a manner of chilly mastery; in person he is open, bending, almost needy, reminding the world of his triumphs — his renown, his Emmys — as though the scale of his accomplishments still surprised him, too.
Besides all this, there are glow-in-the-dark strings that assume all manner of beguiling shapes, an acrobatic larva, huge fabric orbs that roll all over the place and a pack of penguins that play a not-so-sporting but very funny game of musical chairs.
Fashions in goodness change, just like fashions in anything else, and these days some of the very noblest people have assumed the manners of the business world — even though they don't aim for profit.
Increasingly, Dean's willfulness was less subject to her will; her behavior assumed the uneasy manner of a parodist who may no longer be in on her own joke.
Tarski assumed, in the manner of his time, that the object language L and the metalanguage M would be languages of some kind of higher order logic.
Here Dr. Sanyal straightened his back and raised his head imperiously; unconsciously, he assumed the mien and manner of the hero-beast.
We expressed traction-free, infinitesimally thin cracks in a finite-difference staggered grid in probably the simplest manner: we assumed arrays of grid points with zero shear traction.
