By James Mottram

"I slept for a solid three hours last night!" says J.K. Simmons, rubbing his eyes, yawning and removing his rather elegant fedora. It's hardly a surprise. Best known for playing Ellen Page's father in Juno, Simmons is suddenly amid that hurricane that is the awards season for his role in Damien Chazelle's upcoming indie hit Whiplash.

A few days ago, he won Best Supporting Actor at the Golden Globes; with a BAFTA nod also under his belt, tomorrow he could well find himself up for the first Oscar of his career when the nominations are announced. With events to attend and press to complete, gaining the sort of attention rarely afforded to character actors, little wonder he's sleep-deprived right now.

Simmons - whose initials stand for Jonathan Kimble - seems to be taking it all in his stride, though. "I think I only have 45 seconds - shut up!" he jokingly commanded the starry Globes crowd on Sunday, as he took to the stage to roars of approval, before calmly rattling off a list of thank-yous, including his wife Michelle and their three "above-average" children and, sweetly, finishing with a pat on his heart as he uttered the words "Mum and Dad".

Perhaps this laid-back quality comes from being a veteran who just turned 60 last week; his first movie appearance was 20 years ago in 1994's The Ref with Kevin Spacey, following two decades of work in the theatre. Or perhaps it's simply that the momentum is so with Whiplash, after a host of American critics' organizations, including those in New York and Los Angeles, awarded him Best Supporting Actor, he knows he's going to clean up.

He certainly merits it, Simmons delivering a fearsome performance that you simply can't take your eyes off. Set in a fictional New York music conservatory, he plays Terence Fletcher, an insanely demanding teacher who lashes out at his pupils, goading them with insults and bullying them into submission. At the core of the film is his volcanic relationship with Andrew (Miles Teller), an ambitious and aspiring jazz drummer.

Almost as soon as the film had its world premiere a year ago at the Sundance Film Festival, where it claimed both the Grand Jury Prize and the Audience Award, it was being dubbed 'Full Metal Julliard' - a reference both to the prestigious New York arts college and Stanley Kubrick's 1987 Vietnam classic Full Metal Jacket, in which R. Lee Ermey gives a titanic turn as a ball-busting drill sergeant, who - like Simmons - is as bald as a cue-ball.

If Ermey's performance might seem like an influence on Fletcher, as he hurls homophobic slurs in the direction of the shell-shocked Andrew when he so much as misses a beat, Simmons claims otherwise. "I have never seen the whole movie," he says. In a career that famously saw him play a neo-Nazi prisoner in HBO drama Oz, as well as the Colonel in a Broadway production of A Few Good Men, he's had more than enough practice at playing the unhinged.

Developing the character from the ground-up - right down to his almost "militaristic" deportment and all-black wardrobe - Simmons' attention to detail is what impresses, along with the electric dialogue exchanges, something that came from his relationship with the 27 year-old Teller. "Immediately, we settled into that relationship of just being peers - the macho bullshit banter flew back and forth like a couple of guys on the same junior high football team. It was about that level of intellect."

If the film is about striving for perfection to an almost unhealthy degree, Simmons had some experience to draw from. The Detroit-born actor studied music in college and his old professor was similarly exacting. "He said that our first task is to get it perfect and then we can make it great. But you have to be technically proficient and flawless before you can begin to make art; so to play a guy who is a relentless, abusive bastard like that, you have to find the motivation for it."

Curiously, Simmons' own father, Donald William Simmons, was also a music professor at the University of Montana - about as far removed from Fletcher as you could get. "I saw my father as this really charismatic teacher who inspired curiosity and a love of music. It was a beautiful thing to see." Becoming chairman of the university's music department, it seems Simmons' father would not have held much stock in the character's methods. "He definitely would've fired Terence Fletcher immediately!"

While Simmons went on to join the Seattle Repertory Theatre company, his move into film and television has been a slow-burn. "There are many of my own films - that I've had small parts in - that I have never seen," he admits, and it wasn't until he got to work with what his "trifecta" of directors - Sam Raimi, the Coens and Jason Reitman - on a variety of projects including Reitman's Oscar-winning teen pregnancy tale Juno and Raimi's Spider-Man trilogy, that things changed.

Since Whiplash, however, Simmons has been enjoying a career renaissance. He'll be seen later this year alongside Arnold Schwarzenegger in Terminator: Genisys, the fifth installment in the sci-fi series, and he's just been cast in Kong: Skull Island, a prequel to King Kong co-starring Michael Keaton. Simmons squaring up to Arnie and an 800lb gorilla? Judging by the ferocity of his performance in Whiplash, that's not much of a contest.

Whiplash opens tomorrow.