On 17 December last year, the playwright and director Yael Farber was at home, opening her laptop, when a news story popped up on her screen. A 23-year-old Indian student and her male friend had been attacked the night before on a bus in Delhi. She had been savagely gang-raped; he was beaten to a pulp. Both were in hospital.

In the hours that followed the incident, details rushed in: at least four men were involved, maybe more, among them the bus driver. The couple had been stripped, robbed, left for dead, tossed onto the roadside like rubbish. The woman had been penetrated with a metal rod, which had been removed with such force that it had taken nearly all of her intestines with it.

Farber posted a message on Facebook in response. "Normally I find it cheesy when people do that," she half-smiles. "But I was so moved by it. It just said something like: this could have been my sister, my mother, my daughter, myself."

The next day, the case was headline news, and Indian politicians were scrambling to contain public fury. By midweek, there were tens of thousands of protestors on the streets, calling for an end to a culture of sexual violence and harassment. The female victim – as yet unnamed – was hurried by air ambulance to Singapore; on 29 December, she died. Mourners across India wore black. Some pasted black fabric across their mouths.

Farber's message was spotted by a well-known Bollywood actor, Poorna Jagannathan. The pair started talking online about the attack, the protests, what all of it meant. "We were just chatting," says Farber. "She said – you know, women are ready to speak about what's happening right now. You've got to come here." Jagannathan bought Farber and her five-year-old daughter a plane ticket. By early February, they were in a rehearsal room in Mumbai.

The piece has just had its fifth public performance at Riverside Studios in west London, before opening at the Edinburgh fringe. It's called Nirbhaya: Hindi for "fearless", one nickname the Indian press gave the woman who was attacked, Jyoti Singh Pandey, but also now a symbol of the struggle worldwide against sexual violence. "As soon as the rape happened," Jagannathan tells me, "there was a huge feeling of complicitness. OK, I may not be perpetuating the violence, but I'm perpetuating the silence. It was about ending that."

"What was it about this case, about her?" Farber asks. "I think it just broke through the endemic numbness that we all develop. Her story was a tipping point, not only for people in India but outside, too. Sometimes a story just cuts through like a scalpel and says: I need to be heard."

Farber, who was born and grew up in Johannesburg, began her career making drama that responds to real events: before her hot-blooded South African adaptation of Strindberg's Miss Julie, which dominated last year's festival and is currently on a world tour, one of her best-known pieces was 2001's Amajuba, a searing play about life under apartheid assembled from the testimony of five survivors. But rarely had she worked with such furious energy. After she put out a Facebook call for women to contribute their own experiences, the cast rapidly fell into place. By day, they talked and rehearsed; by night, Farber honed the material into something that could stand up on stage. "I had to cook it hot and fast," she says.

What became obvious was that the play, in order to do justice to Pandey, would need to contain more than just her story. Hideous though the attack was, it was anything but rare. Delhi is regularly called the "rape capital" of the world; India has been ranked the worst G20 country in which to be a woman; every Indian newspaper carries lurid reports of "Eve-teasing" – as harassment is dismissively called – and attacks on women, believed to be increasing. But the problem goes deeper: according to the Indian government's own stark figures, 53% of Indian children experience sexual abuse. "Nothing happens in isolation," says Jagannathan. Farber agrees: "When we came together to talk, it was clear that all the women could speak about what they would call typical experiences – being groped on a train platform, far worse things."

The piece that emerged is as much a series of harrowing personal meditations as a straightforward narrative. One woman describes being abused as a nine-year-old by an Indian Air Force officer. "I learn to leave my body behind," she says, describing what it's like to push along a bus, being grabbed at every turn. Another woman is beaten by her father, then suffers marital rape.

What makes Nirbhaya exceptional, and at times almost unbearable to watch, is that only two of the seven cast members (Japjit Kaur, who plays Jyoti Singh Pandey, and Ankur Vikal, who plays one of the male attackers) are acting in any straightforward sense. The five other female performers, among them Jagannathan, enact scenes from their own lives – testimony that's written with painful obviousness on the features of Sneha Jawale, a "dowry bride" who was doused with kerosene and set alight by her husband, leaving her with severe burns. There's no doubting the courage of Jawale's performance: on the night I saw it, I began to wonder whether she'd be able to keep going.

Farber is acutely aware of the toll it takes on her cast, and the sensitivity of the issues; she has no desire to co-opt the Nirbhaya case, currently creeping its way through the Indian courts, nor imply that this is an India-only problem (according to the World Health Organisation, although south-east Asia has the highest rate of sexual violence, around one in three women globally experience physical or sexual abuse).

"I'm a theatremaker," she says. "I want to trigger things. I want people having fierce conversations in the bar afterwards, understanding something better or seeing things differently. Opening up, waking up."

But Farber is ardent that their play contains hope as well as fear: optimism about protest, about ending a culture of silence and shame. Seismic changes, she argues, can come from speaking out – simply from saying, as tens of thousands of men and women did on the streets of India: enough is enough. "The whole idea," she says, "is that urge to speak. Let it not be a defeat that she died. Let it be this that carries us forward."

Nirbhaya is at Assembly Hall, Edinburgh, until 26 August