“Joy” is an ode to the American dream and, more important, the American housewife, starring a dependably steely Jennifer Lawrence as a version of Joy Mangano, the Long Island mother of three whose design for the self-wringing Miracle Mop turned her into a multimillionaire. Unlike Mangano’s invention, “Joy” is a bit unwieldy and hard to get a handle on. At its best, though, it’s a smart, funny, sensitive portrait of the kind of woman whose role in both film and life is often ignored.

Directed by David O. Russell, who co-wrote with Annie Mumolo (“Bridesmaids”), “Joy” introduces its heroine as a woman stumbling on life’s treadmill. She’s a dutiful daughter to her semi-lunatic parents (Robert De Niro and Virginia Madsen, both terrific) and breadwinner for her children and rather likable ex-husband, Tony (Edgar Ramirez). Grandma Mimi (Diane Ladd) provides unnecessary narration, but the film’s early scenes vividly illustrate Joy’s exhausting existence. “I’m just going to close my eyes for a bit,” she says, then sinks into the comatose sleep of the woman who does it all. Even playing a doormat, though, Lawrence conveys Joy’s inner toughness; we know we’ll see it soon enough.

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Using her daughter’s crayons, Joy (no relation to Nassau County Executive Edward Mangano) designs her now-famous mop, then hits up her father’s girlfriend (a beguilingly strange Isabella Rossellini) for seed money. The growth of Joy’s homespun business, a mess of patent laws and shady manufacturers, is fitfully entertaining, but “Joy” hits its stride with the arrival of Neil Walker, an executive at the fledgling home-shopping channel QVC who gives Joy her life-changing chance. Walker, a blue-eyed true believer in capitalism, played by a compelling Bradley Cooper, vocalizes some interesting ideas about American democracy, commerce and social mobility. “I believe,” he says, “that one day television will be by and about regular people.”

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“Joy” could have easily mocked its heroine as a symbol of middle-American consumerism. The film has its laughs, but none come at Joy’s expense. Lawrence plays her with grit and mettle, something she’s famous for both on-screen (“The Hunger Games”) and off (as a proponent of equitable pay for women in Hollywood). Although “Joy” can’t quite decide what it wants to be — the studio insists it’s not a biopic, though clearly it’s not not one — we never doubt the determination and inner strength of Joy herself.