Refers to a person being unable to manage their emotions, usually in response to overwhelming stress. After failing her exam, Jamie had a melt down in front of the whole class.
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Informal Usage
Mostly used in casual conversation, not in formal settings. When her favorite character died in the show, she had a melt down.
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Not Literal
Does not mean a physical meltdown, but a sudden and intense emotional reaction. He's on the verge of a melt down with all the work stress.