Explain the von Mises failure criterion and when it is used.

Von Mises criterion states that yielding occurs when the distortion energy reaches a critical value, expressed as σvm = √[σ₁² + σ₂² + σ₃² - σ₁σ₂ - σ₂σ₃ - σ₃σ₁] ≥ σy. It predicts failure in ductile materials under complex loading and is the default criterion in FEA software. It accounts for all stress components and gives a single equivalent stress for comparison with yield strength.