Hysteresis in Elasticity

Stress-strain curves with loading/unloading loops — energy dissipation

Hysteresis in a stress-strain curve means the loading and unloading paths differ; the enclosed area equals energy dissipated per cycle as heat. Metals show a sharp elastic (linear) region, a yield point at σ_y, then plastic (permanent) deformation. Rubber (Mullins effect) shows large hysteresis from polymer network reorganization. The stored elastic energy is recovered; the hysteresis loop area is permanently lost.