Perfect plasticity idealizes a material whose yield surface does not evolve as plastic deformation accumulates. In one-dimensional elastic-perfectly plastic loading, while ; continued plastic extension can occur at the fixed yield stress . Unloading can still be elastic, so perfect plasticity does not mean that the elastic response is absent.
This model isolates permanent flow from work hardening and is useful in limiting-load calculations. A rigid-perfectly plastic model makes the additional approximation of neglecting elastic strain, as in classical slip-line field theory. A real specimen may harden, soften, damage or show rate dependence, so the constant threshold is an idealization rather than a universal property of metals. It is also a local material law: decreasing cross-sectional area can change the measured axial force even when the local flow stress is constant.
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