deformationhysteresis

Deformation hysteresis refers to the dependence of a material's deformation on its loading history, producing a loop in the relationship between stress and strain during cyclic loading. It reflects irreversible energy dissipation and is observed in metals, polymers, composites, soils, and many other materials. The phenomenon arises from inelastic processes such as plastic deformation, viscoelastic damping, and microstructural rearrangements that do not immediately reverse when the load is removed.

In metals, dislocation motion and interactions lead to yield and work hardening; unloading follows a different path, producing a plastic residual strain known as the permanent set and features like the Bauschinger effect. In polymers and elastomers, molecular mobility and viscoelastic damping create rate- and temperature-dependent hysteresis. In soils and granular materials, particle rearrangement and friction generate significant hysteresis under cyclic loading.

The area of the deformation hysteresis loop corresponds to energy dissipated per cycle. The loop's size and shape depend on loading amplitude, frequency, temperature, and prior conditioning. Reversible hysteresis occurs when deformation is entirely elastic and rate-independent; genuine deformation hysteresis involves irreversible changes and history dependence.

Experimentally, cyclic stress-strain tests and dynamic mechanical analysis reveal hysteresis loops. Models include viscoelastic springs and dashpots for rate effects, plasticity models for permanent set, and hysteresis constitutive laws such as Preisach-type or Bouc–Wowersley-type formulations to capture path dependence.

Understanding deformation hysteresis informs damping and vibration control, seismic analysis of soils, fatigue life assessment, and material design for energy dissipation. It is distinguished from magnetic hysteresis and other history-dependent phenomena by its focus on mechanical deformation.