viscoplastic

Viscoplasticity describes materials that exhibit both viscous flow and plastic yielding. In viscoplastic models, permanent deformation depends on the rate at which load is applied, and the material may flow over time under sustained stress. The behavior combines viscosity, which is time-dependent, with plasticity, which produces irreversible deformation once yielding occurs.

Constitutive models separate elastic, plastic, and viscous contributions. A yield criterion defines when plastic flow begins; a flow rule governs the rate of viscoplastic strain, often a function of the effective stress and temperature. Common formulations include Perzyna, Duvaut–Lions, Bodner–Partom, and Anand-type models, which may be associative or non-associative and may include isotropic or kinematic hardening.

Materials that exhibit viscoplastic behavior include polymers, metals at elevated temperatures (creep), ice, rocks, and some ceramics. Applications range from polymer processing and metal forming to geophysical modeling of Earth's crust and ice sheets, where time-dependent deformation and rate effects are important.

Key parameters include yield stress, viscosity (or strain-rate sensitivity), activation energy, and temperature dependence. Experimental data show that flow strength can decrease with increasing strain rate or temperature, and that time-to-failure under sustained load matters in creep. Numerical implementations require stable time integration and, often, regularization to handle rate effects.