Cyclic Plasticity Modeling in Metallic Materials

Cyclic plasticity modelling addresses the complex, irreversible deformation of metals under repeated loading. At its core, constitutive frameworks describe how metals accumulate permanent strain, exhibit cyclic hardening or softening, and develop mean‐stress drift (ratcheting) when subjected to asymmetric load cycles. Classical approaches combine isotropic hardening, representing uniform expansion of the yield surface, with kinematic hardening, accounting for its translation in stress space. Advanced models incorporate viscoplastic effects to capture rate dependence at elevated temperatures, non-proportional loading to reflect multiaxial service conditions, and microstructurally informed damage accumulation to predict low-cycle and high-cycle fatigue life. Implementation in finite element codes enables detailed component simulations—from nuclear steam‐line nozzles to automotive suspension parts—where accurate hysteresis loop prediction is critical for integrity assessment. Recent efforts have focused on robust calibration methods, such as optimisation and fuzzy logic, to reconcile experimental scatter and ensure predictive capability across strain amplitudes, loading rates and temperature regimes. By integrating cycle-by-cycle evolution laws with continuum damage mechanics, the field now offers comprehensive tools to guide alloy design, inform maintenance intervals and improve lifespan estimates for metallic structures worldwide.

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Cyclic Plasticity Modeling in Metallic Materials publication trend

The graph below shows the total number of articles in cyclic plasticity modeling in metallic materials across all publications each year (not limited to Nature Index journals).

Technical terms

Cyclic plasticity: Accumulation of permanent, irreversible strain in a metal subjected to repeated load–unload cycles.

Kinematic hardening: Translation of the yield surface in stress space to model directional hardening under cyclic loading.

Isotropic hardening: Uniform expansion of the yield surface due to the buildup of plastic strain.

Ratcheting: Progressive mean strain accumulation when cyclic loading is asymmetric about zero stress or strain.

Viscoplasticity: Rate-dependent plastic deformation combining irreversible strain with time-dependent effects.

Hysteresis loop: Closed stress–strain curve traced during one load cycle, indicating energy dissipation and material evolution.

References

1. A thermodynamically-based viscoelastic-viscoplastic model for the high temperature cyclic behaviour of 9–12% Cr steels. International Journal of Plasticity (2018).
2. Identification of Chaboche–Lemaitre combined isotropic–kinematic hardening model parameters assisted by the fuzzy logic analysis. Acta Mechanica (2020).
3. Finite Element Implementation of a Temperature-Dependent Cyclic Plastic Model for SA508-3 Steel. Metals (2018).