Modeling anisotropic low-cycle fatigue behavior based on a two-surface damage–plasticity framework

Based on a two-surface damage–plasticity framework, this work develops a thermodynamically consistent anisotropic low-cycle fatigue model for ductile materials. The proposed formulation addresses a limitation of many existing phase-field fatigue models, where fatigue degradation may influence the regularization properties and consequently affect crack distributions. More specifically, a fatigue degradation function is introduced to progressively reduce the damage threshold, while the regularization properties are preserved as the damage gradient term remains unaffected by fatigue. To capture the tension–compression asymmetry observed under cyclic loading, the model combines the Drucker–Prager yield criterion with a star-convex energy decomposition, enabling asymmetric evolution of plasticity and damage. In addition, a second-order structural tensor is incorporated to describe the anisotropic damage evolution and preferred crack propagation directions. Numerical investigations demonstrate comparable regularization properties of the proposed model under monotonic and cyclic loading, as well as the predictive capability in capturing key fatigue behaviors. In particular, the predicted damage accumulation under various loading sequences is approximately consistent with the Palmgren–Miner rule, and the resulting fatigue lives follow the Coffin–Manson relation.