An adaptive phase-field model integrated with multi-patch isogeometric analysis and adaptive cycle jump scheme for thermo-electro-mechanical fatigue fracture in flexoelectric solids

Abstract

Predicting the thermal fatigue life of flexoelectric components is of great engineering significance. In this study, an effective adaptive phase-field model combined with the cycle jump scheme is proposed to simulate thermo-electro-mechanical fatigue fracture in flexoelectric solids. To provide $C^1$ continuity due to the presence of strain gradients, the phase-field model is implemented in the multi-patch isogeometric analysis framework based on polynomial splines over hierarchical T-meshes (PHT-splines). Multiple PHT-spline patches are employed to exactly model the geometry of the complex structure. Nitsche’s method is used to couple two adjacent patches and ensure the continuity of field variables such as displacement, electric potential, temperature, and phase field at the coupling edges. In order to reduce computational burden, an adaptive refinement strategy is adopted using the phase field as the refinement indicator. Additionally, the adaptive cycle jump method is used to improve computational efficiency further. The accuracy, reliability, and robustness of the proposed method are validated through several fatigue fracture simulations.