On the phase-field modeling of thermo-electromechanical brittle fracture in piezoceramics using an adaptive isogeometric approach

An adaptive phase-field model based on isogeometric analysis is presented to investigate the fracture behaviors of transversely isotropic homogeneous piezoceramics under the effects of thermo-electromechanical loadings. This study employs polynomial splines over hierarchical T-meshes (PHT-splines) for geometric and spatial discretization, constituting an efficient adaptive mesh refinement scheme within the framework of isogeometric analysis that uses a prescribed value of the phase-field parameter as an error indicator. A hybrid-staggered scheme is employed where an isotropic model is used to solve the displacement field while the phase-field parameter is computed based on an anisotropic model. In particular, thermo-electromechanical coupling is considered to determine the effects of temperature, external electric fields, and mechanical deformations on the critical fracture load under different modes of fracture. Numerical simulations reveal that while the influence of temperature on the fracture load is insignificant, it may still expedite or delay the onset of fracture. However, the direction and magnitude of external electric fields can significantly alter the critical fracture loads, for example, a negative electric field impedes crack propagation. Additionally, a series of numerical examples are presented herein to demonstrate the efficacy and robustness of our proposed phase-field framework, which shown enhanced accuracy and robustness with fewer elements and degrees of freedom. The model thereby provides insight into the fracture behaviors of piezoceramics in thermal environments and opens new avenues for the design and development of superior smart materials.