An adaptive dynamic phase-field modeling with variable-node elements for thermoelastic fracture in orthotropic media

In this work, a novel adaptive algorithm integrated into a dynamic phase-field method is developed to model the fracture of orthotropic materials under thermoelastic loading. The procedure of local refinement is synchronized with crack tip advancement, with the phase-field value serving as the criterion for marking elements. To address mesh refinement inconsistencies, variable-node elements are employed. Hughes-Hilbert- Taylor (HHT) and backward difference method are utilized for time discretization of displacement and temperature, respectively. A penalized structural matrix is incorporated into crack surface density to realize the orthotropy of crack growth. The performance of the proposed method is validated through several numerical benchmarks, i.e., the proposed method can effectively simulate the dynamic crack propagation of orthotropic materials under thermoelastic loading, and can assuage computational overhead while keeping acceptable accuracy.