Phase field model for brittle fracture in multiferroic materials

Abstract

Multiferroic materials, which simultaneously possess piezomagnetic, piezoelectric, and electromagnetic coupling effects, have a wide range of applications in various fields. Multiferroic materials are generally brittle with low fracture toughness, and accurate prediction of the fracture behaviors of multiferroics is challenging. In this work, a phase field model for brittle fracture in multiferroic materials is developed with the help of the Hamilton principle. In light of the second law of thermodynamics, the constitutive equations are derived in the context of the phase field method. The present theoretical framework unifies two classical phase field models and four combinations of the electric and magnetic boundary conditions. The residual controlled staggered algorithm, which enjoys a higher accuracy and lower computational cost, is extended to the fracture problems in the context of magneto-electro-elasticity. Systematic numerical simulations are performed in both 2D and 3D cases. The influences of the external magnetic field, electric field, and electric and magnetic boundary conditions on fracture behaviors of multiferroic materials are studied in detail. The applied magnetic field may not only accelerate or delay the fracture, but also influence the crack path. The present work is beneficial to assess the safety of multiferroic-based devices in engineering applications.