Magneto-electro-thermoelastic (METE) materials are novel intelligent materials of significant research value. However, they are highly susceptible to stress concentration and subsequent fracture failure under complex multi-field coupling service conditions, and relevant fracture investigations on such materials remain limited to date. Based on the Muskhelishvili complex variable theory, this paper establishes and solves a fracture mechanical model for an inclined lip-shaped crack in METE media. A novel conformal mapping model is constructed by adopting translation, rotation, and reflection transformation techniques, which accurately maps the exterior domain of the lip-shaped crack to the exterior of a unit circle. Combined with the Stroh formalism, explicit analytical solutions for the dimensionless field intensity factors and energy release rate at the crack tip are derived. A series of numerical examples are performed to systematically explore the effects of crack geometric dimensions, as well as electric, magnetic, and thermal permeable boundary conditions, on fracture parameters.
The results indicate that mechanical loads and heat flux serve as the primary driving forces for crack propagation, while improving the electric, magnetic, and thermal permeability of crack surfaces can effectively restrain crack growth. Increasing the crack inclination angle significantly weakens the tendency for crack propagation. Among the three permeability parameters, the thermal permeability coefficient exhibits the most prominent regulatory effect, whereas the magnetic permeability coefficient has the weakest influence. Notably, the external magnetic field cannot drive crack propagation directly; instead, it modulates the electric field distribution through the magnetoelectric coupling effect, thereby indirectly regulating the system's fracture energy level. As the crack inclination angle increases from 0° to 90°, the field intensity factors at the crack tip decrease monotonically and gradually approach zero. The multi-field coupling fracture driving effect reaches its maximum when the crack is perpendicular to the loading direction. Conversely, when the inclination angle approaches 90°, the "geometric shielding" effect induced by multi-field coupling almost completely blocks the driving effect of the mechanical loads, providing novel physical insights for fracture suppression through crack orientation tuning. Furthermore, enhancing the electric and magnetic permeability of crack surfaces effectively weakens the field singularity at the crack tip and retards crack propagation, while improving thermal conductivity relieves thermal stress concentration and reduces the risk of structural fracture. The proposed model can be reduced to the classical Griffith crack solution under specific boundary conditions, verifying its accuracy and reliability. This study provides a robust theoretical basis and numerical reference for the anti-fracture optimization design of METE intelligent structures.