Energy release rate and path-independent integral in dynamic fracture of magneto-electro-thermo-elastic solids

The energy release rate and associated energy flux integral in dynamic fracture of magneto-electro-thermo-elastic solids are formulated with the inclusion of multi-field fully coupled effects based on fundamental principles of thermodynamics. The difference between the global and local dynamic contour integrals is caused by unsteady state, mechanical body force, electricity conduction and thermal effect as the closed contour including crack faces is chosen. This formulation successfully captures the crack-tip singularity of coupled fields, offers the right expression for the crack driving force, and resolves the controversial issue on magneto-electro-thermo-elastic fracture criterion. Especially, for steady-state crack propagation in a magneto-electro-elastic solid, the path-independent dynamic contour integral is determined from the asymptotic near-tip field solution based on the Stroh-type formalism and the resulting dynamic energy release rate has an odd dependence on the dynamic magnetic induction intensity factor and the dynamic electric displacement intensity factor.