Conservation integrals for the interfacial crack in bimaterial and layered ferroelectrics

•Obtain invariant conditions and conservation integrals for nonlinear ferroelectrics.•Prove the path-independence of J̃1-integral in bimaterial and layered ferroelectrics.•Interpret the crack tip J̃1-integral as the energy release rate of interfacial crack.•Discuss J̃1-integral in layered ferroelectrics versus layer thickness and loading.

This paper focuses on establishing conservation integrals for nonlinear bimaterial and layered ferroelectrics. Employing the infinitesimal transformation, we obtain the invariant condition for ferroelectrics in the sense of Noether’s theorem. A revised J̃i-vector path-independent integral is achieved for homogeneous ferroelectrics both in the global and local coordinate systems. The path-independence of revised J̃1-integral in bimaterial and layered ferroelectrics is demonstrated, with different electric crack surface conditions considered. Moreover, the crack-tip J̃1-integral can be interpreted as energy release rate. Numerical simulations in layered ferroelectrics are presented to show characteristics of conservation integrals with respect to layer thickness and combined external loading.