Numerical simulation of progressive interfacial debonding in three-phase piezoelectric composites using Voronoi cell finite element method

To address the performance degradation caused by interface debonding in three-phase piezoelectric composites under electromechanical loading conditions, this study proposes a novel electromechanical coupling numerical model based on the Voronoi Cell Finite Element Method (VCFEM). A three-phase stochastic Voronoi microstructure generation algorithm is developed to establish heterogeneous geometric representations comprising piezoelectric particles, polymer matrix, and interphase layers. Building upon the derived minimum complementary energy principle, a novel variational functional is formulated through the electromechanical coupling field governing equations. This formulation introduces: (1) independent stress and electric displacement fields within element domains, (2) autonomous displacement and electric potential fields along element boundaries, thereby establishing a unified functional that intrinsically couples these four field variables. The Lagrange multiplier method is employed to enforce displacement-electric potential constraints at interfaces. A modified complementary energy functional is proposed to ensure generalized traction continuity across both matrix-interphase and inclusion-interphase interfaces, while maintaining zero generalized traction on crack surfaces. This approach achieves precise simulation of progressive interfacial debonding under electromechanical interactions. Numerical examples simulating interfacial debonding in three-phase piezoelectric composites demonstrate the validity and robustness of the proposed model through comparative analyses with conventional Finite Element Method (FEM). This research provides an efficient simulation tool for interface optimization design of piezoelectric composites under electromechanical loading conditions, which can be extended to reliability assessment of other multiphase smart material systems through generalization of microstructure generation rules and failure criteria.