Undrained Electromechanical Response of an Apex-Loaded Porous Piezoelectric Cone with Solid–Fluid Coupling under Bending and Torsion

Abstract In this study, we provide a comprehensive analytical framework that examines the undrained electromechanical behavior of porous piezoelectric (PP) cones when bending and torsional moments are applied at the apex. By integrating Biot's theory of poroelasticity with a coupled electroelastic formulation for transversely isotropic materials, this study presents a unified continuum model that accurately captures the interaction between solid and fluid phases. The governing field equations are systematically derived through the potential function method, leading to exact closed-form solutions for the displacements, stresses, and electric potential. The model's accuracy is verified against classical electroelastic benchmark solutions and corresponding Finite Element Method (FEM) simulations. Parametric studies reveal that porosity, apex angle, and electromechanical coupling coefficients, and anisotropy tests significantly influence stress localization, electric displacement, and field attenuation. The results show that field singularities are more pronounced near the apex (e.g., exhibiting a high-order dependency on the radius) and gradually decrease in the far-field region. In addition, when the apex angle approaches π/2, the solutions reduce to the corresponding semi-infinite body (half-space) problem. The developed formulation provides a strong theoretical foundation for understanding and designing advanced porous piezoelectric sensors, actuators, and energy harvesting devices, particularly in environments with complex electromechanical loading conditions.