Investigating the 3D coupling of mechanical and electrical effects on porous materials via Green’s function

Abstract

Porous materials, characterized by fluid-filled interconnected voids, exhibit intricate mechanical–electrical interactions that are essential for understanding and advancing their conductivity, strength, and engineering applications. This study introduces a comprehensive novel analysis of three-dimensional (3D) transversely isotropic poro-piezoelastic (PPE) materials, employing potential theory, displacement functions, operator theory, and Almansi’s theorem. Compact general solutions are derived using harmonic functions that satisfy weighted harmonic and octaharmonic partial differential equations (PDEs). A 3D Green’s function for concentrated forces and point charges in solid and fluid phases is developed, introducing four new harmonic functions to address diverse practical challenges. Numerical results, validated against existing literature, reveal distinct PPE component behaviors, including rapid contour variations near sources, zero-field limits at large distances, increased contour density near point charge sources in fluids, and higher-order singularities in shear stress around concentrated sources. These findings offer valuable insights into the physical mechanisms of PPE materials and expand their potential for innovative engineering applications.