Poroelasticity in infinite orthotropic materials with smooth interfaces via Green’s functions

Abstract

Green’s functions are essential analytical tools in physics, providing key insights into the behavior of complex multiphase systems. This study examines poroelastic effects in infinite orthotropic materials with smooth contact interfaces using Green’s functions, which play a significant role in flotation mattresses and rock–soil systems. By employing strict differential operator theory and potential theory, we present compact mono-harmonic general solutions to the governing equations that satisfy sixth-order homogeneous partial differential equations. Based on the obtained compact general solution, the 2D fundamental solution for a steady line fluid source in an infinite orthotropic poroelastic plane with smooth interfaces is derived using six newly introduced harmonic functions.functions, ensuring their ease of use in practical applications. Numerical simulations, presented through non-dimensional contours and spatial visualization, reveal elliptical behavior, high-density levels near the fluid source, decay at a distance, higher-order singularities, zero-common tangents, and adherence to interface continuity conditions.