Body-Force Effects in Homogenised Models of Anisotropic Double Poroelastic Materials

We develop a rigorous multiscale homogenisation framework for determining the effective behaviour of materials composed of a poroelastic matrix containing embedded poroelastic subphases, each governed by fully anisotropic and heterogeneous Biot equations and subject to body forces. Starting from local balance laws for momentum, Darcy flow, and mass conservation, and assuming scale separation, periodic microstructure, and macroscopic uniformity, we derive a closed system of Biot-type equations at the macroscale. The resulting effective coefficients explicitly capture the influence of microstructural geometry, elastic and hydraulic heterogeneity, and mesoscale forcing. The framework yields well-posed cell problems for the effective elasticity tensor, hydraulic conductivity tensor, and Biot-type coupling coefficients, establishing a unified multiscale theory that extends and subsumes existing single-phase, composite, and double-poroelastic models. As an illustrative application, we specialise the theory to magnetic Lorentz forcing and show that body forces with gradient structure induce additional pressure-like terms in the effective Darcy law, rather than appearing solely as averaged source terms. The proposed framework sets the agenda for modelling complex poroelastic materials with interacting subphases, with applications in biomechanics, engineered composites, and geomechanics.