Monolithic mechanical model incorporating solid contact for anisotropic porous materials

Understanding the mechanical behaviour of anisotropic porous materials as they deform is critical for applications such as geological carbon storage and subsurface energy systems. This study presents a comprehensive finite-elementbased framework to simulate the evolution of porous solid media with frictionless solid contact, capturing anisotropic changes in pore geometry under complex multidirectional loading. The framework follows an innovative workflow with four steps: (1) a finite element formulation and simulator capable of resolving contact interactions with complex geometries; (2) a fast approximation method to the solution of the underlying contact problem; (3) a perturbationbased protocol for updating anisotropic stiffness matrices and Biot coefficients during progressive deformation; and (4) full integration of periodic boundary conditions into both the deformation analysis and perturbation formulations. The numerical framework allows homogenisation of systems that are not analytically tractable. Applied to singleand multi-pore systems, the framework demonstrates that progressive pore closure governs stiffness evolution, driving a transition from skeleton-controlled to contact-network-dominated behaviour. Young's modulus decreases along the loading direction while increasing orthogonally; shear loading reduces modulus in all directions and activates normalshear coupling. Shear modulus initially rises due to oblique load transfer, whereas Poisson's ratio decreases under compression. However, following solid contact, these properties tend to approach those of the intact solid, but still remaining a distance under shear loading. Biot coefficients increase along the loading axis under uniaxial compression and rise in multiple directions under shear loading, but close to zero after solid contact under uniaxial compression process. This framework provides a robust and efficient tool for predicting nonlinear, anisotropic, and path-dependent poromechanical behaviour, linking pore-scale mechanisms to macroscopic material responses.