Finite strain micro-poro-mechanics: Formulation and compared analysis with macro-poro-mechanics

Porous materials are ubiquitous in nature – notably living tissues, which often undergo large deformations – and engineering applications. Poromechanics is an established theory to model the response of such materials; however, it is limited in its description of microscale phenomena, and structure-properties relationships. In this paper, we propose a microscopic poromechanical model based on a novel formulation of the micro-poro-mechanics problem, which allows to compute the response of any porous periodic microstructure to any loading involving fluid pressure, macroscopic strain, and/or macroscopic stress. We systematically compare the global response of our micro-model to macro-poromechanics, in both the infinitesimal and finite strain settings, and investigate in particular three mechanisms, namely solid compressibility, strain-pressure coupling and deviatoric-volumetric strain coupling. We notably illustrate how the micro-model can be used to derive macroscopic parameters, and how these parameters depend on microscopic features like pore shape, porosity, material properties, etc. This modeling framework will be the basis for powerful micro-poro-mechanical models of various materials and tissues, where pore-scale phenomena can be incorporated explicitly.