Self-consistent fractal damage of natural geo-materials in finite strain

This paper investigates the non-linear behaviour of geo-materials both in the reversible and irreversible thermodynamic regimes. Among the common Seth-Hill measures of deformation, we verify that the logarithmic (Hencky) strain produces the closest agreement with Diamond Anvill Cell experimental data obtained for a wide range of minerals. We extend the Eshelby-Hill based self-consistent upscaling of heterogeneous media to the context of logarithmic finite strain. Based on homogenisation, we introduce a novel continuum damage mechanics technique based on self-similar (fractal) distribution of defects and their propagation. The whole framework is implemented numerically using the finite element method with a particular emphasis on material and geometrical non-linearities that are both represented in the proposed integration algorithm. To verify the applicability of the model, we introduce particular examples where solid blocks are subjected to partial/full confinement conditions under force/displacement controlled loading. We solve the problems analytically and numerically and show that the proposed methodologies produce acceptable agreements.