Morphometric description of strength and degradation in porous media

We propose a morphometric strength law for porous media, relating their macroscopic behavior with their microstructural geometry. This relationship is inferred by phase-field modeling the degradation of a wide range of synthetic microstructures and upscaling the minimal amount of morphometric information, as per Hadwiger's theorem. It is found to be best described by an exponential function of the morphometers, thus generalizing early works on metals and ceramics. It is also shown to accurately predict the strength of real microstructures, including geomaterials and biomaterials. The suggested strength law offers a compromise between explicit microstructural modeling and constitutive macroscopic modeling. It thus paves the way for predicting the behavior of porous media with the minimal amount of data possible and in particular, minimizing the use of destructive tests.