Morphometric description of strength and degradation in porous media

TL;DR

This paper introduces a morphometric approach using Minkowski functionals to predict the strength and degradation of porous media, validated on synthetic and real microstructures like rocks and bones.

Contribution

It develops a unifying morphometric strength law linking microstructure geometry with material strength, extending previous models to real porous materials.

Findings

Strength correlates exponentially with morphometric measures.

The model accurately predicts strength in rocks and bones.

Microstructural damage can be tracked via phase-field simulations.

Abstract

The influence of the microstructural geometry on the behavior of porous media is widely recognized, particularly in geomaterials, but also in biomaterials and engineered materials. Recent advances in imaging techniques, such as X-ray microcomputed tomography, and in modeling make it possible to capture the exact morphometry of the microstructure with high precision. However, most existing continuum theories only partially account for the morphometry. We propose here a unifying approach to link the strength of porous materials with the necessary and sufficient microstructural information, using Minkowski functionals, as per Hadwiger's theorem. A morphometric strength law is inferred from synthetic microstructures with a wide range of porosities and heterogeneities, through qualitative 2D phase-field simulations. Namely, the damage is modeled at the microstructural level by tracking the solid-pore interfaces under mechanical loading. The strength is found to be best described by an exponential function of the morphometers, thus generalizing early works on metals and ceramics. We then show that the predictiveness of this relationship extends to real porous media, including rocks and bones.