A Thermodynamically Based Modified Cam‐Clay Model for Post‐Bifurcation Behavior of Deformation Bands

Abstract

Compaction bands are a type of localized deformation that can occur as diffuse or discrete bands in porous rocks. While modeling of shear bands can replicate discrete and diffusive bands, numerical models of compaction have so far only been able to describe the formation of discrete compaction bands. In this study, we present a new thermodynamic approach to model compaction bands that is able to capture both discrete and diffuse compaction band growth. The approach is based on a reaction‐diffusion formalism that includes an additional entropy flux. This entropic velocity regularizes the solution, by introducing a characteristic diffusion length scale and controlling the mode change from discrete to diffusive post‐localisation growth. The approach is used to model compaction band growth in highly porous carbonates. The model can replicate the areas of material damage exhibiting reduced porosity which are often observed as nuclei for the growth of compaction bands in experiments. The model also has the versatility to predict the formation of diffuse compaction bands, which is a significant advance in the field of compaction band modeling. The method can potentially be used for investigating the effect of material heterogeneities on compaction band growth and is heuristic for developing new methodologies for forecasting compaction band formation.