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

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. Compaction bands are areas of localized deformation in materials with multiple phases, such as porous rocks. They form when one of the phases localizes and forms bands perpendicular to the direction of the maximum principal effective stress. In this study, we present a new thermodynamically consistent model for compaction bands in porous materials. The model is based on the modified Cam-Clay plasticity model, but it includes a number of additions to make it more realistic and to account for the mesh sensitivity of numerical solutions. We test the new model against experimental results for compaction bands in highly porous carbonate (Mt Gambier limestone). We find that the model can accurately match the experimental results. This new model is a significant advance in the modeling of compaction bands. It has the potential to be used to investigate the effect of material properties, heterogeneity and loading conditions on compaction band formation, and to develop new methods for predicting compaction bands. A new thermodynamically consistent Cam-Clay model for deformation bands in porous rocks is presented, alleviating the numerical problem of mesh sensitivity The model is based on the modified Cam-Clay plasticity model augmented by an entropic regularization technique, accurately capturing the experimental results for compaction bands in highly porous carbonate The mode change from discrete to diffuse post-localisation evolution is found to be related to the reaction-diffusion processes of microstructure interactions