Dynamic strain localization into a compaction band via a phase-field approach

We present a new phase-field formulation for the formation and propagation of a compaction band in high-porosity rocks. Novel features of the proposed formulation include (a) the effects of inertia on the rate of development of compaction bands, and (b) degradation mechanisms in tension, compression, and shear appropriate for dynamic strain localization problems where disturbances propagate in time in a wave-like fashion to induce micro-cracking, grain crushing, and frictional grain rearrangement in the rock. We also present a robust numerical technique to handle the spatiotemporal formation and evolution of the compaction band. We validate the model by simulating a benchmark problem involving a V-shape notched cylindrical specimen of Bentheim sandstone tested in conventional triaxial compression. The model is shown to reproduce different geometric styles of deformation that include pure compaction, shear -enhanced compaction, and a combination of pure and shear-enhanced compaction, where the combination mechanism consists of a straight primary compaction band surrounded by secondary chevron bands.