Origin of compaction bands: Anti-cracking or constitutive instability?
Résumé
Based on the theoretical analysis and finite-difference simulations, we study the onset and evolution of tabular compaction bands. In numerical models the bands are initiated as constitutive instabilities resulting from the deformation bifurcation. Then some bands are dying, while others continue to evolve accumulating the inelastic deformation/damage and compressive stress at their tips. The stress concentration/increase, however, does not exceed 0.1% of the background value. Starting from some stage, the bands begin to propagate similarly to cracks. At the next stage the propagation slows down simultaneously with the beginning of bands' thickening that occurs due to incorporation of not yet compacted material at the band flanks. The response of the already compacted "core" part of the band becomes mostly elastic. Then the propagation practically stops and the bands undergo only the heterogeneous thickening, maximal in the middle of the band and reducing toward its tips. This scenario obtained directly in the models (without any specific hypotheses about the propagation mechanism) appears more complicated than what can be expected from the linear elastic fracture mechanics (anti-crack) model. The band propagation distance is proportional to the initial (resulted from the bifurcation) band length that in turn is proportional to the hardening modulus and theoretically can reach infinity.