Models for compaction band propagation

A compaction band is modelled as a thin, ellipsoidal heterogeneity with an imposed inelastic compactive strain and different elastic moduli from the surrounding matrix.Previously published results are used to determine the stress state in the band. For a wide variation of properties, stress conditions, and inelastic strain, the stress state in the band for aspect ratios observed in the field, 10 ^-3-10 ^-4, is indistinguishable from the result in the zero aspect ratio limit. In this limit, the compressive stress immediately adjacent to the band tip is roughly 10-100 times the far-field stress for parameters representative of field conditions. This value is relatively insensitive to the elastic mismatch between the band and the surrounding material, and is primarily controlled by the ratio of the far-field stress to twice the shear modulus times the inelastic compactive strain. This ratio is inferred to be about 0.02-0.05 from published field results, but may be several times larger for laboratory specimens. The ratio of tip to far-field stress increases with decrease of band shear modulus and becomes unbounded if both the shear modulus and aspect ratio go to zero. A combined anti-crack-dislocation model, in which a compactive relative displacement 2h is specified in the centre of the band and uniform traction elsewhere, predicts that for growth at constant energy release rate h is proportional to √L- where L is the half-length of the band. For an energy release rate of 40 kJ m ^-2, inferred in an earlier study from field observations and comparable with compaction energies inferred from laboratory tests on circumferentially notched compression samples, the constant of proportionality is consistent with that inferred from laboratory observations and earlier field data.