Flow of a friable medium with possible unlimited slip over the localization surfaces

Conclusions

1. In the general case, steady loading conditions of a friable medium result in a deformation process that is either steady or near-periodic.

2. The pattern of localization lines depends on the contour of the deformed region. At small compression, the lines resemble logarithmic spirals. With increase in compression, they become closed and resemble Cassinian ovals. Families of Cassinian ovals are encountered in the most diverse branches of mechanics and physics (in phase portraits of different physical pictures, patterns of equipotential and electrostatic lines, etc.). In the present work, this family, in all its diversity, including Bernoulli lemniscates, is obtained in experiments with friable material. This agreement cannot be random and evidently indicates the appearance of some general law.

3. Steady slip lines, at which slip continues for as long as is desired, are obtained. This result may be used to investigate the properties of various geological materials in conditions of unlimited shear.