AbstractSome theoretical criteria are set forth to study the onset of a strong and/or a weak discontinuity in hypoplastic granular materials under some simple motion fields. The theoretical criteria were based on direct analysis, considering both kinematical and dynamical conditions necessary to be satisfied in order to make a discontinuity of either type possible. We mean by simple motion fields those motion fields that are typically observed in standard laboratory tests, including homogeneous motion fields. A series of comparisons with available experimental data have been made for a simple hypoplastic constitutive equation.Practical ApplicationsIn geomechanics and other fields related to granular or porous materials, it is of particular importance to see whether the material is stable while deforming under applied loads. The phrase stability means, in a general sense, an ability to sustain the applied loads or remain in a particular form, without further deformation, following total loss of strength. Examples are the stability of underground tunnels or deep excavations prior to the construction of, say, a high-rise building. In both cases, deformation occurs while tunnel boring or ground excavation takes place, resulting in the alteration of the stress state followed by possible instabilities. A good example of instability is the catastrophic failure of tunnels in rock that takes place by sliding and falling of heavy blocks of rock along cracks and joints, in general, along planes of discontinuity. A plane of discontinuity often indicates the onset of instability in most materials. The results of this paper are expected to be useful in performing stability analysis in terms of assessing the possibility of the formation of such planes of discontinuity in a particular class of materials called hypoplastic materials.