Liapunov instability of the hypoplastic model for soils

The hypoplastic constitutive model is known for its numerous application to the problems of soil mechanics and also for its excessive ratcheting. The paper shows that this deficiency can be interpreted as Liapunov instability in dynamic case. This is demonstrated with a simple one-dimensional swinger. Infinitesimally small as well as finite oscillations are analytically examined and the variability of stiffness upon a single cycle is considered. Several methods to circumvent the problem of ratcheting are discussed: implementation of ‘elastic’ range by means of so-called intergranular strain, usage of overlay modelling with parallel coupling of hypoplastic materials as originally proposed by Valanis in his endochronic theory and a special coupling of hypoplastic models based on comparison of partial stiffnesses.