The focus of the present paper is on constitutive modelling of the influence of grain fragmentation on the mechanical behaviour of cohesionless granular materials like sand, gravel or broken rock. To this end the so-called solid hardness of a grain assembly is defined within a continuum description and is a key parameter for modelling the effect of both grain fragmentation and grain rearrangement. While in the original version by Bauer the solid hardness is a constant parameter, an extended concept has recently been proposed where the solid hardness is considered as a state dependent quantity. The general format of the evolution equation for the solid hardness allows the modelling of the influence of various factors on grain fragmentation. Such factors are, for instance, an increase in the mean stress, the deviatoric stress and the rotation resistance of particles and also a time dependent process caused by progressive weathering. The embedding of the solid hardness into hypoplasticity follows the consistency condition originally proposed by Gudehus. In this paper the consistency condition is also applied to proposed constitutive equations for time independent as well as rheological material properties. The performance of these different models is verified with experiments.