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Perturbed parameters are considered in a hypoplastic model of granular materials. For fixed parameters, the model response to a periodic stress loading and unloading converges to a limit state of strain. The focus of this contribution is the assessment of the change in the limit strain caused by varying model parameters.

We investigate rate-independent strain paths in a granular material generated by periodically oscillating stress cycles using a particular constitutive model within the hypoplasticity theory of Kolymbas type. It is assumed that the irreversible hypoplastic effects decay to zero when the void ratio reaches its theoretical minimum, while the void ratio is in turn related to the evolution of the volumetric strain through the mass conservation principle. We show that under natural assumptions on material parameters, both isotropic and anisotropic stress cycles are described by a differential equation whose solution converges asymptotically to a limiting periodic process taking place in the shakedown state when the number of loading cycles tends to infinity. Furthermore, an estimation of how fast, in terms of the number of cycles, the system approaches the limit state is derived in explicit form. It is shown how it depends on the parameters of the model, on the initial void ratio, and on the prescribed stress interval.