Stress-controlled ratchetting in hypoplasticity: a study of periodically proportional loading cycles

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