Incorporating a predefined limit condition in a hypoplastic model by means of stress transformation

Hypoplasticity, as an alternative approach of elastoplasticity for describing inelastic, irreversible behaviour of materials, appreciates the advantages of elegance of mathematical formulation and ease in numerical implementation. A successful hypoplastic model for sand proposed by Gudehus and Bauer, which consists of stress and void ratio as state variables, can capture qualitatively the pressure- and density-dependence with 8 state-independent parameters. In this paper, we demonstrate that by using a stress transformation technique, either the Matsuoka–Nakai failure criterion or the Lade failure criterion can be easily incorporated in the model for the description of critical states. Numerical results are presented to display the improvement in the model performance under three-dimensional stress condition.