On implicit integration of the bounding surface model based on swell-shrink rules

The bounding surface model has become one of the most widely used constitutive models for representing the elastoplastic behavior of soils under cyclic loads. Using a bounding surface model modified to include swell-shrink rules, this paper gives a full description of a popular return mapping algorithm based on implicit integration. The algorithm allows complete implicit integration and consistent linearization of the model to be achieved. Several modifications are made to force the algorithm to satisfy the computational needs of the model and a Newton-Simpson iterative method is introduced to ensure high numerical accuracy. Numerical simulations are used to demonstrate the validity of the algorithm presented.