On the integration of an ACST-based bounding surface model

Abstract

Anisotropic critical state theory (ACST) provides a framework for incorporating fabric effects in constitutive models. However, most previous efforts have focused on constitutive aspects with comparatively limited attention to numerical implementations. This study presents a comprehensive assessment of explicit and implicit implementations of the ACST-based bounding surface model, SANISAND-F. Assessments are conducted in terms of stability, accuracy, computational efficiency, and both local and global performance.

In the implicit implementation, the critical importance of accurate gradient calculations is highlighted, introducing a verification procedure that enables quadratic convergence. The explicit and implicit implementations exhibit stability, producing smooth and bounded responses across a wide range of strain increments and numerical tolerances. However, their accuracy differs significantly. The implicit implementation is sensitive to the initial loading state, strain increment, and loading direction, showing minor dependence on the solver tolerance. In contrast, the explicit implementation is influenced by both strain increment and substepping tolerance, and at practical tolerance and strain increment levels, it often outperforms the implicit scheme in accuracy. Regarding efficiency, the explicit implementation proves more efficient at the local integration level. However, at the global level, the implicit implementation with the consistent tangent exhibits a faster rate of convergence in global equilibrium iterations. Nonetheless, the overall computational cost at the global level is not definitive when comparing explicit and implicit schemes; it varies with simulations and loading-specific parameters, as demonstrated through the included boundary-value problems.