A closest point projection method for stress integration of 3D sand models generalised by transformed stress method

Abstract

ABSTRACT It is significant to generalise constitutive models from the triaxial space to the multi-axial space for soils. Different from the popular approaches by a g(θ) function to interpolate failure curve, the transformed stress (TS) method can bring the effect of the third stress invariant and stress-induced anisotropy into constitutive models without adding any extra parameters. The closest point projection method (CPPM) is the most popular implicit integration algorithm for the implementation of constitutive model in the finite element analysis. The disadvantage of the CPPM is that it requires the deduction of the quadratic derivative of the plastic potential function, which is extremely difficult for a complex plastic potential. This study employed the TS method with the spatially mobilised plane criterion to generalise a state-dependent sand model, in which the analytical expression of the quadratic derivative of the plastic potential can be obtained. A novel CPPM integration scheme was proposed for the generalised model, which employed an accurate integration of the non-linear elastic constitutive law and a sub-stepping technique to improve the elastic trial state before the Newton’s iteration. The numerical examples demonstrated that the proposed CPPM algorithm has the higher efficiency and better robustness than the conventional cutting plane algorithm.