Performance of explicit substepping integration scheme for complex constitutive models in finite element analysis

Abstract

Advanced constitutive models for soils are critical to achieve reliable results in geotechnical analyses, but their implementation in finite element programs should be accurate, efficient, and robust. This paper describes the algorithm used to integrate a complex elastoplastic constitutive model for clays, the MIT-E3, in the finite element framework, followed by extensive evaluations. The explicit substepping scheme with different order of accuracy is adopted in the integration due to its simplicity, and also because of complexities in the model formulation. Several important issues are highlighted in the integration to improve the model performance in the analysis, (i) rigorous update of the void ratio, (ii) efficient intersection with the bounding surface, (iii) consistent correction of the drifted stress to the bounding surface, and (iv) consistently linearized tangent operator in the explicit substepping scheme. The numerical integration is verified by reproducing the stress-strain behaviour in single element tests, and also by checking the error behaviour with the order of accuracy of the integration method. The accuracy and efficiency of different methods in the integration are evaluated in a rigorous and consistent manner, which has practical implications for choosing suitable methods and parameters in the analysis. Good convergence rate can be achieved using the proposed consistently linearized tangent operator. The substepping scheme with error control is shown to be stable in the challenging geotechnical problems, while the efficiency is affected by the strain increment size which is problem dependent.