Formulation of the return mapping algorithm for elastoplastic soil models

Abstract In this paper, a new stress integration algorithm which falls in the category of closest point return mapping method is proposed for some soil models in which stress invariants I1, J2 and J3 are involved. The stress integration is implemented based on a `two-stage iteration' scheme. The first-stage iteration is to implicitly calculate the scalar consistency parameter Δλ. The second-stage iteration is to obtain stress components p and Sij once Δλ is available. The two-stage iteration algorithm, which has been proved more efficient, effectively identifies the physical differences between the plasticity consistency parameter Δλ and the stress components, whose values are in totally different orders. The corresponding tangential moduli, consistent with the return-mapping algorithm, are also derived. They are achieved by simply solving a group of linear equations, which are defined by the converged stresses and state variables. The methodology is successfully extended to the finite strain case where multiplicative decomposition of the total deformation gradient is used. The return-mapping algorithm has been applied to some soil models such as the Mohr–Coulomb, and the Matsuoka–Nakai models. Several examples, from the sequential excavation subject to large strain, to the embankment construction with water and soils fully coupled, and to the propagation of shear band localization in a triaxial test, are presented. Those solutions confirm the good performance of the proposed stress integration algorithm.

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