Implicit and explicit integration schemes in the anisotropic bounding surface plasticity model for cyclic behaviours of saturated clay

Abstract

a b s t r a c tTwo integration algorithms, namely the implicit return mapping and explicit sub-stepping schemes, are adopted in the anisotropic bounding surface plasticity model for cyclic behaviours of saturated clay and are implemented into finite element code. The model is a representative of a series of bounding surface models that have typical characteristics, including isotropic and kinematic hardening rules and a rotational bounding surface to capture complex but important cyclic behaviours of soils, such as cyclic shakedown and degradation. However, there is no explicit current yield surface in the model to which the conventional implicit algorithm returns the stress state back or the sub-stepping integration corrects the drift of the stress state. Hence, necessary modifications have been made for both of the integration schemes. First, the image stress point is mapped or corrected to the bounding surface instead of mapping back or correcting the stress state to the yield surface. Second, the unloading-loading criterion is checked to determine the image stress point rather than checking the yield criterion after giving the trial stress state in a conventional way. Comparative studies on the accuracy, stability and efficiency of the two integration schemes are conducted not only at the element level but also in solving boundary value problems of monotonic and cyclic bearing behaviours of rigid footings on saturated clay. For smaller strain increments, there is no significant difference in the accuracy between the two integration schemes, but the explicit integration shows a higher efficiency and accuracy. For relatively larger increments, the implicit return mapping algorithm presents good accuracy and more robustness, while the sub-stepping algorithm shows deteriorating accuracy and suffers the convergence problem. With the tolerance used in the present model, the bearing capacity of the rigid footing predicted by the return mapping algorithm is closer to the available analytical and numerical solutions, while the bearing capacity predicted by the sub-stepping algorithm shows a marginal increase.

Integrating a micromechanical model for multiscale analyses

“…The obtained relative errors are in the same range as those obtained by typical return mapping schemes with smaller loading increments leading to lower errors. () The proposed two schemes have the same performance with the changes of the vertical strains and the lateral stresses and are much more sensitive to strain increments than to stress step sizes.…”

“…However, the integration of only a limited number of models has been subjected to comparison through the two aforementioned methods. () Additional comparisons should be made to assess the efficiency of these two methods for a specific micromechanical model.…”

A hysteretic multiscale formulation for nonlinear dynamic analysis of composite materials

“…This is accomplished by treating inelasticity at the local microlevel through the introduction of the additional hysteretic components [Eq. (32)]. These, account for the plastic part of the strain tensor, measured at specific collocation points.…”

“…In this work, an Euler scheme is implemented to retrieve the updated stress field at the Gauss points for brevity. However, more refined sub-stepping explicit [32,51] or implicit methods [49] can be implemented for the solution of the incremental equations of plasticity. Thus, at the end of the iterative procedure, both the current stress field and the interaction matrix [R] are evaluated.…”

Elasto-plasticity and pore-pressure coupled analysis on the pullout behaviors of a plate anchor

“…In this study, a numerical method for the elasto-plasticity and pore-pressure coupled analysis on the pullout behaviors of a plate anchor is proposed, in which the bounding-surface plasticity (BSP) model [10,11] combined with the Biot's consolidation theory is employed to model the cyclic loading induced elastoplastic deformation of the soil skeleton and the accompanying generation/dissipation of the excess pore water pressure. The finite element mesh of a plane strain model and its boundary conditions are schematically shown in Fig.…”