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Many practical problems in engineering require fast, accurate numerical results. In particular, in cyclic plasticity or fatigue simulations, the high number of loading cycles increases the computation effort and time. The purpose of this study is to show that the return mapping technique in the framework of unconventional plasticity theories is a good compromise between efficiency and accuracy in finite element analyses.

The accuracy of the closest point projection method and the cutting plane method implementations for the subloading surface model are discussed under different loading conditions by analyzing the error as a function of the input step size and the efficiency of the algorithms.

Monotonic tests show that the two different implicit integration schemes have the same accuracy and are in good agreement with the solution obtained using an explicit forward Euler scheme, even for large input steps. However, the closest point projection method seems to describe better the evolution of the similarity centre in the cyclic loading analyses.

The purpose of this work is to show two alternative implicit integration schemes of the extended subloading surface method for metallic materials. The backward Euler integrations can guarantee a good description of the material behaviour and, at the same time, reduce the computational cost. This aspect is particularly important in the field of low or high cycle fatigue, because of the large number of cycles involved.

A detailed description of both the cutting plane and closest point projection methods is offered in this work. In particular, the two integrations schemes are compared in terms of accuracy and computation time for monotonic and cyclic loading tests.

Semi-implicit type cutting plane method (CPM) and fully implicit type closest point projection method (CPPM) are the two most widely used frameworks for numerical stress integration. CPM is simple, easy to implement and accurate up to first order. CPPM is unconditionally stable and accurate up to second order though the formulation is complex. Therefore, this study aims to develop a less complex and accurate stress integration method for complex constitutive models.

Two integration techniques are formulated using the midpoint and Romberg method by modifying CPM. The algorithms are implemented for three different classes of soil constitutive model. The efficiency of the algorithms is judged via stress point analysis and solving a boundary value problem.

Stress point analysis indicates that the proposed algorithms are stable even with a large step size. In addition, numerical analysis for solving boundary value problem demonstrates a significant reduction in central processing unit (CPU) time with the use of the semi-implicit-type midpoint algorithm.

Traditionally, midpoint and Romberg algorithms are formulated from explicit integration techniques, whereas the present study uses a semi-implicit approach to enhance stability. In addition, the proposed stress integration algorithms provide an efficient means to solve boundary value problems pertaining to geotechnical engineering.

The purpose of this paper is to evaluate the co-seismic and post-seismic behaviors of an existed soil-foundation system in an actual alternately layered sand/silt ground including pore water pressure, acceleration response, and displacement et al. during and after earthquake.

The evaluation is performed by finite element method and the simulation is performed using an effective stress-based 2D/3D soil-water coupling program DBLEAVES. The calculation is carried out through static-dynamic-static three steps. The soil behavior is described by a new rotational kinematic hardening elasto-plastic cyclic mobility constitutive model, while the footing and foundation are modeled as elastic rigid elements.

The shallow (short-pile type) foundation has a better capacity of resisting ground liquefaction but large differential settlement occurred. Moreover, most part of the differential settlement occurred during earthquake motion. Attention should be paid not only to the liquefaction behavior of the ground during the earthquake motion, but also the long-term settlement after earthquake should be given serious consideration.

The co-seismic and post-seismic behavior of a complex ground which contains sand and silt layers, especially long-term settlement over a period of several weeks or even years after the earthquake, has been clarified sufficiently. In some critical condition, even if the seismic resistance is satisfied with the design code for building, detailed calculation may reveal the risk of under estimation of differential settlement that may give rise to serious problems.