Assessment on the performance of distinct stress integration algorithms for complex non-quadratic anisotropic yield criteria

An effective stress constitutive model to study the problem numerically of creep in the field is presented. A double-yield surface model for the stress–strain–time behaviour of wet clay is described. The model adopts the concept of separating the total deformation into immediate and delayed components. The yield surfaces employed are the modified Cam-clay ellipsoid and the Von Mises cylinder inscribed in the ellipsoid. The proposed numerical scheme incorporates the pore pressure based on field observations into a finite element analysis. An interpolation technique is used to determine the pore pressure at every element. A field example is presented to illustrate the interpolation technique procedure. The scheme not only avoids the complexity of making predictions of pore-water pressure, but also allows the analysis to be carried out in terms of effective stresses based on the actual observed pore pressure. Two stress integration algorithms based on the implicit calculation of plastic strain are implemented and tested for the double-yield surface model. A numerical simulation of stress-controlled drained creep tests confirms the numerical procedure. Key words : constitutive equations, creep, finite element, stress integration algorithms, effective stress approach, pore-water pressure.

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Development of semi-implicit midpoint and Romberg stress integration algorithms for single hardening soil constitutive models

Engineering Computations ◽

10.1108/ec-08-2019-0358 ◽

2020 ◽

Vol 37 (9) ◽

pp. 3477-3503

Author(s):

Divyanshu Kumar Lal ◽

Arghya Das

Keyword(s):

Boundary Value Problem ◽

Boundary Value ◽

Constitutive Models ◽

Processing Unit ◽

Content Type ◽

Point Analysis ◽

Stress Point ◽

Integration Techniques ◽

Stress Integration ◽

Integration Algorithms

Purpose 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. Design/methodology/approach 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. Findings 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. Originality/value 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.

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