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

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...

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Vydáno v:Engineering computations Ročník 37; číslo 9; s. 3477 - 3503
Hlavní autoři: Lal, Divyanshu Kumar, Das, Arghya
Médium: Journal Article
Jazyk:angličtina
Vydáno: Bradford Emerald Publishing Limited 28.10.2020
Emerald Group Publishing Limited
Témata:
Accuracy
Algorithms
Boundary value problems
Central processing units
Constitutive models
CPUs
Geotechnical engineering
Mathematical models
Methods
Numerical analysis
Soil mechanics
Soils
Stress state
Borja Spain
Spain
Finite elements
Stress return algorithm
Implicit integration
Constitutive modeling
ISSN:0264-4401, 1758-7077
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Shrnutí: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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ISSN:0264-4401
1758-7077
DOI:10.1108/EC-08-2019-0358