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 |
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| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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Bradford
Emerald Publishing Limited
28.10.2020
Emerald Group Publishing Limited |
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| ISSN: | 0264-4401, 1758-7077 |
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| Abstract | 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. |
|---|---|
| AbstractList | 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. PurposeSemi-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/approachTwo 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.FindingsStress 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/valueTraditionally, 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. |
| Author | Das, Arghya Lal, Divyanshu Kumar |
| Author_xml | – sequence: 1 givenname: Divyanshu Kumar surname: Lal fullname: Lal, Divyanshu Kumar email: divyanshu0602@gmail.com – sequence: 2 givenname: Arghya surname: Das fullname: Das, Arghya email: arghya@iitk.ac.in |
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| CitedBy_id | crossref_primary_10_1016_j_compgeo_2023_105992 crossref_primary_10_1155_2022_3765169 |
| Cites_doi | 10.1680/geot.12.P.008 10.1002/nme.5245 10.1002/nme.1620240505 10.1002/nag.294 10.1016/S0045-7825(00)00301-7 10.1002/nag.217 10.1061/(ASCE)0733-9399(2009)135:4(276) 10.1016/0045-7825(91)90256-6 10.1002/(SICI)1099-1484(199701)2:1<1::AID-CFM23>3.0.CO;2-P 10.1016/0045-7825(90)90152-C 10.1016/0266-352X(96)00005-5 10.1002/nag.1610090204 10.1108/eb023736 10.1016/j.compgeo.2012.03.007 10.3208/sandf.51.395 10.1061/(ASCE)0733-9399(1999)125:1(60) 10.1002/nme.279 10.1002/nme.1470 10.1016/j.cma.2015.07.014 10.1002/(SICI)1097-0207(19971030)40:20<3839::AID-NME245>3.0.CO;2-6 10.1016/j.compgeo.2017.09.012 10.1002/nme.1620210902 10.1061/(ASCE)1532-3641(2005)5:3(244) 10.1002/nme.1620230303 10.1016/j.jmps.2006.11.003 10.1002/nme.2790 10.1002/1099-1484(200008)5:6<469::AID-CFM105>3.0.CO;2-9 10.1002/nme.1620220310 10.1016/0045-7825(85)90070-2 10.1016/0022-5096(67)90030-0 10.1002/nag.2778 10.1063/1.1698348 10.1108/02644400110365842 10.1016/0020-7683(89)90038-3 10.1680/geot.1958.8.1.22 |
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| Keywords | Finite elements Stress return algorithm Implicit integration Constitutive modeling |
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Semi-implicit type cutting plane method (CPM) and fully implicit type closest point projection method (CPPM) are the two most widely used frameworks... PurposeSemi-implicit type cutting plane method (CPM) and fully implicit type closest point projection method (CPPM) are the two most widely used frameworks for... |
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| SubjectTerms | Accuracy Algorithms Boundary value problems Central processing units Constitutive models CPUs Geotechnical engineering Mathematical models Methods Numerical analysis Soil mechanics Soils Stress state |
| Title | Development of semi-implicit midpoint and Romberg stress integration algorithms for single hardening soil constitutive models |
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