An Exact Implementation Of The Hoek–Brown Criterion For Elasto-Plastic Finite Element Calculations

Johan Clausen; Lars Damkilde

doi:10.1016/j.ijrmms.2007.10.004

An Exact Implementation Of The Hoek–Brown Criterion For Elasto-Plastic Finite Element Calculations

Johan Clausen
, Lars Damkilde

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

88 Citationer (Scopus)

Abstract

I denne artikel præsenteres en simpel spændingsopdateringsalgoritme for generaliseret Hoek-Brown-plasticitet. Denne tænkes brugt i elasto-plastiske elementmetodeberegninger og anvender 'return-mapping' konceptet til beregning af spændingsinkrementet ud fra et givet tøjningsinkrement i et materialepunkt. Alle manipulationer udføres i hovedspændingsrummet, hvor Hoek-Brown-kriteriet er givet på en særlig simpel form sammenlignet med den tilvarende formulering i det generelle spændingsrum. I hovedspændingsrummet er det også simpelt at fastlægge om spændingen skal returneres til en af kriteriets kanter eller til kriteriets spids, samt at danne de konstitutive matricer. I modsætning til tidligere elementmetodeudgaver af Hoek-Brown plasticitet er det eksakte kriterium anvendt. Dvs. at kriteriets hjørner og spidser ikke er forsøgt afrundet. Numeriske eksempler og en sammenligning med en ofte brugt metode til at overvinde hjørnesingulariteterne viser den præsenterede algoritmes effektivitet.

Originalsprog	Engelsk
Tidsskrift	International Journal of Rock Mechanics and Mining Sciences
Vol/bind	45
Udgave nummer	6
Sider (fra-til)	831-847
ISSN	1365-1609
DOI	https://doi.org/10.1016/j.ijrmms.2007.10.004
Status	Udgivet - 26 nov. 2007

Emneord

Plastisk spændingsopdatering
Hoek-Brown materiale
Ikke-lineær elementmetode

Adgang til dokumentet

10.1016/j.ijrmms.2007.10.004

AUB Link

Søg efter materialet i Aalborg Universitetsbiblioteks søgemaskine

Citationsformater

@article{186cf7c021b311dd9b07000ea68e967b,

title = "An Exact Implementation Of The Hoek{\textendash}Brown Criterion For Elasto-Plastic Finite Element Calculations",

abstract = "A simple stress update algorithm for generalised Hoek-Brown plasticity is presented. It is intended for use in elasto-plastic finite element computations and utilises the return mapping concept for computing the stress increment belonging to a given increment in strain at a material point. In the algorithm all manipulations are carried out in principal stress space, where the Hoek-Brown failure criterion has a very simple form compared to its formulation in general stress space. In principal stress space it is also simple to determine whether the stress should be returned to one of the edges or to the apex of the yield surface and to form the constitutive matrices. As opposed to earlier finite element implementations of Hoek-Brown plasticity the exact criterion is used, i.e. no rounding of the yield surface corners or edges is attempted. Numerical examples and a comparison with an often used method for dealing with the corner singularities indicates the efficiency of the presented.",

keywords = "Plastisk sp{\ae}ndingsopdatering, Hoek-Brown materiale, Ikke-line{\ae}r elementmetode, Plastic stress update, Hoek-Brown materiale, Non-linear FEM",

author = "Johan Clausen and Lars Damkilde",

year = "2007",

month = nov,

day = "26",

doi = "10.1016/j.ijrmms.2007.10.004",

language = "English",

volume = "45",

pages = "831--847",

journal = "International Journal of Rock Mechanics and Mining Sciences",

issn = "1365-1609",

publisher = "Elsevier",

number = "6",

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TY - JOUR

T1 - An Exact Implementation Of The Hoek–Brown Criterion For Elasto-Plastic Finite Element Calculations

AU - Clausen, Johan

AU - Damkilde, Lars

PY - 2007/11/26

Y1 - 2007/11/26

N2 - A simple stress update algorithm for generalised Hoek-Brown plasticity is presented. It is intended for use in elasto-plastic finite element computations and utilises the return mapping concept for computing the stress increment belonging to a given increment in strain at a material point. In the algorithm all manipulations are carried out in principal stress space, where the Hoek-Brown failure criterion has a very simple form compared to its formulation in general stress space. In principal stress space it is also simple to determine whether the stress should be returned to one of the edges or to the apex of the yield surface and to form the constitutive matrices. As opposed to earlier finite element implementations of Hoek-Brown plasticity the exact criterion is used, i.e. no rounding of the yield surface corners or edges is attempted. Numerical examples and a comparison with an often used method for dealing with the corner singularities indicates the efficiency of the presented.

AB - A simple stress update algorithm for generalised Hoek-Brown plasticity is presented. It is intended for use in elasto-plastic finite element computations and utilises the return mapping concept for computing the stress increment belonging to a given increment in strain at a material point. In the algorithm all manipulations are carried out in principal stress space, where the Hoek-Brown failure criterion has a very simple form compared to its formulation in general stress space. In principal stress space it is also simple to determine whether the stress should be returned to one of the edges or to the apex of the yield surface and to form the constitutive matrices. As opposed to earlier finite element implementations of Hoek-Brown plasticity the exact criterion is used, i.e. no rounding of the yield surface corners or edges is attempted. Numerical examples and a comparison with an often used method for dealing with the corner singularities indicates the efficiency of the presented.

KW - Plastisk spændingsopdatering

KW - Hoek-Brown materiale

KW - Ikke-lineær elementmetode

KW - Plastic stress update

KW - Hoek-Brown materiale

KW - Non-linear FEM

U2 - 10.1016/j.ijrmms.2007.10.004

DO - 10.1016/j.ijrmms.2007.10.004

M3 - Journal article

SN - 1365-1609

VL - 45

SP - 831

EP - 847

JO - International Journal of Rock Mechanics and Mining Sciences

JF - International Journal of Rock Mechanics and Mining Sciences

IS - 6

ER -

An Exact Implementation Of The Hoek–Brown Criterion For Elasto-Plastic Finite Element Calculations

Abstract

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