A primal–dual interior point method to implicitly update Gurson–Tvergaard–Needleman model
Abstract This study proposes an implicit algorithm applying the primal–dual interior point method (PDIP method) to stabilize the stress update when using a class of the Gurson–Tvergaard–Needleman model (GTN model). The GTN model is widely used to realize the change in void volume fraction that gover...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Shintaku, Yuichi [verfasserIn] Inaoka, Tatsuhiko [verfasserIn] Terada, Kenjiro [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2024 |
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| Schlagwörter: |
Gurson–Tvergaard–Needleman model |
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| Anmerkung: |
© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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| Übergeordnetes Werk: |
Enthalten in: Computational mechanics - Springer Berlin Heidelberg, 1986, 74(2024), 5 vom: 15. Apr., Seite 1037-1054 |
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| Übergeordnetes Werk: |
volume:74 ; year:2024 ; number:5 ; day:15 ; month:04 ; pages:1037-1054 |
| Links: |
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| DOI / URN: |
10.1007/s00466-024-02466-4 |
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| Katalog-ID: |
SPR057982953 |
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| 100 | 1 | |a Shintaku, Yuichi |e verfasserin |0 (orcid)0000-0003-0721-8355 |4 aut | |
| 245 | 1 | 0 | |a A primal–dual interior point method to implicitly update Gurson–Tvergaard–Needleman model |
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| 520 | |a Abstract This study proposes an implicit algorithm applying the primal–dual interior point method (PDIP method) to stabilize the stress update when using a class of the Gurson–Tvergaard–Needleman model (GTN model). The GTN model is widely used to realize the change in void volume fraction that governs ductile fracture in metals, but numerical instabilities arise due to shrinkage of the yield surface and the accelerated void growth. In fact, such shrinkage can lead to misjudgment of yield conditions when using conventional return mapping algorithms, since trial elastic stresses are computed assuming zero incremental plastic strain. In addition, the change in void volume fraction is often approximated in bilinear form to represent the acceleration of void growth, but should be smooth to apply nonlinear solution methods such as the Newton’s method. To avoid such inconvenience in the implicit stress update for the GTN model and ensure numerical stability, we propose an algorithm that replaces the constitutive equations with inequality constraints with an equivalent constrained optimization problem by applying the PDIP method. After verifying the numerical accuracy and convergence of the proposed implicit algorithm using iso-error maps, we demonstrate its capability through several numerical examples that cannot be solved by the conventional return mapping algorithm or the PDIP method applied only to the inequality constraint corresponding to the yield condition. | ||
| 650 | 4 | |a Gurson–Tvergaard–Needleman model |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Primal–dual interior point method |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Return mapping algorithm |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Ductile fracture |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Inaoka, Tatsuhiko |e verfasserin |4 aut | |
| 700 | 1 | |a Terada, Kenjiro |e verfasserin |4 aut | |
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10.1007/s00466-024-02466-4 doi (DE-627)SPR057982953 (SPR)s00466-024-02466-4-e DE-627 ger DE-627 rakwb eng 530 004 VZ 33.11 bkl 50.31 bkl 50.33 bkl 50.38 bkl 51.32 bkl Shintaku, Yuichi verfasserin (orcid)0000-0003-0721-8355 aut A primal–dual interior point method to implicitly update Gurson–Tvergaard–Needleman model 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract This study proposes an implicit algorithm applying the primal–dual interior point method (PDIP method) to stabilize the stress update when using a class of the Gurson–Tvergaard–Needleman model (GTN model). The GTN model is widely used to realize the change in void volume fraction that governs ductile fracture in metals, but numerical instabilities arise due to shrinkage of the yield surface and the accelerated void growth. In fact, such shrinkage can lead to misjudgment of yield conditions when using conventional return mapping algorithms, since trial elastic stresses are computed assuming zero incremental plastic strain. In addition, the change in void volume fraction is often approximated in bilinear form to represent the acceleration of void growth, but should be smooth to apply nonlinear solution methods such as the Newton’s method. To avoid such inconvenience in the implicit stress update for the GTN model and ensure numerical stability, we propose an algorithm that replaces the constitutive equations with inequality constraints with an equivalent constrained optimization problem by applying the PDIP method. After verifying the numerical accuracy and convergence of the proposed implicit algorithm using iso-error maps, we demonstrate its capability through several numerical examples that cannot be solved by the conventional return mapping algorithm or the PDIP method applied only to the inequality constraint corresponding to the yield condition. Gurson–Tvergaard–Needleman model (dpeaa)DE-He213 Primal–dual interior point method (dpeaa)DE-He213 Return mapping algorithm (dpeaa)DE-He213 Ductile fracture (dpeaa)DE-He213 Inaoka, Tatsuhiko verfasserin aut Terada, Kenjiro verfasserin aut Enthalten in Computational mechanics Springer Berlin Heidelberg, 1986 74(2024), 5 vom: 15. Apr., Seite 1037-1054 (DE-627)253721687 (DE-600)1458937-0 1432-0924 nnns volume:74 year:2024 number:5 day:15 month:04 pages:1037-1054 https://dx.doi.org/10.1007/s00466-024-02466-4 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_72 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2574 GBV_ILN_4029 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4116 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4155 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4318 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4598 GBV_ILN_4700 33.11 VZ 50.31 VZ 50.33 VZ 50.38 VZ 51.32 VZ AR 74 2024 5 15 04 1037-1054 |
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10.1007/s00466-024-02466-4 doi (DE-627)SPR057982953 (SPR)s00466-024-02466-4-e DE-627 ger DE-627 rakwb eng 530 004 VZ 33.11 bkl 50.31 bkl 50.33 bkl 50.38 bkl 51.32 bkl Shintaku, Yuichi verfasserin (orcid)0000-0003-0721-8355 aut A primal–dual interior point method to implicitly update Gurson–Tvergaard–Needleman model 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract This study proposes an implicit algorithm applying the primal–dual interior point method (PDIP method) to stabilize the stress update when using a class of the Gurson–Tvergaard–Needleman model (GTN model). The GTN model is widely used to realize the change in void volume fraction that governs ductile fracture in metals, but numerical instabilities arise due to shrinkage of the yield surface and the accelerated void growth. In fact, such shrinkage can lead to misjudgment of yield conditions when using conventional return mapping algorithms, since trial elastic stresses are computed assuming zero incremental plastic strain. In addition, the change in void volume fraction is often approximated in bilinear form to represent the acceleration of void growth, but should be smooth to apply nonlinear solution methods such as the Newton’s method. To avoid such inconvenience in the implicit stress update for the GTN model and ensure numerical stability, we propose an algorithm that replaces the constitutive equations with inequality constraints with an equivalent constrained optimization problem by applying the PDIP method. After verifying the numerical accuracy and convergence of the proposed implicit algorithm using iso-error maps, we demonstrate its capability through several numerical examples that cannot be solved by the conventional return mapping algorithm or the PDIP method applied only to the inequality constraint corresponding to the yield condition. Gurson–Tvergaard–Needleman model (dpeaa)DE-He213 Primal–dual interior point method (dpeaa)DE-He213 Return mapping algorithm (dpeaa)DE-He213 Ductile fracture (dpeaa)DE-He213 Inaoka, Tatsuhiko verfasserin aut Terada, Kenjiro verfasserin aut Enthalten in Computational mechanics Springer Berlin Heidelberg, 1986 74(2024), 5 vom: 15. Apr., Seite 1037-1054 (DE-627)253721687 (DE-600)1458937-0 1432-0924 nnns volume:74 year:2024 number:5 day:15 month:04 pages:1037-1054 https://dx.doi.org/10.1007/s00466-024-02466-4 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_72 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2574 GBV_ILN_4029 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4116 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4155 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4318 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4598 GBV_ILN_4700 33.11 VZ 50.31 VZ 50.33 VZ 50.38 VZ 51.32 VZ AR 74 2024 5 15 04 1037-1054 |
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10.1007/s00466-024-02466-4 doi (DE-627)SPR057982953 (SPR)s00466-024-02466-4-e DE-627 ger DE-627 rakwb eng 530 004 VZ 33.11 bkl 50.31 bkl 50.33 bkl 50.38 bkl 51.32 bkl Shintaku, Yuichi verfasserin (orcid)0000-0003-0721-8355 aut A primal–dual interior point method to implicitly update Gurson–Tvergaard–Needleman model 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract This study proposes an implicit algorithm applying the primal–dual interior point method (PDIP method) to stabilize the stress update when using a class of the Gurson–Tvergaard–Needleman model (GTN model). The GTN model is widely used to realize the change in void volume fraction that governs ductile fracture in metals, but numerical instabilities arise due to shrinkage of the yield surface and the accelerated void growth. In fact, such shrinkage can lead to misjudgment of yield conditions when using conventional return mapping algorithms, since trial elastic stresses are computed assuming zero incremental plastic strain. In addition, the change in void volume fraction is often approximated in bilinear form to represent the acceleration of void growth, but should be smooth to apply nonlinear solution methods such as the Newton’s method. To avoid such inconvenience in the implicit stress update for the GTN model and ensure numerical stability, we propose an algorithm that replaces the constitutive equations with inequality constraints with an equivalent constrained optimization problem by applying the PDIP method. After verifying the numerical accuracy and convergence of the proposed implicit algorithm using iso-error maps, we demonstrate its capability through several numerical examples that cannot be solved by the conventional return mapping algorithm or the PDIP method applied only to the inequality constraint corresponding to the yield condition. Gurson–Tvergaard–Needleman model (dpeaa)DE-He213 Primal–dual interior point method (dpeaa)DE-He213 Return mapping algorithm (dpeaa)DE-He213 Ductile fracture (dpeaa)DE-He213 Inaoka, Tatsuhiko verfasserin aut Terada, Kenjiro verfasserin aut Enthalten in Computational mechanics Springer Berlin Heidelberg, 1986 74(2024), 5 vom: 15. Apr., Seite 1037-1054 (DE-627)253721687 (DE-600)1458937-0 1432-0924 nnns volume:74 year:2024 number:5 day:15 month:04 pages:1037-1054 https://dx.doi.org/10.1007/s00466-024-02466-4 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_72 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2574 GBV_ILN_4029 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4116 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4155 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4318 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4598 GBV_ILN_4700 33.11 VZ 50.31 VZ 50.33 VZ 50.38 VZ 51.32 VZ AR 74 2024 5 15 04 1037-1054 |
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10.1007/s00466-024-02466-4 doi (DE-627)SPR057982953 (SPR)s00466-024-02466-4-e DE-627 ger DE-627 rakwb eng 530 004 VZ 33.11 bkl 50.31 bkl 50.33 bkl 50.38 bkl 51.32 bkl Shintaku, Yuichi verfasserin (orcid)0000-0003-0721-8355 aut A primal–dual interior point method to implicitly update Gurson–Tvergaard–Needleman model 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract This study proposes an implicit algorithm applying the primal–dual interior point method (PDIP method) to stabilize the stress update when using a class of the Gurson–Tvergaard–Needleman model (GTN model). The GTN model is widely used to realize the change in void volume fraction that governs ductile fracture in metals, but numerical instabilities arise due to shrinkage of the yield surface and the accelerated void growth. In fact, such shrinkage can lead to misjudgment of yield conditions when using conventional return mapping algorithms, since trial elastic stresses are computed assuming zero incremental plastic strain. In addition, the change in void volume fraction is often approximated in bilinear form to represent the acceleration of void growth, but should be smooth to apply nonlinear solution methods such as the Newton’s method. To avoid such inconvenience in the implicit stress update for the GTN model and ensure numerical stability, we propose an algorithm that replaces the constitutive equations with inequality constraints with an equivalent constrained optimization problem by applying the PDIP method. After verifying the numerical accuracy and convergence of the proposed implicit algorithm using iso-error maps, we demonstrate its capability through several numerical examples that cannot be solved by the conventional return mapping algorithm or the PDIP method applied only to the inequality constraint corresponding to the yield condition. Gurson–Tvergaard–Needleman model (dpeaa)DE-He213 Primal–dual interior point method (dpeaa)DE-He213 Return mapping algorithm (dpeaa)DE-He213 Ductile fracture (dpeaa)DE-He213 Inaoka, Tatsuhiko verfasserin aut Terada, Kenjiro verfasserin aut Enthalten in Computational mechanics Springer Berlin Heidelberg, 1986 74(2024), 5 vom: 15. Apr., Seite 1037-1054 (DE-627)253721687 (DE-600)1458937-0 1432-0924 nnns volume:74 year:2024 number:5 day:15 month:04 pages:1037-1054 https://dx.doi.org/10.1007/s00466-024-02466-4 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_72 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2574 GBV_ILN_4029 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4116 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4155 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4318 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4598 GBV_ILN_4700 33.11 VZ 50.31 VZ 50.33 VZ 50.38 VZ 51.32 VZ AR 74 2024 5 15 04 1037-1054 |
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10.1007/s00466-024-02466-4 doi (DE-627)SPR057982953 (SPR)s00466-024-02466-4-e DE-627 ger DE-627 rakwb eng 530 004 VZ 33.11 bkl 50.31 bkl 50.33 bkl 50.38 bkl 51.32 bkl Shintaku, Yuichi verfasserin (orcid)0000-0003-0721-8355 aut A primal–dual interior point method to implicitly update Gurson–Tvergaard–Needleman model 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract This study proposes an implicit algorithm applying the primal–dual interior point method (PDIP method) to stabilize the stress update when using a class of the Gurson–Tvergaard–Needleman model (GTN model). The GTN model is widely used to realize the change in void volume fraction that governs ductile fracture in metals, but numerical instabilities arise due to shrinkage of the yield surface and the accelerated void growth. In fact, such shrinkage can lead to misjudgment of yield conditions when using conventional return mapping algorithms, since trial elastic stresses are computed assuming zero incremental plastic strain. In addition, the change in void volume fraction is often approximated in bilinear form to represent the acceleration of void growth, but should be smooth to apply nonlinear solution methods such as the Newton’s method. To avoid such inconvenience in the implicit stress update for the GTN model and ensure numerical stability, we propose an algorithm that replaces the constitutive equations with inequality constraints with an equivalent constrained optimization problem by applying the PDIP method. After verifying the numerical accuracy and convergence of the proposed implicit algorithm using iso-error maps, we demonstrate its capability through several numerical examples that cannot be solved by the conventional return mapping algorithm or the PDIP method applied only to the inequality constraint corresponding to the yield condition. Gurson–Tvergaard–Needleman model (dpeaa)DE-He213 Primal–dual interior point method (dpeaa)DE-He213 Return mapping algorithm (dpeaa)DE-He213 Ductile fracture (dpeaa)DE-He213 Inaoka, Tatsuhiko verfasserin aut Terada, Kenjiro verfasserin aut Enthalten in Computational mechanics Springer Berlin Heidelberg, 1986 74(2024), 5 vom: 15. Apr., Seite 1037-1054 (DE-627)253721687 (DE-600)1458937-0 1432-0924 nnns volume:74 year:2024 number:5 day:15 month:04 pages:1037-1054 https://dx.doi.org/10.1007/s00466-024-02466-4 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_72 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2574 GBV_ILN_4029 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4116 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4155 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4318 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4598 GBV_ILN_4700 33.11 VZ 50.31 VZ 50.33 VZ 50.38 VZ 51.32 VZ AR 74 2024 5 15 04 1037-1054 |
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A primal–dual interior point method to implicitly update Gurson–Tvergaard–Needleman model |
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Abstract This study proposes an implicit algorithm applying the primal–dual interior point method (PDIP method) to stabilize the stress update when using a class of the Gurson–Tvergaard–Needleman model (GTN model). The GTN model is widely used to realize the change in void volume fraction that governs ductile fracture in metals, but numerical instabilities arise due to shrinkage of the yield surface and the accelerated void growth. In fact, such shrinkage can lead to misjudgment of yield conditions when using conventional return mapping algorithms, since trial elastic stresses are computed assuming zero incremental plastic strain. In addition, the change in void volume fraction is often approximated in bilinear form to represent the acceleration of void growth, but should be smooth to apply nonlinear solution methods such as the Newton’s method. To avoid such inconvenience in the implicit stress update for the GTN model and ensure numerical stability, we propose an algorithm that replaces the constitutive equations with inequality constraints with an equivalent constrained optimization problem by applying the PDIP method. After verifying the numerical accuracy and convergence of the proposed implicit algorithm using iso-error maps, we demonstrate its capability through several numerical examples that cannot be solved by the conventional return mapping algorithm or the PDIP method applied only to the inequality constraint corresponding to the yield condition. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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Abstract This study proposes an implicit algorithm applying the primal–dual interior point method (PDIP method) to stabilize the stress update when using a class of the Gurson–Tvergaard–Needleman model (GTN model). The GTN model is widely used to realize the change in void volume fraction that governs ductile fracture in metals, but numerical instabilities arise due to shrinkage of the yield surface and the accelerated void growth. In fact, such shrinkage can lead to misjudgment of yield conditions when using conventional return mapping algorithms, since trial elastic stresses are computed assuming zero incremental plastic strain. In addition, the change in void volume fraction is often approximated in bilinear form to represent the acceleration of void growth, but should be smooth to apply nonlinear solution methods such as the Newton’s method. To avoid such inconvenience in the implicit stress update for the GTN model and ensure numerical stability, we propose an algorithm that replaces the constitutive equations with inequality constraints with an equivalent constrained optimization problem by applying the PDIP method. After verifying the numerical accuracy and convergence of the proposed implicit algorithm using iso-error maps, we demonstrate its capability through several numerical examples that cannot be solved by the conventional return mapping algorithm or the PDIP method applied only to the inequality constraint corresponding to the yield condition. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
| abstract_unstemmed |
Abstract This study proposes an implicit algorithm applying the primal–dual interior point method (PDIP method) to stabilize the stress update when using a class of the Gurson–Tvergaard–Needleman model (GTN model). The GTN model is widely used to realize the change in void volume fraction that governs ductile fracture in metals, but numerical instabilities arise due to shrinkage of the yield surface and the accelerated void growth. In fact, such shrinkage can lead to misjudgment of yield conditions when using conventional return mapping algorithms, since trial elastic stresses are computed assuming zero incremental plastic strain. In addition, the change in void volume fraction is often approximated in bilinear form to represent the acceleration of void growth, but should be smooth to apply nonlinear solution methods such as the Newton’s method. To avoid such inconvenience in the implicit stress update for the GTN model and ensure numerical stability, we propose an algorithm that replaces the constitutive equations with inequality constraints with an equivalent constrained optimization problem by applying the PDIP method. After verifying the numerical accuracy and convergence of the proposed implicit algorithm using iso-error maps, we demonstrate its capability through several numerical examples that cannot be solved by the conventional return mapping algorithm or the PDIP method applied only to the inequality constraint corresponding to the yield condition. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000naa a22002652 4500</leader><controlfield tag="001">SPR057982953</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20241024064920.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">241024s2024 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00466-024-02466-4</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR057982953</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s00466-024-02466-4-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">530</subfield><subfield code="a">004</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">33.11</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">50.31</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">50.33</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">50.38</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">51.32</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Shintaku, Yuichi</subfield><subfield code="e">verfasserin</subfield><subfield code="0">(orcid)0000-0003-0721-8355</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">A primal–dual interior point method to implicitly update Gurson–Tvergaard–Needleman model</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2024</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract This study proposes an implicit algorithm applying the primal–dual interior point method (PDIP method) to stabilize the stress update when using a class of the Gurson–Tvergaard–Needleman model (GTN model). The GTN model is widely used to realize the change in void volume fraction that governs ductile fracture in metals, but numerical instabilities arise due to shrinkage of the yield surface and the accelerated void growth. In fact, such shrinkage can lead to misjudgment of yield conditions when using conventional return mapping algorithms, since trial elastic stresses are computed assuming zero incremental plastic strain. In addition, the change in void volume fraction is often approximated in bilinear form to represent the acceleration of void growth, but should be smooth to apply nonlinear solution methods such as the Newton’s method. To avoid such inconvenience in the implicit stress update for the GTN model and ensure numerical stability, we propose an algorithm that replaces the constitutive equations with inequality constraints with an equivalent constrained optimization problem by applying the PDIP method. After verifying the numerical accuracy and convergence of the proposed implicit algorithm using iso-error maps, we demonstrate its capability through several numerical examples that cannot be solved by the conventional return mapping algorithm or the PDIP method applied only to the inequality constraint corresponding to the yield condition.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Gurson–Tvergaard–Needleman model</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Primal–dual interior point method</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Return mapping algorithm</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Ductile fracture</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Inaoka, Tatsuhiko</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Terada, Kenjiro</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Computational mechanics</subfield><subfield code="d">Springer Berlin Heidelberg, 1986</subfield><subfield code="g">74(2024), 5 vom: 15. 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