On the accuracies of numerical integration algorithms for Gurson-based pressure-dependent elastoplastic constitutive models
A class of generalized mid-point algorithms for pressure-dependent elastoplastic models is formulated in the paper. The accuracies of the formulated generalized mid-point algorithms including the Euler backward algorithm and the one-step Euler forward algorithm are systematically analyzed against th...
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| Vydáno v: | Computer methods in applied mechanics and engineering Ročník 121; číslo 1; s. 15 - 28 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Amsterdam
Elsevier B.V
01.03.1995
Elsevier |
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| ISSN: | 0045-7825, 1879-2138 |
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| Abstract | A class of generalized mid-point algorithms for pressure-dependent elastoplastic models is formulated in the paper. The accuracies of the formulated generalized mid-point algorithms including the Euler backward algorithm and the one-step Euler forward algorithm are systematically analyzed against the exact solution for Gurson-based pressure-dependent elastoplastic model. The accuracies of the algorithms are assessed by means of iso-error maps. Results show that the formulated generalized mid-point algorithms are reasonably accurate in both small and large increment steps. It is found that in all the cases considered, the maximum errors in the presence of volumetric strain increments are less than those without volumetric strain increments. When the deviatoric strain increments are given in the radial direction, the true mid-point algorithm is the most accurate one. Furthermore, the optimal value α of the generalized mid-point algorithms, in terms of maximum errors, is observed between 0.5 and 1. For both small and large increment steps, the one-step Euler forward algorithm gives the worst accuracy. |
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| AbstractList | A class of generalized mid-point algorithms for pressure-dependent elastoplastic models is formulated in the paper. The accuracies of the formulated generalized mid-point algorithms including the Euler backward algorithm and the one-step Euler forward algorithm are systematically analyzed against the exact solution for Gurson-based pressure-dependent elastoplastic model. The accuracies of the algorithms are assessed by means of iso-error maps. Results show that the formulated generalized mid-point algorithms are reasonably accurate in both small and large increment steps. It is found that in all the cases considered, the maximum errors in the presence of volumetric strain increments are less than those without volumetric strain increments. When the deviatoric strain increments are given in the radial direction, the true mid-point algorithm is the most accurate one. Furthermore, the optimal value α of the generalized mid-point algorithms, in terms of maximum errors, is observed between 0.5 and 1. For both small and large increment steps, the one-step Euler forward algorithm gives the worst accuracy. |
| Author | Zhang, Z.L. |
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| Cites_doi | 10.1007/BF00036191 10.1002/nme.1620210902 10.1002/nme.1620260212 10.1002/nme.1620240713 10.1002/nme.1620330505 10.1002/nme.1620230303 10.1115/1.3454568 10.1002/nme.1620170103 10.1016/0001-6160(84)90213-X 10.1115/1.3224807 10.1007/BF00015686 10.1115/1.3443401 |
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| Keywords | Constitutive equation Algorithms Numerical integration Elastoplasticity Numerical method Pressure Quadratures |
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| References | Ortiz, Simo (BIB4) 1986; 23 Gurson (BIB7) 1975 Gratacos, Montmitonnet, Chenot (BIB3) 1992; 33 Nagtegaal, De Jong (BIB5) 1981; 17 Tvergaard (BIB9) 1981; 17 Chu, Needleman (BIB13) 1980; 102 Krieg, Krieg (BIB2) 1977; 99 Gurson (BIB8) 1977; 99 Tvergaard, Needleman (BIB11) 1984; 32 Aravas (BIB12) 1987; 24 Ortiz, Popov (BIB1) 1985; 21 Lee (BIB6) 1988; 26 Tvergaard (BIB10) 1982; 18 Krieg (10.1016/0045-7825(94)00706-S_BIB2) 1977; 99 Tvergaard (10.1016/0045-7825(94)00706-S_BIB9) 1981; 17 Gurson (10.1016/0045-7825(94)00706-S_BIB8) 1977; 99 Tvergaard (10.1016/0045-7825(94)00706-S_BIB11) 1984; 32 Aravas (10.1016/0045-7825(94)00706-S_BIB12) 1987; 24 Tvergaard (10.1016/0045-7825(94)00706-S_BIB10) 1982; 18 Chu (10.1016/0045-7825(94)00706-S_BIB13) 1980; 102 Nagtegaal (10.1016/0045-7825(94)00706-S_BIB5) 1981; 17 Gurson (10.1016/0045-7825(94)00706-S_BIB7) 1975 Ortiz (10.1016/0045-7825(94)00706-S_BIB4) 1986; 23 Gratacos (10.1016/0045-7825(94)00706-S_BIB3) 1992; 33 Lee (10.1016/0045-7825(94)00706-S_BIB6) 1988; 26 Ortiz (10.1016/0045-7825(94)00706-S_BIB1) 1985; 21 |
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| SubjectTerms | Exact sciences and technology Fundamental areas of phenomenology (including applications) Inelasticity (thermoplasticity, viscoplasticity...) Physics Solid mechanics Structural and continuum mechanics Viscoelasticity, plasticity, viscoplasticity |
| Title | On the accuracies of numerical integration algorithms for Gurson-based pressure-dependent elastoplastic constitutive models |
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