Nonlinear Regression Problem of Material Functions Identification for Porous Media Plastic Flow
In the paper we present the identification problem arising in modelling the processes of nucleation and growth of voids in the elastic–plastic media. Identification is carried out on the basis of Fisher's data measured on the cylindrical steel specimens subjected to the uniaxial tension. The id...
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Institute of Fundamental Technological Research
2015-06-01
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| Series: | Engineering Transactions |
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| Online Access: | https://et.ippt.pan.pl/index.php/et/article/view/546 |
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| author | Z. Nowak A. Stachurski |
| author_facet | Z. Nowak A. Stachurski |
| author_sort | Z. Nowak |
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| description | In the paper we present the identification problem arising in modelling the processes of nucleation and growth of voids in the elastic–plastic media. Identification is carried out on the basis of Fisher's data measured on the cylindrical steel specimens subjected to the uniaxial tension. The identification problem is formulated as the standard nonlinear regression problem. Our aim was to select appropriate formulae of the material functions appearing in the porosity model in the right-hand side of the differential equation, and to identify their unknown parameters. The resulting nonlinear regression problem was solved by means of the global optimization method of Boender et al. As the local minimizer we have implemented the modified famous BFGS quasi-Newton method. Modifications were necessary to take into account box constraints posed on the parameters. As the directional minimizer we have prepared a special procedure joining quadratic and cubic approximations and including a new switching condition. We have tested two variants of the porosity model; in the first one with variable shape of the material function $g$, and the second one – with constant $g$. The results suggest that the model with material function $g \equiv 1$ describes well the nucleation and growth of voids. However, our attempt to identify that constant has brought an unexpected value smaller than 1, and approximately equal to 0.84. |
| format | Article |
| id | doaj-art-45f7cde0e9524d8fa77a32e15aed2227 |
| institution | Matheson Library |
| issn | 0867-888X 2450-8071 |
| language | English |
| publishDate | 2015-06-01 |
| publisher | Institute of Fundamental Technological Research |
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| series | Engineering Transactions |
| spelling | doaj-art-45f7cde0e9524d8fa77a32e15aed22272025-07-11T05:05:23ZengInstitute of Fundamental Technological ResearchEngineering Transactions0867-888X2450-80712015-06-0149410.24423/engtrans.546.2001Nonlinear Regression Problem of Material Functions Identification for Porous Media Plastic FlowZ. Nowak0A. Stachurski1Institute of Fundamental Technological ResearchInstitute of Control and Computation EngineeringIn the paper we present the identification problem arising in modelling the processes of nucleation and growth of voids in the elastic–plastic media. Identification is carried out on the basis of Fisher's data measured on the cylindrical steel specimens subjected to the uniaxial tension. The identification problem is formulated as the standard nonlinear regression problem. Our aim was to select appropriate formulae of the material functions appearing in the porosity model in the right-hand side of the differential equation, and to identify their unknown parameters. The resulting nonlinear regression problem was solved by means of the global optimization method of Boender et al. As the local minimizer we have implemented the modified famous BFGS quasi-Newton method. Modifications were necessary to take into account box constraints posed on the parameters. As the directional minimizer we have prepared a special procedure joining quadratic and cubic approximations and including a new switching condition. We have tested two variants of the porosity model; in the first one with variable shape of the material function $g$, and the second one – with constant $g$. The results suggest that the model with material function $g \equiv 1$ describes well the nucleation and growth of voids. However, our attempt to identify that constant has brought an unexpected value smaller than 1, and approximately equal to 0.84.https://et.ippt.pan.pl/index.php/et/article/view/546plastic flow of porous mediamaterial functions identificationglobal optimizationnonlinear regressionnonlinear programming |
| spellingShingle | Z. Nowak A. Stachurski Nonlinear Regression Problem of Material Functions Identification for Porous Media Plastic Flow Engineering Transactions plastic flow of porous media material functions identification global optimization nonlinear regression nonlinear programming |
| title | Nonlinear Regression Problem of Material Functions Identification for Porous Media Plastic Flow |
| title_full | Nonlinear Regression Problem of Material Functions Identification for Porous Media Plastic Flow |
| title_fullStr | Nonlinear Regression Problem of Material Functions Identification for Porous Media Plastic Flow |
| title_full_unstemmed | Nonlinear Regression Problem of Material Functions Identification for Porous Media Plastic Flow |
| title_short | Nonlinear Regression Problem of Material Functions Identification for Porous Media Plastic Flow |
| title_sort | nonlinear regression problem of material functions identification for porous media plastic flow |
| topic | plastic flow of porous media material functions identification global optimization nonlinear regression nonlinear programming |
| url | https://et.ippt.pan.pl/index.php/et/article/view/546 |
| work_keys_str_mv | AT znowak nonlinearregressionproblemofmaterialfunctionsidentificationforporousmediaplasticflow AT astachurski nonlinearregressionproblemofmaterialfunctionsidentificationforporousmediaplasticflow |