Numerical approximation for algorithmic tangent moduli for nonlinear viscoelastic model with CSDA method
Abstract This work revisits the notion of complex step derivative approximation (CSDA) and presents its use in constitutive model of a class of nonlinear viscoelastic materials. The effectiveness of a CSDA is evaluated by putting it through a series of straightforward examples. After that, the idea...
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Nature Portfolio
2024-08-01
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| Series: | Scientific Reports |
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| Online Access: | https://doi.org/10.1038/s41598-024-65441-2 |
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| author | Xinggui Fan Jinsheng Xu Xiong Chen |
| author_facet | Xinggui Fan Jinsheng Xu Xiong Chen |
| author_sort | Xinggui Fan |
| collection | DOAJ |
| description | Abstract This work revisits the notion of complex step derivative approximation (CSDA) and presents its use in constitutive model of a class of nonlinear viscoelastic materials. The effectiveness of a CSDA is evaluated by putting it through a series of straightforward examples. After that, the idea of the CSDA is put to use in order to carry out a numerical evaluation of the algorithmic tangent moduli of a viscoelastic constitutive model. The performance of the constitutive models is evaluated through the use of three different numerical tests, and the results are compared to those that were achieved by the application of an analytical method. In comparison to other numerical differentiation techniques, It has been found that the CSDA scheme is the most computationally efficient and robust method of numerical differentiation, regardless of the size of the finite difference interval. |
| format | Article |
| id | doaj-art-5166f2debaf34a5cb05f4baf24e87a16 |
| institution | Kabale University |
| issn | 2045-2322 |
| language | English |
| publishDate | 2024-08-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj-art-5166f2debaf34a5cb05f4baf24e87a162025-01-26T12:34:40ZengNature PortfolioScientific Reports2045-23222024-08-0114111410.1038/s41598-024-65441-2Numerical approximation for algorithmic tangent moduli for nonlinear viscoelastic model with CSDA methodXinggui Fan0Jinsheng Xu1Xiong Chen2Nanjing University of Science and TechnologyNanjing University of Science and TechnologyNanjing University of Science and TechnologyAbstract This work revisits the notion of complex step derivative approximation (CSDA) and presents its use in constitutive model of a class of nonlinear viscoelastic materials. The effectiveness of a CSDA is evaluated by putting it through a series of straightforward examples. After that, the idea of the CSDA is put to use in order to carry out a numerical evaluation of the algorithmic tangent moduli of a viscoelastic constitutive model. The performance of the constitutive models is evaluated through the use of three different numerical tests, and the results are compared to those that were achieved by the application of an analytical method. In comparison to other numerical differentiation techniques, It has been found that the CSDA scheme is the most computationally efficient and robust method of numerical differentiation, regardless of the size of the finite difference interval.https://doi.org/10.1038/s41598-024-65441-2Viscoelastic modelAlgorithmic tangent moduliCSDAFinite element method |
| spellingShingle | Xinggui Fan Jinsheng Xu Xiong Chen Numerical approximation for algorithmic tangent moduli for nonlinear viscoelastic model with CSDA method Scientific Reports Viscoelastic model Algorithmic tangent moduli CSDA Finite element method |
| title | Numerical approximation for algorithmic tangent moduli for nonlinear viscoelastic model with CSDA method |
| title_full | Numerical approximation for algorithmic tangent moduli for nonlinear viscoelastic model with CSDA method |
| title_fullStr | Numerical approximation for algorithmic tangent moduli for nonlinear viscoelastic model with CSDA method |
| title_full_unstemmed | Numerical approximation for algorithmic tangent moduli for nonlinear viscoelastic model with CSDA method |
| title_short | Numerical approximation for algorithmic tangent moduli for nonlinear viscoelastic model with CSDA method |
| title_sort | numerical approximation for algorithmic tangent moduli for nonlinear viscoelastic model with csda method |
| topic | Viscoelastic model Algorithmic tangent moduli CSDA Finite element method |
| url | https://doi.org/10.1038/s41598-024-65441-2 |
| work_keys_str_mv | AT xingguifan numericalapproximationforalgorithmictangentmodulifornonlinearviscoelasticmodelwithcsdamethod AT jinshengxu numericalapproximationforalgorithmictangentmodulifornonlinearviscoelasticmodelwithcsdamethod AT xiongchen numericalapproximationforalgorithmictangentmodulifornonlinearviscoelasticmodelwithcsdamethod |