A reduced simulation applied to viscoelastic fatigue of polymers using a time multi-scale approach based on Partition of Unity method
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arXiv
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| Main Authors: | , , , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910561616265216 |
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| author | Rodriguez, Sebastian Pasquale, Angelo Mounayer, Jad Canales, Diego Beringhier, Marianne Ghnatios, Chady Ammar, Amine Chinesta, Francisco |
| author_facet | Rodriguez, Sebastian Pasquale, Angelo Mounayer, Jad Canales, Diego Beringhier, Marianne Ghnatios, Chady Ammar, Amine Chinesta, Francisco |
| contents | The simulation of viscoelastic time-evolution problems described by a large number of internal variables and with a large spectrum of relaxation times requires high computational resources for their resolution. Furthermore, the internal variables evolution is described by a set of linear differential equations which involves many time scales. In this context, the use of a space-time PGD approximation is proposed here to boost their resolution, where the temporal functions are constructed following a multi-scale strategy along with the Partition of Unity method, in order to catch each dynamic efficiently. The feasibility and the robustness of the method are discussed in the case of a polymer in a non-equilibrium state under cyclic loading. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_05143 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A reduced simulation applied to viscoelastic fatigue of polymers using a time multi-scale approach based on Partition of Unity method Rodriguez, Sebastian Pasquale, Angelo Mounayer, Jad Canales, Diego Beringhier, Marianne Ghnatios, Chady Ammar, Amine Chinesta, Francisco Computational Engineering, Finance, and Science The simulation of viscoelastic time-evolution problems described by a large number of internal variables and with a large spectrum of relaxation times requires high computational resources for their resolution. Furthermore, the internal variables evolution is described by a set of linear differential equations which involves many time scales. In this context, the use of a space-time PGD approximation is proposed here to boost their resolution, where the temporal functions are constructed following a multi-scale strategy along with the Partition of Unity method, in order to catch each dynamic efficiently. The feasibility and the robustness of the method are discussed in the case of a polymer in a non-equilibrium state under cyclic loading. |
| title | A reduced simulation applied to viscoelastic fatigue of polymers using a time multi-scale approach based on Partition of Unity method |
| topic | Computational Engineering, Finance, and Science |
| url | https://arxiv.org/abs/2408.05143 |