Characterization of polyconvex isotropic functions
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866908671726845952 |
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| author | Wiedemann, David Peter, Malte A. |
| author_facet | Wiedemann, David Peter, Malte A. |
| contents | Polyconvexity is an important concept in the analysis of energies related to elasticity. A function $f \colon \R^{d\times d} \to \R$ is called polyconvex if it can be written as a convex function in the minors of the argument. We show that for isotropic functions it suffices to consider diagonal matrices. For $d=3$, this leads to a dimension reduction for the convex representative of $f$ from $\R^{19}$ to $\R^7$. Moreover, we present a new result for the polyconvexity of functions formulated in the principal invariant of the left or right stretch tensor. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2304_08385 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Characterization of polyconvex isotropic functions Wiedemann, David Peter, Malte A. Analysis of PDEs 49J10, 74B20, 74G65 Polyconvexity is an important concept in the analysis of energies related to elasticity. A function $f \colon \R^{d\times d} \to \R$ is called polyconvex if it can be written as a convex function in the minors of the argument. We show that for isotropic functions it suffices to consider diagonal matrices. For $d=3$, this leads to a dimension reduction for the convex representative of $f$ from $\R^{19}$ to $\R^7$. Moreover, we present a new result for the polyconvexity of functions formulated in the principal invariant of the left or right stretch tensor. |
| title | Characterization of polyconvex isotropic functions |
| topic | Analysis of PDEs 49J10, 74B20, 74G65 |
| url | https://arxiv.org/abs/2304.08385 |