Non-linear visco-elasto-plastic rheology of a viscous vertex model
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914352888545280 |
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| author | Anand, Shalabh Kumar Merkel, Matthias |
| author_facet | Anand, Shalabh Kumar Merkel, Matthias |
| contents | Morphogenesis involves complex shape changes of biological tissues. Yet, tissue shape changes depend on tissue rheology, which in turn arises from the interplay of large numbers of cells. Here, we link cell- and tissue-scale mechanics by constructing mean-field rheological relations for the vertex model. In contrast to past work in the field, we study a vertex model with an explicit viscous friction. We also include two different cellular mechanisms creating active, anisotropic stresses. Our mean-field model accounts for cell shape and the non-linear elastic and visco-plastic regimes. We validate our results by predicting the response to large-amplitude oscillatory shear. There are several vertex model variants, and comparing to results from the literature, we show that their rheology depends on a number of model details. Our approach should be sufficiently general to construct non-linear mean-field constitutive relations for any cell-based tissue model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_22855 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-linear visco-elasto-plastic rheology of a viscous vertex model Anand, Shalabh Kumar Merkel, Matthias Soft Condensed Matter Tissues and Organs Morphogenesis involves complex shape changes of biological tissues. Yet, tissue shape changes depend on tissue rheology, which in turn arises from the interplay of large numbers of cells. Here, we link cell- and tissue-scale mechanics by constructing mean-field rheological relations for the vertex model. In contrast to past work in the field, we study a vertex model with an explicit viscous friction. We also include two different cellular mechanisms creating active, anisotropic stresses. Our mean-field model accounts for cell shape and the non-linear elastic and visco-plastic regimes. We validate our results by predicting the response to large-amplitude oscillatory shear. There are several vertex model variants, and comparing to results from the literature, we show that their rheology depends on a number of model details. Our approach should be sufficiently general to construct non-linear mean-field constitutive relations for any cell-based tissue model. |
| title | Non-linear visco-elasto-plastic rheology of a viscous vertex model |
| topic | Soft Condensed Matter Tissues and Organs |
| url | https://arxiv.org/abs/2602.22855 |