Abstract
A continuum model of the embryonic epithelial tissue with account for the active deformations and rearrangements of the cells is proposed. The stress tensor is represented as the sum of the stresses undergone by the cell directly and the tensor of active stresses that arise owing to contracting cellular protrusions anchored on the surface of neighboring cells and developing in response to cell reshaping (deformation). The strain rate tensor includes three components: elastic and two inelastic related to the active deformation of the cells and their rearrangement. The first of these components depends on the stresses in the cells and the reached cellular deformation level, whereas the second is determined by the active stresses. The problem of reaction of a thin sheet to a rapid stretching is solved and agreement with experimental data is obtained.
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Original Russian Text © L.V. Beloussov, S.A. Logvenkov, A.A. Stein, 2015, published in Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, 2015, Vol. 50, No. 1, pp. 3–14.
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Beloussov, L.V., Logvenkov, S.A. & Stein, A.A. Mathematical model of an active biological continuous medium with account for the deformations and rearrangements of the cells. Fluid Dyn 50, 1–11 (2015). https://doi.org/10.1134/S0015462815010019
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DOI: https://doi.org/10.1134/S0015462815010019