Speaker
Description
Since D'Arcy Thompson, the interplay between mechanics and shape in living organisms has been a central question in mathematical biology. In tissue mechanics, shape variation has been studied through growth, development, and wound healing with various modeling approaches and objectives (\cite{10.1088/1367-2630/adcd93,10.1039/d3sm01419c}).
We develop a variational approach to active deformable materials where shape evolution is characterized by its dissipative behavior in response to internal activity. Inspired by Generalized Standard Materials’ extension to tissue mechanics (\cite{10.1140/epje/i2015-15033-4, 10.1038/s41578-018-0066-z}), the tissue is described by an Eulerian velocity field determined at each instant by minimizing a functional combining energy dissipation and active energy input. The tissue boundary evolves as a free boundary carried by this velocity — making shape a dynamical consequence of the material's internal processes rather than a prescribed input.
We will discuss the mechanistic insights of this modeling approach for tissue mechanics, its mathematical properties, and its biological interpretation in physiology and pathology.
This is joint work with L. Alasio (INRIA & LJLL) & M. Szopos (UPCité & MAP5).
Bibliography
@article{10.1140/epje/i2015-15033-4,
author = {Tlili, S. and Gay, C. and Graner, F. and Marcq, P. and Molino, F. and Saramito, P.},
title = {Colloquium: Mechanical formalisms for tissue dynamics},
journal = {The European Physical Journal E},
year = {2015},
volume = {38},
issue = {5},
doi = {10.1140/epje/i2015-15033-4}
}
@article{10.1038/s41578-018-0066-z,
author = {Xi, W. and Saw, T. B. and Delacour, D. and Lim, C. T. and Ladoux, B.},
title = {Material approaches to active tissue mechanics},
journal = {Nature Reviews Materials},
year = {2018},
volume = {4},
issue = {1},
pages = {23-44},
doi = {10.1038/s41578-018-0066-z}
}
@article{10.1088/1367-2630/adcd93,
author = {Mirza, W. and Torres-Sànchez, A. and Vilanova, G. and Arroyo, M.},
title = {Variational formulation of active nematic fluids: theory and simulation},
journal = {New Journal of Physics},
year = {2025},
volume = {27},
issue = {4},
pages = {043025},
doi = {10.1088/1367-2630/adcd93}
}
@article{10.1039/d3sm01419c,
author = {Pozzi, G. and Ciarletta, P.},
title = {Geometric control by active mechanics of epithelial gap closure},
journal = {Soft Matter},
year = {2024},
volume = {20},
issue = {4},
pages = {900-908},
doi = {10.1039/d3sm01419c}
}
