Speaker
Description
Biological tissues frequently feature complex internal architectures, such as fiber networks, that strictly govern their mechanical behavior. Although the continuum mechanics of isotropic thin bodies incorporating biological effects, such as morphogenesis and internal activity, is well established $[1,2]$, a unified framework capturing anisotropy remains lacking.
This talk presents a rigorous continuum theory for active, anisotropic inelastic plates. By employing a multiplicative decomposition of the deformation gradient alongside fiber-dependent constitutive laws, we integrate incompatible active deformations with structural directionality. Through an asymptotic expansion of the three-dimensional energy functional under suitable scaling, we derive an effective plate theory within the Föppl–von Kármán regime. The resulting system of PDEs transparently captures the mathematical interplay between geometry, activity, and anisotropy $[3]$.
We apply this limit theory to investigate curvature-induced cell alignment. Modeling a cell as a fiber-reinforced active plate, we reveal that the system's response is governed by a dimensionless ratio comparing internal activity to substrate curvature. This ratio drives a bifurcation predicting a non-trivial range of optimal fiber orientations. Offering qualitative agreement with experimental observations, this framework is able to capture the essential mechanics of active, anisotropic thin biological structures.
References
$[1]$ J. Dervaux, P. Ciarletta, and M. Ben Amar. “Morphogenesis of thin hyperelastic plates: a constitutive theory of biological growth in the Föppl–von Kármán. Journal of the Mechanics and Physics of Solids 57.3 (2009), pp. 458–471.
$[2]$ L. A. Mihai and A. Goriely. “A plate theory for nematic liquid crystalline solids”. In:Journal of the Mechanics and Physics of Solids 144 (2020), p. 104101.
$[3]$ G. Fioretto et al. “The mechanics of anisotropic active plates with applications to cell alignment on curved substrates”. In: arXiv preprint arXiv:2512.19755 (2025), (under review)