Speaker
Description
We investigate the growth and remodeling of biological tissues, described as multi-constituent materials, and the structural evolution associated with these phenomena. We generalize the results obtained in [1, 2], and we frame them within the context of the Analytical Mechanics of nonholonomic systems. We do this to study growth variationally.
Inspired by [3, 4], we start from a multiplicative decomposition of the deformation gradient tensor in which the factor associated with the growth-induced distortions evolves according to prescribed “growth laws” [3, 4]. Without suitable assumptions, the resulting constraints are nonholonomic. By appending such constraints to a proper Lagrangian density function, we derive the dynamic equations through the extended Hamilton-Suslov Principle, and we show that they agree with those obtained by exploiting the Principle of Virtual Work.
References
[1] Grillo, A., Federico, S., Wittum, G., “Growth, mass transfer, and remodeling in fiber-reinforced, multi-constituent materials”, Int. J. Non-Linear Mech., 47, 388–401 (2012).
[2] Licari, V., “Considerazioni sulla possibilità di formulare alcune leggi evolutive della crescita volumetrica di aggregati cellulari ”, Tesi di Laurea Magistrale in Ingegneria Matematica, Politecnico di Torino, (2021).
[3] Grillo, A., Pastore, A. and Di Stefano, S., “An Approach to Growth Mechanics Based on the Analytical Mechanics of Nonholonomic Systems”, J. Elast., 157, 388–401 (2024).
[4] Pastore, A., Giammarini, A., Grillo, A., “Reconciling Kozlov’s vakonomic method with the traditional non-holonomic method: solution of two benchmark problems”, Acta Mech., 235, 2341–2379 (2024).