Deformation of an elastic material paired with a tree structure

Michaël Brunengo
Laboratoire J.A. Dieudonné, Parc Valrose, 28 Avenue Valrose, 06108 Nice Cedex 02, 06000 Nice
In order to model effects of automated treatment of respiratory physiotherapy with focused pulses, we study deformation of an elastic material under oscillating constraints on its boundaries. Moreover the system is linked to a symmetrical and dichotomous tree built as series of cylinders, idealizing bronchial tree. To do so, under infinitesimal strain theory, we consider that a change a volume on an area of the material creates airflow. Then we force it to flow in the tree and to go through hydrodynamic resistance. This coupling adds friction to the system and gives information on total airflow created at the top of the tree, i.e. at the mouth, under pressure on boundaries.