• 3D Cosserat rod model
• ensamble effects
• helical rods
• large deformation regime

This thesis studies the mechanical properties of tubular structures composed of assemblies of helical rods, which are found in nature and in several engineering applications.
In particular, we investigate the response under compression of assemblies of pin-jointed helical springs via numerical simulations, and we compare the behavior of the assemblies as the number of springs composing the assembly increases.
The assemblies are modelled as 3D Cosserat rods in the large deformation regime. We parametrize the rotations of directors using quaternions.
The equilibrium equations in weak form are derived from the Principle of Virtual Work and they are solved numerically through a
custom-made implementation in the software package COMSOL Multiphysics (Weak Form PDE mode).
The numerical results allow to compute the load-displacement curve and show that:
1. the mutual support between helices of an assembly stabilizes its behavior with respect to the single helix case: the buckling observed in the compression of a single helix is suppressed in the response of the ensemble;
2. the collective behavior of the assemblies can be described in terms of a bulk behavior, where each rod deforms as a perfect circular helix, and a boundary behavior, where rods deviate from perfect helices in a way that is aected by the specific boundary conditions applied.