A planar finite element model for axial strain of helical structures

In this paper, we elaborate and verify a generic planar (two dimensional) finite element model formulation of the mechanical response of helical structures, which exploits the symmetry of helical guidelines. To this end, we employ a single helix cross section which can capture the response of the helix body, classifying the model in the realm of volume representative models. The axial straining of helical structures is described through an appropriately selected displacement field. The model is conveniently compared and verified to established analytic expressions for the entire range of helix configurations. It is noteworthy that the helix symmetry exploitation allows for very robust numerical calculations resulting in a significant reduction of the computational time. The latter constitutes a basic prerequisite for the efficient computation of complex helical structures both in the field of classical engineering applications (cable construction) as well in the realm of engineering biomechanical applications where the large number of constituents along with the necessity of optimization processes renders the use of volume models too expensive if not prohibitive.