Nonlinear planar model for helical structures

Abstract

The paper contributes a new fully nonlinear planar finite element formulation, taking into accouint large deformations as well as material nonlinearity, for helical structures where helical constancy can be exploited. the helical structures may consist of one or several helices that may be free or embedded in some matrix material. While diverse homogeneous deformation modes could be considered, the present paper focuses on axial elongation and axial torsion, being the dominant ones. The derivations are explained and the model predictions are verified by comparison with those of three-dimensional finite element models using commercial software. Suggested applications of the numerically efficient model include analysis of highly hierarchical helical structures found in tendons.