Continuous Approach of Helical Material

Abstract

This work introduces a novel 3D formulation that presents helical motion within the framework of continuum mechanics. By leveraging the principle of virtual power, a comprehensive theoretical model is proposed, incorporating the extension-torsion coupling. The model establishes equilibrium equations and boundary conditions; its behavior is inspired from cable theory. Additionally, expressions are derived to establish the relationship between tensile stresses and torsion torques, based on the mechanical and geometric parameters. To shown case the influence of various parameters, such as helix pitch and torque, on mechanical stresses, illustrative examples are presented. These results are then compared with those obtained using the Cauchy continuum model.