Mechanical response of a helical body to axial, torsional and radial strain

• Radial strain incorporation as a loading scheme of helical structures.
• Closed-form stiffness term expressions retrieval.
• Verification of stiffness term expressions with commercial finite element software.
• Discussion on significance and relevance to engineering practice.

The axial and torsional response of helical bodies as well as their inner coupling has been in depth analyzed, both from an analytical and a numerical modeling perspective. Herein, the radial deformation is appended as an additional kinematic degree of freedom. To this end, an existing analytical theory is employed and advanced so as to account for radial strain. The extended stiffness matrix entries are further verified with the use of a finite element model over a wide range of helix angular configurations. Overall, closed-form expressions of the 3×3 structural response of the helical body are provided, relating axial, torsional and radial strain to their force and moment resultants.