Mechanical modeling of helical structures accounting for translational invariance. Part 1: Static behavior

The purpose of this paper is to investigate the static behavior of helical structures under axial loads. Taking into account their translational invariance, the homogenization theory is applied. This approach, based on asymptotic expansion, gives the first-order approximation of the 3D elasticity problem from the solution of a 2D microscopic problem posed on the cross-section and a 1D macroscopic problem, which turns out to be a Navier–Bernoulli–Saint-Venant beam problem. By contrast with earlier references in which a reduced 3D model was built on a slice of the helical structure, the contribution of this paper is to propose a 2D microscopic model. Homogenization is first applied to helical single wire structures, i.e. helical springs. Next, axial elastic properties of a seven-wire strand are computed. The approach is validated through comparison with reference results: analytical solution for helical single wire structures and 3D detailed finite element solution for seven-wire strands.