A two-dimensional formulation for the homogenization of helical beam-like structures under bending loads

In this paper, a two-dimensional formulation is proposed for modeling the mechanical behavior of helical beam-like structures subjected to bending loads. Helical include multi-wire cables, which are widely used in engineering applications. An accurate representation their typically requires large-size three-dimensional finite element models. The formulation, written on cross-section only, offers tremendous reduction computational cost. Based asymptotic expansion method, derived within framework homogenization theory. first-order approximation problem obtained from solution two successive problems: microscopic and macroscopic one-dimensional problem. latter corresponds equilibrium equations straight Navier–Bernoulli–Saint Venant beam, effective elastic properties can be post-processed problem, rewritten curvilinear coordinate system (twisting system). Thanks system, we demonstrate that reduced solved by analysis. twisting it shown loads yet depend axial require specific treatment leading separate variable solutions complex type. Therefore, paper advances one step further than previous papers was with drawback only (extensional or torsional) could considered. Numerical results presented cylinders, springs, seven-wire strands. Good agreement analytical achieved. Interestingly, allows an analysis contact effects homogenized properties.