Homogenization of helical beam-like structures: application to single-walled carbon nanotubes

International audienceThis work is devoted to the computation of axial stiffness of helical beam-like structures. Starting from the homogenization theory of periodic slender domains and taking benefit of the property of helical symmetry, the overall elastic behavior can be obtained from the solution of three-dimensional problems posed on a reduced basic cell. The mechanical analysis of this reduced basic cell performed using a concise FE model allows therefore to compute easily the anisotropic beam homogenized stiffness coefficients. The accuracy and usefulness of this approach is demonstrated by comparisons with reference solutions and large FE model results for two numerical volume structure examples: a wire spring and a stranded “6 + 1” rope. The homogenization procedure is then applied to single-walled carbon nanotubes and it is shown from the two helical symmetries that their basic cell can be reduced to three beam elements