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Torsion of elliptical composite beams with auxetic phase

The torsion of a prismatic beam has been a classic problem of structural mechanics since the famous works of Saint‐Venant. In this paper, an analysis is extended on a composite beam with elliptical cross‐section. We consider a beam in which the elliptical cross‐section is split into sectors in which two materials, one of which is auxetic, are distributed alternately. The influence of auxetic phase on the total elastic strain energy is analyzed as well as geometrical parameters representing both the shape of the cross‐section, and the arrangements of sectors. An unexpected behavior of a beam with strong auxetic phase is presented as, in the case of selected parameters, the beam with elliptical cross‐section is more rigid than the beam with a circular one.