Bifurcation-induced <i>dual Poynting effect</i> in transversely isotropic hyperelastic bodies

Inspired by the behaviour exhibited by certain biological systems, we demonstrate, through analytical solutions, a new coupling phenomenon in fibre-reinforced materials, which we term the dual Poynting effect . Specifically, we show that, in a transversely isotropic, nonlinear elastic prismatic body, constituted by a soft matrix embedded with sufficiently stiff fibres aligned along the prism axis, compression can induce a supercritical bifurcation at a specific stretch threshold. Both in the shear of a rectangular block and in the torsion of a cylindrical body, compressing beyond a bifurcation stretch threshold results in combined shear-extension or torsion-extension deformed configurations, where the object prefers to accommodate to minimize the total potential energy. Here, we rigorously analyse this effect within the framework of the nonlinear theory of hyperelastic fibre-reinforced materials, determine the constitutive requirements that make the dual solution energetically favoured, describe the (supercritical) bifurcation diagrams, and establish the corresponding stretch thresholds.