Exact large strain analysis for the Poynting effect of freely twisted thin-walled tubes made of highly elastic soft materials

Abstract

Toward handling nonlinear coupling effects at large elastic deformations, a decoupled form of the multi-axial elastic potential for highly elastic soft materials is first constructed based on Hencky’s logarithmic strain, and this new potential is then used to obtain analytic results for the uniaxial extension and compression of a bar, the equi-biaxial extension of a plate, the plane-strain extension of a strip and, in particular, the large torsion of a thin-walled tube with free ends. Novelties are included in the following three respects: (a) Experimental data for responses of the uniaxial extension, equi-biaxial extension (uniaxial compression) and plane-strain extension (simple shear) may be accurately matched up to large strain with strain-stiffening effects; (b) exact responses for the Poynting effect of freely twisted thin-walled tubes may be derived for changes in the axial length and the wall thickness as well as the averaged radius; and (c) the coupling nonlinear complexities involved in all such responses may be worked out in a decoupled sense.