Material tailoring in finite torsional deformations of axially graded Mooney–Rivlin circular cylinder

Abstract

We study direct and material tailoring (or inverse) problems for finite torsional deformations of a solid circular cylinder made of a Mooney–Rivlin material with the two elastic moduli continuously varying in the axial direction and deformed by applying equal and opposite torques on its two end faces. We note that a Mooney–Rivlin material is isotropic and incompressible. For the direct problem, we derive the condition that the two material moduli must satisfy in order for the problem to have a solution. In particular, it is shown that finite torsional deformations can be produced if one modulus equals the negative one-half of the other one. For the material tailoring problem, we find the axial variation of the two material moduli to produce finite torsional deformations with prescribed axial variation of the angle of twist per unit length.