NORMAL STRESS EFFECTS INDUCED DURING CIRCULAR SHEAR OF A COMPRESSIBLE NONLINEAR ELASTIC CYLINDER

The response of compressible non-linear isotropic elastic materials is studied using the problem of the circular shearing of a hollow cylinder. The hollow cylinder's inner surface is fixed and its outer surface is allowed to rotate but not move radially. The present work is concerned with several issues not considered in previous studies, namely, how the load condition and material properties affect the distribution of local volume change and the local shear response. The study is carried out using a generalization of the Blatz-Ko constitutive equation. First, the homogeneous deformation of simple shear superposed on triaxial extension is considered because it can be compared to the local deformation of a material element in a hollow cylinder subjected to circular shear. It is shown that for plane strain without normal tractions, the shear modulus depends on the magnitude of shear K and a loss of monotonicity in the ($) over bar sigma(12) vs K curve is possible for certain material parameters. In circular shear, the cylindrical surfaces rotate about the centerline which produce shear strains in the circumferential direction and associated normal stresses in the radial and circumferential directions. The compressibility of the material allows the cylindrical surfaces to undergo radial expansion or contraction. The radial distribution of shear strain, radial and circumferential stretch ratios, and local volume changes are determined for different values of the material parameters. It is shown that the local volume changes vary monotonically with radius. Regions of volume increase and decrease depend on the values of the material parameters. It is also shown that there is a value of the material parameter for which the local shear stress-shear strain response is found to be non-monotonic, which can lead to kinks in the moment-rotation relation.