NORMAL STRESS EFFECTS INDUCED DURING CIRCULAR SHEAR OF A COMPRESSIBLENONLINEAR ELASTIC CYLINDER

The response of compressible non-linear isotropic elastic materials is studied using the problem of the circular shearing of a hollow cylind er. The hollow cylinder's inner surface is fixed and its outer surface is allowed to rotate but not move radially. The present work is conce rned with several issues not considered in previous studies, namely, h ow the load condition and material properties affect the distribution of local volume change and the local shear response. The study is carr ied out using a generalization of the Blatz-Ko constitutive equation. First, the homogeneous deformation of simple shear superposed on triax ial extension is considered because it can be compared to the local de formation of a material element in a hollow cylinder subjected to circ ular 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 surfac es rotate about the centerline which produce shear strains in the circ umferential direction and associated normal stresses in the radial and circumferential directions. The compressibility of the material allow s the cylindrical surfaces to undergo radial expansion or contraction. The radial distribution of shear strain, radial and circumferential s tretch ratios, and local volume changes are determined for different v alues of the material parameters. It is shown that the local volume ch anges vary monotonically with radius. Regions of volume increase and d ecrease depend on the values of the material parameters. It is also sh own that there is a value of the material parameter for which the loca l shear stress-shear strain response is found to be non-monotonic, whi ch can lead to kinks in the moment-rotation relation.