Antiplane axisymmetric elastic-plastic shear in an isotropic hardening material

The paper presents an analytical solution to the problem of axisymmetric antiplane shear. The deformable material is enclosed between two cylindrical surfaces, one of which is fixed, and the other moves along the generatrix. This problem models a shear-off testing scheme. We use a geometrically nonlinear formulation of the elastic-plastic problem, taking the multiplicative decomposition of the deformation gradient tensor into elastic and plastic parts. The elastic properties of the specimen are described by the Mooney–Rivlin hyperelastic model. We consider an isotropic hardening material with the hardening law that is an arbitrary monotonic function of the accumulated plastic strain. The Tresca yield condition is utilized. The original nonlinear coupled system of partial differential equations is reduced to ordinary linear differential equations, the solution of which requires the calculation of definite integrals. The resulting solution includes deformation in the elastic range, the initiation of plastic flow, propagation of the plastic deformation region, and subsequent intensive plastic flow. The solution is illustrated with examples of materials with linear hardening, quadratic hardening, and Voce-type hardening with saturation. For these examples, ''force – displacement'' relationships, the distribution of accumulated plastic strain over the sample cross-section, and data on the distortion of material fibers, which were located in the radial direction before deformation, are
presented.