A mathematical analysis of the elastoplastic anti-plane shear problem of a power-law material and one class of closed-form solutions

A mathematical analysis of the elasto-plastic anti-plane shear problem of a power-law hardening material with infinitesimal deformations is presented in this paper. Hencky's deformation theory and von Mises' yield criterion are used in the analysis. The formulation is facilitated by using a complex variable representation and by choosing the only non-vanishing displacement component as the basic unknown. By introducing a differential transformation, the non-linear equation system describing the problem is first reduced to a solvable system of two partial differential equations. A general solution of this equivalent system is then derived using analytic function theory. Finally, one class of closed-form solutions is obtained for the telescope shear type problem of the power-law material by applying the general solution directly. Copyright (C) 1996 Elsevier Science Ltd.