A mathematical analysis of the elasto-plastic plane stress problem of a power-law material

In this paper a generic study on the plane stress problem of a power-law material undergoing infinitesimal deformations is carried out, and a general solution for the stress and strain fields is derived using a stress function method and analytic function theory. Hencky's deformation theory and von Mises' yield criterion are used, and a differential transformation is invoked in the analysis. As an example, the closed-form solution of the pure bending problem of a thin beam of power-law material is obtained by applying the general solution directly.