Analytical solution for the plane strain inclusion problem of an elastic power-law hardening matrix containing an elastic cylindrical inclusion

An elasto-plastic analytical solution is presented for the plane strain inclusion problem of an elastic power-law hardening matrix containing an elastic cylindrical inclusion and subjected to equi-biaxial tension. Hencky’s deformation theory and von Mises’ yield criterion are used. All stress, strain and displacement components are derived in explicit forms in terms of two constant parameters, which are determined from the boundary conditions using a simple iterative procedure. Three specific solutions of practical interest are obtained as limiting cases. Illustrative numerical results are also provided to demonstrate applications of the solution. It is quantitatively shown that the extent of plastic deformation in the matrix is controlled by the ratio of Young’s moduli of the inclusion and matrix materials, Poisson’s ratio of the inclusion material and the strain-hardening effect of the matrix material, of which the first two factors are dominant. These findings are of practical importance to the design of fiber-filled metal-matrix composites.