Uniformity of anti-plane stresses inside a nonlinear elastic elliptical or parabolic inhomogeneity.

We study the anti-plane strain problem associated with a -Laplacian nonlinear elastic elliptical inhomogeneity embedded in an infinite linear elastic matrix subjected to uniform remote anti-plane stresses. A full-field exact solution is derived using complex variable techniques. It is proved that the stress field inside the elliptical inhomogeneity is nevertheless uniform. The uniformity of stresses is also observed inside a -Laplacian nonlinear elastic parabolic inhomogeneity.