The necking of the rectangular block with surface imperfection (Q1819596)

It is well known that the problem of necking of plane strain rectangular block with surface imperfection is very important. In this paper this problem is studied based on the theory of finite elasticity. For convenience of study the constitutive relation is deduced to the theory of incrementally-linear solids discussed by \textit{M. A. Biot} [Mechanics of incremental deformation (1965)], \textit{R. Hill} and \textit{J. W. Hutchinson} [J. Mech. Phys. Solids 23, 239-264 (1975; Zbl 0331.73048)]. As in buckling theory the surface imperfection (concave and convex on the surface) is considered to be made by a small axisymmetric stress free deformation.