The remarkable nature of cylindrically orthotropic elastic materials underplane strain deformations

In a recent paper by the author, a wedge of cylindrically orthotropic elast ic material under anti-plane deformations was studied. The solution depends on one non-dimensional material parameter gamma, which is the square root of the ratio of the two shear moduli. For any given wedge angle 2 alpha (no matter how small), one can choose a gamma so that the stress at the wedge apex is infinite. In the special case of a crack (2 alpha = 2 pi) there may be more than one stress singularity at the wedge apex. Some of them can be larger than the square-root singularity. On the other hand, one can also c hoose a gamma so that there is no stress singularity at the wedge apex for any wedge angle, including the special case of a crack. In this paper we sh ow that the same remarkable nature for anti-plane deformations prevails for the more complicated plane strain deformations. (The phrase 'remarkable na ture' was used in the title of a paper by Antman and Negron-Marrero who con sidered the pressuring of radially symmetric nonlinear elastic bodies.) The solution now depends on two non-dimensional material parameters eta and ga mma. The gamma here is the square root of the ratio of the two principal el astic stiffnesses. The existence or nonexistence of a singularity at the we dge apex depends on both eta and gamma. The classical paradox of Levy also appears here. The existence of a critical wedge angle depends entirely on e ta, not on gamma. A critical wedge angle can be any angle, and there may be more than one critical wedge angle.