*Article* **Compression of a Polar Orthotropic Wedge between Rotating Plates: Distinguished Features of the Solution**

### **Sergei Alexandrov 1,2,\*, Elena Lyamina 2, Pham Chinh 3 and Lihui Lang 1**


Received: 29 January 2019; Accepted: 19 February 2019; Published: 20 February 2019

**Abstract:** An infinite wedge of orthotropic material is confined between two rotating planar rough plates, which are inclined at an angle 2α. An instantaneous boundary value problem for the flow of the material is formulated and solved for the stress and the velocity fields, the solution being in closed form. The solution may exhibit the regimes of sliding or sticking at the plates. It is shown that the overall structure of the solution significantly depends on the friction stress at sliding. This stress is postulated by the friction law. Solutions, which exhibit sticking, may exist only if the postulated friction stress at sliding satisfies a certain condition. These solutions have a rigid rotating zone in the region adjacent to the plates, unless the angle α is equal to a certain critical value. Solutions which exhibit sliding may be singular. In particular, some space stress and velocity derivatives approach infinity in the vicinity of the friction surface.

**Keywords:** polar orthotropy; Hill's yield criterion; friction regimes; singularity
