Solution Behavior in the Vicinity of Characteristic Envelopes for the Double Slip and Rotation Model

• Main Authors: Yao Wang, Sergei Alexandrov, Elena Lyamina
• Format: Article
• Language: English
• Published: MDPI AG 2020-05-01
• Series: Applied Sciences
• Subjects: pressure-dependent plasticity; double slip and rotation model; envelope of characteristics; singularity; asymptotic analysis
• Online Access: https://www.mdpi.com/2076-3417/10/9/3220

The boundary conditions significantly affect solution behavior near rough interfaces. This paper presents general asymptotic analysis of solutions for the rigid plastic double slip and rotation model in the vicinity of an envelope of characteristics under plane strain and axially symmetric conditions. This model is used in the mechanics of granular materials. The analysis has important implications for solving boundary value problems because the envelope of characteristics is a natural boundary of the analytic solution. Moreover, an envelope of characteristics often coincides with frictional interfaces. In this case, the regime of sticking is not possible independently of the friction law chosen. It is shown that the solution is singular in the vicinity of envelopes. In particular, the profile of the velocity component tangential to the envelope is described by the sum of the constant and square root functions of the normal distance to the envelope in its vicinity. As a result, some components of the strain rate tensor approach infinity. This finding might help to develop an efficient numerical method for solving boundary value problems and provide the basis for the interpretation of some experimental results.