Solution Behavior Near Very Rough Walls under Axial Symmetry: An Exact Solution for Anisotropic Rigid/Plastic Material
Round 1
Reviewer 1 Report
The study provides an exact solution for an axisymmetric boundary value problem representing the mode of deformation in the vicinity of frictional interfaces with high friction stresses. It is shown that some strain rate and spin components follow an inverse square rule near the friction surface; an essential difference from the available analysis under plane strain conditions is that the system of equations is not hyperbolic. The paper could be interesting for Symmetry journal readership - it is well structured and written, it is of high technical quality, too. Therefore I recommend its publication and there are only a few issues that are to be addressed prior to its publication.
Specific comments and suggestions
The title, abstact and keywords are good; perhaps, "anisotropic material" (or something like this) could be added to current keywords (even if "orthotropy" is already included)
Introduction is well written providing information on current state of knowledge (and knowledge gaps); its length is good as well and there are no multiple (lumped) references.
References throughout the manuscript. For example, line 245 [11, 12] or line 249 [14, 15] please remove the "space" between the numbers in the square brackets and check the overall manuscript for similar cases.
Conclusions are well written; perhaps, it could be expanded a little by highlighting the limitations and namely some examples of applications of this theoretic study - it could be interesting for the journal readership.
Author Response
Specific comments and suggestions
- The title, abstact and keywords are good; perhaps, "anisotropic material" (or something like this) could be added to current keywords (even if "orthotropy" is already included)
We have added this keyword.
- References throughout the manuscript. For example, line 245 [11, 12] or line 249 [14, 15] please remove the "space" between the numbers in the square brackets and check the overall manuscript for similar cases.
We have made these corrections.
- Conclusions are well written; perhaps, it could be expanded a little by highlighting the limitations and namely some examples of applications of this theoretic study - it could be interesting for the journal readership.
Assuming that the model adopted in our manuscript is used, the limitation is that the normal strain rate in the direction orthogonal to the friction surface does not vanish. We have clarified it in Section 5. The application of the general theory is at least twofold. Firstly, the singular behavior found should be taken in to account in numerical codes. We refer to [11,12] to emphasize this point. Secondly, high gradients of velocity components found are in qualitative agreement with numerous experimental results. We refer to [14,15] to emphasize this point.
Reviewer 2 Report
The paper presents as stated by the authors “focuses on a particular boundary value problem for anisotropic material obeying Hill’s quadratic yield criterion under axial symmetry”.
The work, mainly a theoretical mechanics approach, is conducted using a complex set of mathematical equations.
The flow of and the use of the mathematical apparatus is quite hard to follow by anyone which is not highly specialized in theoretical mechanics.
Of course, these above-mentioned issues cannot be considered flaws of the paper, but just observations which regards of its readability and potential interest for the readers.
However, it is not clear (in my opinion) which is (if any) the practical use of the results of the research. I strongly suggest a much more detailed presentation of how the results of the research are useful in any way.
Moreover, I strongly suggest the introduction of a graphical presentation of the research program (a flowchart), emphasizing the objectives and the results (and their usability).
Author Response
- However, it is not clear (in my opinion) which is (if any) the practical use of the results of the research. I strongly suggest a much more detailed presentation of how the results of the research are useful in any way.
The application of the general theory is at least twofold. Firstly, the singular behavior found should be taken in to account in numerical codes. We refer to [11,12] to emphasize this point. Secondly, high gradients of velocity components found are in qualitative agreement with numerous experimental results. We refer to [14,15] to emphasize this point.
- Moreover, I strongly suggest the introduction of a graphical presentation of the research program (a flowchart), emphasizing the objectives and the results (and their usability).
We have looked through a dozen papers recently published in Symmetry. We did not find that such charts are used. The objective of the paper is to derive the asymptotic representation of solutions near frictional interfaces. Equation (69) represents the final result. We do not understand what to show in the chart.
