Elasticity Problem with a Cusp between Thin Inclusion and Boundary

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper investigates an equilibrium problem involving an elastic body with a thin, rigid inclusion intersecting the body's external boundary at a zero angle. The inclusion is considered delaminated from the surrounding elastic material, leading to the formation of an interfacial crack. Boundary conditions governing the crack faces ensure a mutual non-penetration, dependent on a cohesion parameter that is positive. The research establishes the existence of a solution for the problem under various conditions applied to the external boundary.Furthermore, the paper explores the behavior of the system as the damage parameter approaches both infinity and zero, evaluating the limiting scenarios. Additionally, an optimal control problem is addressed, particularly focusing on instances where a portion of the rigid inclusion extends beyond the elastic body.

We suggest:

1- The figures should be redrawn very well

2- We ask the author to improve overal quality to the paper by revising the abstract, introduction and discussion.

3- The subtitles are not very clear and will not connected very well to the explanations given by the author.

4- We detect inappropriate selfcitations by author.

5- The author should improve the introduction by adding the suggested reference of boundary value problem, add the following reference :

https://doi.org/10.1080/23324309.2023.2271229

6- We notice some misspelling and gram

 

 

Comments on the Quality of English Language

The authors should read the article carefully for typos and grammatical errors by correcting the entire text and improving the technical writing aspect of this paper.

Author Response

 

I would like to thank the reviewer for the remarks and proposals for improving the manuscript.The following changes have been done:

 

 

1. The quality of  figures is  improved
2. Abstract, Introduction and discussion are improved
3. Several subtitles were changed
4. Three self-citations were removed from References
5. The  paper indicated by the reviewer is added to References. Introduction is changed.
6. English was improved in the paper ( page 1, line 4,  line14, line 32; page 3, line 48;  page 8, line 87)

Reviewer 2 Report

Comments and Suggestions for Authors

Please see the file in the attachment.

Comments for author File: Comments.pdf

Author Response

I would like to thank the reviewer for the review

Reviewer 3 Report

Comments and Suggestions for Authors

According to my opinion, the manuscript is well-written and has merits for publication in the Journal. I therefore recommend publication of this work after some minor revisions based on the following:

1) Authors are encouraged to indicate again the main practical applications of this work.

2) Authors are encouraged to discuss the possibility to apply this method for other materials such as functionally graded materials (FGMs) by discussing the following works:

- Tounsi et al. (2023), “Influences of different boundary conditions and hygro-thermal environment on the free vibration responses of FGM sandwich plates resting on viscoelastic foundation”, International Journal of Structural Stability and Dynamics, https://doi.org/10.1142/S0219455424501177

- Hanifi Hachemi Amar et al. (2023), “Buckling analysis of FG plates via 2D and quasi-3D refined shear deformation theories”, Structural Engineering and Mechanics, 85(6), 765-780.

3) Further polish the English writing of the full article.

4) Equation (22) should be more discussed.

5) Theorem 6 should be more clarified.

6) Future research direction must be shown in conclusion.

  After revisions I recommend strongly this paper for publication.

Comments on the Quality of English Language

The Quality of English is good.

Author Response

I would like to thank the reviewer for the remarks and proposals for improving the manuscript.The following changes have been done:

1. Practical applications are indicated in Introduction
2. Two  papers indicated  by the reviewer  are added to References;  possibility to apply the approaches used in the paper are mentioned in Introduction
3. English was improved in the paper (page 1, line 4, line14, line 32; page 3, line 48;  page 8, line 87)
4. We added the reference to the formula before (23). Thus, the statement became clear.
5. Several sentences were added before Theorem 6 to clarify the assertion to be proved.
6. Future research direction is shown in Conclusion

 

 

 

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

I propose the publication of this article