The Influence of Multi-Level Structure on the Bearing and Crack Propagation Mechanism of Tooth Enamel

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The article by Yiyun Kong et al., "The influence of multi-level structure on the bearing mechanism and crack propagation mechanism of tooth enamel," examines the influence of multi-level structure on enamel properties and fracture resistance. The authors demonstrate the enamel structure-characteristic relationship and present important recommendations for optimizing the design of dental materials.

To enhance understanding of the article, it is necessary to consider several recommendations and answer the following questions:

1. Explain how the enamel was divided into layers to obtain SEM images and measure the hardness of the various enamel layers.
2. How, and for which enamel layer, were the elastic modulus (E) and average crack length (c) determined for calculating Kc.
3. The authors modeled differences in the physical and mechanical properties of the surface and deep layers of enamel without supporting their conclusions with actual studies. Among the tools presented in the article, the authors utilize scanning electron microscopy, which can be used to demonstrate differences in crack propagation in different enamel layers.
4. Is it possible to verify the proposed model of the deformation and strength properties of the surface and inner layers of enamel using real measurements?
5. In conclusion, briefly summarize the structural features that a structural composite material must possess to achieve maximum physical and mechanical properties.

Author Response

1. Comments:Explain how the enamel was divided into layers to obtain SEM images and measure the hardness of the various enamel layers.
2. Comments: How, and for which enamel layer, were the elastic modulus (E) and average crack length (c) determined for calculating Kc.

3. Comments: The authors modeled differences in the physical and mechanical properties of the surface and deep layers of enamel without supporting their conclusions with actual studies. Among the tools presented in the article, the authors utilize scanning electron microscopy, which can be used to demonstrate differences in crack propagation in different enamel layers.

4. Comments: Is it possible to verify the proposed model of the deformation and strength properties of the surface and inner layers of enamel using real measurements?

5. Comments: In conclusion, briefly summarize the structural features that a structural composite material must possess to achieve maximum physical and mechanical properties.

   "Please see the attachment."

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors Pay attention to the figures in the text "Fig.1", etc. The use of rats as a model requires justification. How is rat enamel (with constantly growing incisors) relevant for studying the mechanical properties of human enamel (not growing)? This is a critical point affecting the interpretation of all the results. It is indicated that diamond pastes with particle sizes W5, W3.5, W1.5 were used. It is necessary to indicate that this is a classification according to GOST, and provide an equivalent size in microns (5, 3.5, 1.5 microns) for an international audience. The main weakness of the work is the acceptance of key assumptions that both hydroxyapatite (HAP) crystals and the protein matrix are isotropic materials. GAP crystals are inherently anisotropic. Their mechanical properties (Young's modulus, strength) vary significantly along and across the crystal axis. Modeling them as isotropic cylinders completely ignores this fundamental fact, which casts doubt on all subsequent conclusions about stress distribution, the mechanism of deformation and crack propagation. When discussing Figure 8, it is stated that the crack in the outer layer is deflected by the inclined beam, contradicting another statement that cracks in the outer layer tend to propagate in a straight line. This point requires a clearer explanation and quantitative analysis of the angle of deviation.

Author Response

1. Comments:Pay attention to the figures in the text "Fig.1", etc.
2. Comments: The use of rats as a model requires justification. How is rat enamel (with constantly growing incisors) relevant for studying the mechanical properties of human enamel (not growing)?
3. Comments: It is indicated that diamond pastes with particle sizes W5, W3.5, W1.5 were used. It is necessary to indicate that this is a classification according to GOST, and provide an equivalent size in microns (5, 3.5, 1.5 microns) for an international audience.

4. Comments: The main weakness of the work is the acceptance of key assumptions that both hydroxyapatite (HAP) crystals and the protein matrix are isotropic materials. GAP crystals are inherently anisotropic. Their mechanical properties (Young's modulus, strength) vary significantly along and across the crystal axis. Modeling them as isotropic cylinders completely ignores this fundamental fact, which casts doubt on all subsequent conclusions about stress distribution, the mechanism of deformation and crack propagation.

5. Comments: When discussing Figure 8, it is stated that the crack in the outer layer is deflected by the inclined beam, contradicting another statement that cracks in the outer layer tend to propagate in a straight line. This point requires a clearer explanation and quantitative analysis of the angle of deviation."Please see the attachment."

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The article entitled The influence of multi-level structure on the bearing mechanism and crack propagation mechanism of tooth enamel presents interesting research on the hierarchical structure of enamel and its influence on mechanical properties.  

The introduction is comprehensive and well-grounded in the literature. The authors first present the general properties of hard biomaterials such as bone and enamel, emphasizing the role of hierarchical structure in shaping their mechanical properties. They then discuss key numerical data on the hardness, modulus of elasticity, and fracture toughness of enamel, providing a solid theoretical framework. The sources are diverse and include both classic works (e.g., Gao and Ji, 2004) and very recent publications from 2023–2024, demonstrating a thorough literature review. The study's objective is clearly stated: the authors emphasize the lack of quantitative models that explain the mechanisms of crack propagation and load transfer based on the microstructure of enamel crystals. The research gap is aptly defined: numerous experimental studies exist, but in-depth numerical models are lacking. The introduction can be considered complete, coherent, and well-motivated.

The description of the methodology is detailed and, for the most part, very clear. The authors explain how the animal modeling was performed (including reference to ethical approvals), how the samples were prepared, and how the SEM observations and hardness tests were performed. A strength of the work is the precise description of sample preparation (polishing, etching, gold plating) and test conditions (e.g., loading during nanoindentation). In the numerical modeling section, the authors provide a detailed discussion of material parameters, the method of creating modules, the types of mesh elements in ABAQUS, boundary conditions, and failure criteria. This is presented in a very technical manner, increasing clarity and enabling study replication. A limitation is that the authors assume the materials are isotropic and homogeneous, which simplifies the actual conditions in the enamel—this aspect should be emphasized as a potential source of interpretation errors.

The results are presented systematically and logically, from experimental studies (hardness and fracture toughness), through load-transfer mechanism simulations, to crack propagation analyses. Numerous and clear stress/strain graphs and maps are provided, and their interpretation is performed step-by-step. The description of the results is consistent with the illustrations – the authors not only present the data but also explain their significance in a biological and biomimetic context. A strength of the paper is the detailed analysis of the differences between the outer and inner layers of enamel, as well as the reference to previous experimental observations. A drawback is the repetitive nature of the arguments (e.g., the greater stiffness of the outer layer and the greater fracture toughness of the inner layer), which could be shortened for brevity.

This article is a valuable and reliable study that makes a significant contribution to research on enamel mechanics from the perspective of multiscale modeling. The introduction is sufficiently comprehensive and supported by current sources, the methodology is described clearly and in detail, and the results are presented in a systematic and understandable manner. Despite minor comments regarding the repetitiveness of descriptions and simplifications in the models, the publication deserves a positive assessment.

Author Response

1. Comments: A limitation is that the authors assume the materials are isotropic and homogeneous, which simplifies the actual conditions in the enamel—this aspect should be emphasized as a potential source of interpretation errors.
2. Comments: A drawback is the repetitive nature of the arguments (e.g., the greater stiffness of the outer layer and the greater fracture toughness of the inner layer), which could be shortened for brevity.

      "Please see the attachment."

 

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

Dear authors,

Thank you very much for submitting your work to Coatings.

I hope that my remarks and suggestions will be useful in order to increase the quality of your manuscript.

Please find them bellow:

General remarks:

The manuscript presents a study regarding rat tooth enamel, highlighting it’s unique hierarchical structure and the relationship between crystal orientation and mechanical performance. The work is relevant to biomaterials and biomimetics, and it provides valuable insights into how enamel’s gradient architecture contributes to both hardness and toughness. The findings may inspire the design of novel composite materials with enhanced mechanical properties.

I would suggest that the abstract should respect the structure of a scientific paper (Introduction, Material and Methods, Discussion, Consclusion) taking into account that the paper is original and not a review one.

Minor issues:

1. Authorship: Equal contribution means that the two authors contributed exactly the same to the paper. The contribution section is incorrectly written in accordance with the MDPI standards and doesn’t reflect that.
2. Please provide a proper and professional correspondence e-mail.
3. Please clarify if all figures are original.

Main issues:

1. Please elaborate and explain more regarding the role of the formulas that you included in the text. It might be misleading for a reader who doesn’t possess the special knowledge in this field.
2. Please carefully examine if part of the Discussion section doesn’t belong to the Results one. From my point of view you should double check that. In the same time, please kindly keep in mind that the Discussion section should reflect you own finding compared what was already researched.
3. Conclusions section should be entirely rewritten in such a way that will be more synthetic and will reflect the practical impact of your findings. Parts of this section should be included in the Discussion one.
4. Please provide a statement regarding the Ethical Approval, if is it needed or was waived.

Please receive my best regards!

 

Author Response

1. Comments: Authorship: Equal contribution means that the two authors contributed exactly the same to the paper. The contribution section is incorrectly written in accordance with the MDPI standards and doesn’t reflect that.
2. Comments: Please provide a proper and professional correspondence e-mail.

3. Comments: Please clarify if all figures are original.

4. Comments: Please elaborate and explain more regarding the role of the formulas that you included in the text. It might be misleading for a reader who doesn’t possess the special knowledge in this field.

5. Comments: Please carefully examine if part of the Discussion section doesn’t belong to the Results one. From my point of view you should double check that. In the same time, please kindly keep in mind that the Discussion section should reflect you own finding compared what was already researched.

6. Comments: Conclusions section should be entirely rewritten in such a way that will be more synthetic and will reflect the practical impact of your findings. Parts of this section should be included in the Discussion one.

7. Comments: Please provide a statement regarding the Ethical Approval, if is it needed or was waived.

   "Please see the attachment."

Author Response File: Author Response.pdf