Local Thickness Optimization of Functionally Graded Lattice Structures in Compression

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The section 2.3.2 Thickness Optimization Method must be improved. The mathematical formulation of the optimization problem is not included. The objective function (s), design variables and constraints of the problem must be clearly defined.

Author Response

Dear Reviewer,

 

Thank you kindly for your valuable feedback. Regarding the description of section 2.3.2 Thickness Optimization Method, we feel that the points mentioned are adequately covered.

 

-The section 2.3.2 Thickness Optimization Method must be improved. The mathematical formulation of the optimization problem is not included.

The objective function is to maximize the specific energy absorption as mentioned in the text. Its equation is defined in Equation 4.

 

 

-The objective function (s), design variables and constraints of the problem must be clearly defined.

The design variables are the function parameters a, b, and c/n of the chosen function (Eqs. 1-3). The constraints are given in the form of maximum and minimum allowable thickness values of the lattice's beams as mentioned in the text. Hyperstudy's solver documentation of the GRSM algorithm does not provide an in-depth explanation of its functionality apart from a high-level description. It can be added if that is what was requested.

 

Does the issue lie in the text's clarity, or is there any missing information that should be added? Please elaborate on the points that should be improved further.

 

Best regards,

Thierry Decker

Reviewer 2 Report

Comments and Suggestions for Authors

Strengths:

 (+) The problem is well-defined.

Weaknesses:

 (-) The introduction must be improved.

 (-) The related work section must be enhanced.

 (-) Finite Element Model and Optimization evaluation must be improved.

 (-) Some improvements are needed in the description of the method and result.

 ==== FIGURES ====

The text of some figures is too small, e.g., Fig. 5, 11,12,13.  Authors should make sure that the text can be read if printed on paper.

==== INTRODUCTION ====

The introduction should clearly explain the key limitations of prior work that are relevant to this paper.

Contributions should be highlighted more. It should be made clear what is novel and how it addresses the limitations of prior work.

It would be worth briefly mentioning some of the background information of FGMs, it’s characterises, advantages, etc, along with references. Such as ‘Preparation and thermodynamic analysis of the porous ZrO2/(ZrO2+Ni) functionally graded bolted joint; Load distribution in threads of porous metal–ceramic functionally graded composite joints subjected to thermomechanical loading’

==== RELATED WORK ====

The authors should explain clearly what the differences are between the prior work and the solution presented in this paper.

==== METHOD ====

The authors should first give an overview of their solution before explaining the details.

The FEA model should be explained in more detail. Where is the geometry model and meshed model?

It is important to clearly explain what is new and what is not in the proposed solution. If some parts are identical, they should be appropriately cited and differences should be highlighted.

All parameters in equations should be explained properly, such as those in Eqs 1-3, Eq. 4.

==== RESULTS ====

There is not enough discussion of the experimental results.

Table 2 does not have a proper caption.

==== CONCLUSION ====

The conclusion section is too lengthy, please make it more concise with only the important concluding remarks. It would be better to move the discussion to the results section.

Author Response

Dear Reviewer,

 

Thank you very much for your thorough feedback, it is highly appreciated, and we agree with the majority of your points. They are replied to individually in the text below.

 

 

1. The text of some figures is too small, e.g., Fig. 5, 11,12,13.  Authors should make sure that the text can be read if printed on paper.

Agreed, the text will be enlarged for better readability.

 

 

2. The introduction should clearly explain the key limitations of prior work that are relevant to this paper.

Agreed, a more thorough explanation is required.

 

3. Contributions should be highlighted more. It should be made clear what is novel and how it addresses the limitations of prior work.

Agreed, a clearer distinction between prior work and what is added to existing methods will be added.

 

4. It would be worth briefly mentioning some of the background information of FGMs, it’s characterises, advantages, etc, along with references. Such as ‘Preparation and thermodynamic analysis of the porous ZrO2/(ZrO2+Ni) functionally graded bolted joint; Load distribution in threads of porous metal–ceramic functionally graded composite joints subjected to thermomechanical loading’

Agreed, a mention of the concept of FGMs to put FGLS into context will be added. The mentioned paper appears to be an excellent example and will be included.

 

5. The authors should explain clearly what the differences are between the prior work and the solution presented in this paper.

Generally agreed, however we feel that this point overlaps with the second and third points and is redundant.

 

6. The authors should first give an overview of their solution before explaining the details.

Agreed, a flowchart or other sort of graph depicting the method will be added.

 

7. The FEA model should be explained in more detail. Where is the geometry model and meshed model?

The geometries of the unit cells are depicted in Figure 2, they are repeated throughout the lattice. If it helps with clarity, a picture showing the complete geometries of both lattices will be added.

The meshed model is depicted in Figure 4, it is a screenshot taken from Altair HyperMesh and modified with Inkscape. The coloured lattice structure depicts the actual meshes of the lattice and shell plates, and the nodes are visualized by the circles in the image's detail. The FE model's setup is thoroughly described including element type, contact type and settings, material law, friction assumption, and relevant solver settings. Which further explanations or pictures should be added?

 

8. It is important to clearly explain what is new and what is not in the proposed solution. If some parts are identical, they should be appropriately cited and differences should be highlighted.

Agreed, the section introducing the differences of the proposed method with previous publications will be expanded.

9. All parameters in equations should be explained properly, such as those in Eqs 1-3, Eq. 4.

The parameters are defined in the text below Figure 4. Quote:

In each approach the number of optimization variables is decreased from ten to three, reducing the computational effort for finding an optimum distribution drastically. The parameter n is the power law’s exponent, a is a scaling factor, b adds a constant value and c allows a horizontal shift of the function to allow control over the inflection point position in the linear and quadratic law. The power law is set up symmetrically with respect to the middle plane, whereas the linear and quadratic law possess no inherent symmetry. 

For better clarity, the paragraph can be moved directly below the equations and above Figure 4. The parameters of Eq. 4 are explained directly above its definition:

 

10. There is not enough discussion of the experimental results.

While we disagree that there is not a sufficient discussion as it is covered by the continuous text of the Results section, we agree that it should be separated from the main text into its own section.

 

11. Table 2 does not have a proper caption.

Agreed, this will be mitigated.

 

12. The conclusion section is too lengthy, please make it more concise with only the important concluding remarks. It would be better to move the discussion to the results section.

Agreed, the conclusion will be shortened and the discussion will be moved.

 

Thank you very much for your valuable work and best regards,

Thierry Decker

Reviewer 3 Report

Comments and Suggestions for Authors

This paper presents a finite-element-based analysis on the optimization of the thickness of lattice cells on the performance of compression resistance. There are a few parts seeming problematic, please provide proper responses to my following concerns.

Can the authors provide a summary of their optimization method? It appears that the manuscript used three different math functions to control the local thickness density of the truss-like lattice. They then used a numerical-based method to test compression responses, followed by experiments to validate the computed results. If optimization was involved, based on what I have been taught, there should be some kind of objective and an iterative process or procedure, but I did not see any in the current manuscript.

The literature review involved a variety of materials and fabrication methods, where different methods may yield different side-effects on the final parts of the lattice cells. However, in the presented method, the material is fixed at PA12, with a JetFusion 3D printer. The main novelty lies in the lattice configuration, if I understood correctly, where the thickness of the component trusses is controlled by different math functions. In such a case, I would suggest enriching the related literature on the mechanical tests on lattice structures.

In conjunction with the above question, how would the authors justify that their presented method is universally applicable to all materials categories, including polymers and metal/alloy, for instance? From my understanding, the plastic nature of these different types of materials inherently exhibits different collapse patterns subjected to compression loads.

The numerical analysis employed a compression load with a loading speed of 1000mm/s, which is not typically seen in real-world compression tests. In fact, the physical tests carried out by the authors also used an alternative loading speed (1mm/s) due to the limit of the testing machine. This contributes significantly to the error seen between the computed results and measured data curves. I think the authors also noticed this. However, I was wondering how the authors could justify that, except for the initial loading period, the rest of the compression behaviors between the simulation and the experiments could be comparable. I would doubt that the simulated loading condition was totally different from the physical experiments, unless the authors provide a convincing argument.

In addition to the points mentioned above, I observe a discrepancy in the collapse patterns between the simulations and the experiments (refer to Figures 8 and 9). How do the authors plan to justify this inconsistency? I perceive this as unfavorable evidence regarding the validation of the numerical simulation.

In the conclusion, the authors suggested that simulation could be improved by considering different unit cell types, relative densities, and material options. I would suggest them to continue their current work and at least include one or more “future work” together with their current results. Otherwise, the novelty of the method could not be supported firmly, only by comparing the local density variations controlled by three math functions. In other words, I also doubt the applicability of this method when it comes to different lattice configurations, different materials, etc.

 

In addition, please consider refine the manuscript with the following suggestions:

In lines 199-201, the mention of the specimen's construction direction prompts the suggestion to include a visual representation, such as a diagram or image, illustrating the specimen's construction direction and the force application during experiments. This addition would enhance the clarity of the experimental setup and facilitate a better understanding for readers.

In line 266, please provide justification for constructing three mathematical functions resembling the patterns presented in EQNs 1, 2, and 3.

In Section 2.4, it is recommended to supplement the physical testing with relevant photographs, including images of the specimens. This addition would help showcase the quality of specimen preparation and provide a visual context for the experimental procedures.

Concerning the data "1273N" mentioned in line 320, there appears to be a potential discrepancy when compared to the stress-strain curve depicted in Figure 5(a), where the upper scale of y-axis is 1200N.

Comments on the Quality of English Language

I think it is fine.

Author Response

Please see the attachment

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

N/A

Reviewer 3 Report

Comments and Suggestions for Authors

The authors have addressed my concerns.

Comments on the Quality of English Language

Language quality is fine.