Additive Manufacturing, Numerical and Experimental Analyses for Pentamode Metamaterials
, Efstathios E. Theotokoglou 1,*, Dimitrios Dragatogiannis 2, Dimitrios Karalekas 3 and Constantina Matsika-Klossa 3
Zhifei Deng
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThis work by Lymperopoulos and Theotokoglou presented a relatively complete characterization on Penatmode lattice designs via experimental and computational methods. They focused on the experimental comparison of two designs with different parameters of the bicone beams, and later their investigation extended to parametric designs in computational modeling by including more variations in parameters. However, the reviewer recommends further edits and analysis on this work before being considered as a publication in Infractures. Please find the reviewer’s comments below in details:
Major comments
1.- The authors should consider re-paragraphing the discussion, introduction, and abstract to highlight their new contributions in this field from previous research.
First of all, the discussion in this work is not well supported. For instance, lines 322-324 in the script claimed ductile fracture behavior in 1st batch sample in comparison to the brittle fracture in 2nd batch sample. However, the authors did not explain the reasons to explain such differences. Similarly, from line 343-345, the authors found that the maximum stress in 2nd batch had lower values than the 1st batch without giving detailed explanation; this sentence also provided contradictory claim from line 346-347 “consequently the final strength of the 2nd batch of specimens was higher than that of the 1st batch”.
Second, the authors should provide a better introduction of the background and previous works in this field in the introduction section. For instance, from line 333-336, the authors claimed one new contribution in this work to be providing the first study on the fracture behaviors of Penatmode metamaterials. To better highlight this contribution, the authors should have a corresponding paragraph in introduction to summarize the works and references on these aspects. Similarly, the authors found that d diameter was a significant factor to the bulk strength, which is a similar conclusion in other previous studies (lines 327,328 in the script). It is recommended to have a paragraph to summarize some important prior works related to the present work to show the reader about the current knowledge and process about Penatmode metamaterials. In lines 61-66, the authors explained the tension/compression to test Pentamodes metamaterials, but ideally, the readers expect to read on the typical results of the properties and behaviors under these loadings.
Third, the abstract (lines 12-19) in this work is not well structured. It includes the workflow but does not highlight the new contributions to this field. Please consider paragraphing this section.
2.- The authors provided contradictory information about resin materials used in 3D printing, please check and correct.
In section 2.3 and figure 4, “The tough resin is the resin having cured with ultraviolet (UV) process, while the standard resin is without any curing” vs. “It is observed that after the curing process, the resin had increased ultimate strength, but brittle behaviour.” In the figure, it is the standard resin that has higher ultimate strength.
3.- Please provide more details and explanation of the results?
a) How many experiments did the author perform in each batch of samples? In the comparative plot between experimental and computational results (Figs. 7,8), only one experimental curve is provided. Is it sufficient enough to represent the actual mechanical response? Considering the printed structures were cured, so brittle fracture response is expected, it is recommended to have enough experiments to make sure the stochastic nature of brittle solids won’t affect the conclusions
b) In Fig. 7,8, the authors provided four computational curves, small vs. large displacement, and linear vs. bilinear material. Please add the corresponding description in the Method section 2.5. Also, please indicate which computational method is better and why.
3) Please provide evidence, explanation, or reference to support the claims. In line 197-198, “deviations are observed up to 1.5 mm between the numerical and experimental results which may be due to the prestress effect which does not appear for the 1st batch of specimens, (Fig. 7).” How did the prestress occur in batch 2 sample but not in batch 1 sample? In addition, the experimental curve of batch 2 sample in figure 8 does not start from 0, please provide explanation.
4) The authors provide different calculations of the modulus as an important index of structural properties. Please check and provide the definition of the different moduli and explain why the equation is preferred. In line 286, “the Young modulus is also calculated under different vertical displacement (Figs. 14, 15)”, based on this description, the modulus obtained at different depth is not “Young’s modulus” (elastic modulus obtained at the elastic stage of deformation), please check.
Minor comments:
1.-Please provide clear definition of the design parameters in the Pentamodes metamaterials design.
a) –Explain or define d, D, and a parameters in the text (section 2.1).
b) –Please be consistent. Sometimes the authors use α instead of a to represent the unit cell size in the design, e.g., table 1 and line 98.
2.-Figure 2 shows the conceptual designs of the two batches, since the authors only modified the d and D dimensions, it would be better to align these two CAD models at the same angle.
The reviewer mistakenly thought you also changed the orientations of the individual unit in your design but could not find a corresponding analysis.
3.-The authors might consider providing concise and accurate information only in their work.
a) –The photos of the 3D printer in Figure 3 are not necessary.
b) –Line 64-66, the authors explained how tension and compression is applied on the printed specimen, which is not necessary.
Comments on the Quality of English LanguageThe English writing in the work is easy to understand, but minor editing is needed to provide a more accurate and precise draft.
Author Response
Please see the attachment
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsPeer Review report #1
Recommendation: Major Revision
Comments to Authors
Manuscript Number: infrastructures-3134128
Title: Additive Manufacturing, Numerical and Experimental Analyses for Pentamode Metamaterials
Authors: Panagiotis N. Lymperopoulos, Efstathios E. Theotokoglou, Dimitrios Dragatogiannis, Dimitrios Karalekas, Constantina Matsika-Klossa
Overview and general recommendations/remarks:
In this manuscript the authors realize Pentamode lattice structures using 3D printing and tested them. They then performed computational analyses to evaluate bulk strength and compared different Pentamode geometries by means force-displacements curves. Experimental results were compared with numerical simulations in the scenario in which the lattice structure is subjected to compression.
The topic is very interesting and worth addressing, also if it partially fit scope of the Journal.
Language and writing, in terms of syntax and grammar, are sufficiently fluent and clear.
The introduction summarizes some strategies followed in the literature to address the mechanical characterization of lattices structures and metamaterials. The cited references are appropriate, although much more could be said in the field of lattice and metamaterials structures to have a comprehensive introduction.
Overall, the paper addresses a relatively already-seen topic, and to garner interest in the scientific community, it should discuss/cover some aspects that are less conventional and more interesting today in the field of lattice structures.
There are several major points that need to be addressed to improve the quality, the interest and the comprehensiveness of this paper:
1) The quality of all figures needs to be improved as they appear very pixelated.
2) At the end of the manuscript, the sections "Funding," "Data Availability Statement," "Acknowledgments," "Conflicts of Interest," and "Appendix A" should be either completed or removed, as they currently display the default template text.
3) In Section 2.2, the authors mention using the parametric CAD software “PTC Creo Parametric,” known for its powerful implicit topological modelling capabilities. The Reviewer requests the authors to justify this choice to the reader: Could the work have been done using other CAD software with B-REP modelling? Or is implicit modelling software is strictly necessary?
4) Sections 2.2 and subsequent sections lack printing parameters. The Reviewer asks the authors to include this information as it could be very useful to the readers.
5) In Section 2.3, the authors state that they used Clear V4 resin (tough type) for printing. The reviewer requests justification for this choice: Why choose this resin that requires UV post-processing? Does it aid the experimentation, or was it simply available in the lab? The reviewer inquires because the mechanical properties of this resin, in terms of Young's modulus and yield stress, are comparable to classic materials like ABS or PLA. However, it exhibits extraordinary ductility with an ultimate strain of 30%. This behavior needs to be adequately modelled in a FEM environment to compare experimentation with numerical modelling (in fact the modelling section the authors chose the bilinear model, that do not catch the entire behaviour of this material). This complicates the choice of material model since it does not behave as a hyperelastic material but rather tends towards the behavior of “damaged” materials (such as a Voce model).
6) In Section 2.4, the authors describe the experimental setup, which has several aspects that need further specification:
6a) The authors mention conducting the compression test using "grips," but it is unclear what is meant, as the immages in Figure 5 do not capture the whole experimental setup. The Reviewer asks the authors to modify the images in Figure 5 to provide a broader overview. Additionally, they should clarify what the "grips" are: Are they compression plates? If so, do they have a spherical hinge to maintain load centering during deformation?
6b) The imposed displacement is applied with a strain rate of 10mm/min, which is not low enough to be considered static. What strain-rate was used for the stress-strain curve in Figure 4? This aspect is crucial because the nature of the material could lead to viscoelasticity issues, such as stress relaxation under imposed deformation. This would justify applying such a high strain rate but would require recalculating the curve in Figure 4, and thus the mechanical parameters of the material, at the same deformation speed.
7) In Section 2.5, the authors state that they used the BEAM189 element of Ansys Classic (APDL). This element is isoparametric with quadratic shape functions, making it generally linear (in geometry) only in the natural (mapped) reference, but not in the physical one. The Reviewer suggests removing the term "linear" as it is inappropriate.
8) In the remaining sections, the authors discuss the results of the numerical modelling by comparing it with experimental data in terms of force-displacement curves. The Reviewer asks the authors to address the following points:
8a) In the interconnection regions between elements, beam modelling fails as it is one-dimensional and can at most represent a plane stress state. A solid modelling using quadratic elements SOLID186 must be performed for at least one case (or better, for all the cases) and compared with beam modelling in terms of peak stress and stiffness.
8b) The force-displacements results obtained by varying the geometries are interesting. However, it would be even more insightful to compare the force-displacement curves associated to different geometries relative to the weight of the structures. The Reviewer recommend the authors refer to recent publications [1,2], where this approach has been employed to reveal how the mechanical strength to weight ratio varies. It would be crucial for the authors to conduct a similar comparison to understand the trend in mechanical behavior with changing geometry. They might discover that less is better, or perhaps not?
8c) The Reviewer recommends discussing, either for future work or as a new idea for readers, the effect of modifying the fillet radius at the connections between beam elements. This aspect has been recently considered in publications [1,2], showing it significantly improves the mechanical response of lattice structures. Since Pentamodes are lattice structures with the weak point at the element connections, as evident from Figures 11 in this manuscript, strengthening their mechanical response with an appropriate fillet shape would be crucial to discuss and possibly work on in the future.
Addressing the eight points outlined above will improve the clarity, depth, and relevance of the manuscript, making it more useful for the readers and the experts in the field.
Reviewer proposes a major revision and defers the publication decision pending the authors' response and modifications according to these remarks.
REFERENCES CITED IN THIS REVIEW REPORT
[1] The Beneficial Effect of a TPMS-Based Fillet Shape on the Mechanical Strength of Metal Cubic Lattice Structures. Materials 2024, 17(7), 1553; https://doi.org/10.3390/ma17071553
[2] The role of node fillet, unit-cell size and strut orientation on the fatigue strength of Ti-6Al-4V lattice materials additively manufactured via laser powder bed fusion. Int. J. Fatigue 2021, 142, 105946. https://doi.org/10.1016/j.ijfatigue.2020.105946
Author Response
Please see the attachment
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsThis revised work by the authors showed improvements based on the reviewer’s comments. In general, the authors provided improvements to the corresponding comments, but additional minor edits are necessary. Following are the further comments on the revised manuscript based on the previous comments (highlighted in blue fonts).
Comments for author File: Comments.pdf
Author Response
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Author Response File: 
Author Response.docx
Reviewer 2 Report
Comments and Suggestions for AuthorsPeer Review report #2
Recommendation: Accepted
Comments to Authors
Manuscript Number: infrastructures-3134128
Title: Additive Manufacturing, Numerical and Experimental Analyses for Pentamode Metamaterials
Authors: Panagiotis N. Lymperopoulos, Efstathios E. Theotokoglou, Dimitrios Dragatogiannis, Dimitrios Karalekas, Constantina Matsika-Klossa
Second Review:
The authors have addressed some, but not all, of the Reviewer's comments. Several points raised by the Reviewer have been left unresolved and, according to the authors, will be addressed in future research and publications. I hope this will indeed be done, and that this paper will pave the way for further lines of inquiry.
However, the manuscript overall is presented in an improved form compared to its initial state.
Its strength lies in the experimental tests, which are interest and undoubtedly enrich the scientific literature related to Pentamode Metamaterials.
For this reason, the Reviewer consider the manuscript to be sufficient for acceptance for publication on Infrastructures.
Author Response
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Author Response File: Author Response.docx
