Effect of Two-Dimensional Re-Entrant Honeycomb Configuration on Elastoplastic Performance of Perforated Steel Plate

Round 1

Reviewer 1 Report

I reviewed the original version of this resubmitted work. The original submission is applsci-741365 (see my report there). The authors have much extended their knowledge what results in essential improvement of their paper. They took into account almost all my comments except one. For this reason, I again pay attention to that comment. It would be good if the authors could respond to it either presenting expanded studies in this paper or referencing to a future research.

The following comment has been ignored by the authors of the reviewed paper:
“Did the authors try to analyze qualitatively/quantitatively the size-dependence of the effects they study? I mean, what happens (qualitatively/quantitatively) when the length of the perforated area is less/more than L=76mm ?”

I must add that the authors additionally examined the dependence of the Poisson's ratio on the length of the sample but they considered only the length of the solid area. In contrast, I had in mind the perforated area, as it is written in my original comments (see above). Namely, what happens if we increase or decrease the number of re-entrant honeycomb unit cells. Now it's 5x4, what will happen for 5x6 or 5x8? This size effect can be very important, see e.g. the paper by J.N.Grima and co-workers [R. Gatt, et al., phys. stat. sol. (b) 251, No. 2, 321–327 (2014)]

I think after responding to the above comment and correcting minor remarks below, this manuscript should be published in Applied Sciences.

Minor remarks
Line 36: “In the past decades, Since Lakes [7] and Evans [6] found the early forms …” should be corrected.
Line 40-43: The following text “Well-known planar structures with chiral [11] and rotation [12] behaviors were studied. Various materials [13] and simulations [14] of auxetics have been investigated.” could be corrected to “Well-known planar structures with chiral [11] and rotation [12] auxetic behaviors were studied. Simulations of auxetic materials [13], auxetic structures [14], auxetic two-dimensional hard body systems [K.V. Tretiakov et al., phys. stat. sol. (b) 244, No. 3, 1038–1046 (2007)], auxetic nanocomposite models in two dimensions [M. Bilski, et al., phys. stat. sol. (b) 253, No. 7, 1318–1323 (2016)] and in three dimensions [P.M. Piglowski, et al., Phys. Status Solidi RRL 10, No. 7, 566–569 (2016)],and auxetic metamaterials [V.H. Ho, et al., phys. stat. sol. (b) 253, No. 7, 1303–1309 (2016)] have been performed.”

Author Response

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Reviewer 2 Report

Generally, the paper is well written and the ideas presented by the Authors are quite clear. Neverthless, a sentence like (cit.) "Three-dimensional FE models using solid elements were established in ABAQUS" may suggest that the Authors have implemented some kind of new finite element in this system to model auxetic material. It should be reminded that the system ABAQUS offers some constitutive relations corresponding porous metal plasticity options, for instance. 

This paper is specifically about mechanics of materials so that it fits the best other journal by MDPI, namely "Materials". The fundamental problem with this work is that it includes some specific equations only without solid presentation of the entire numerical model. Equation 1 brings no new knowledge, equation 2 is well known, while the third one is incomplete because dD[ini] looks like a part of some derivative as D[ini] is some physical quantity. The overview of the literature and basic ideas available in this literature is incomplete - one may apply here some homogenization method to complete this study, look at M. Kaminski, B.A. Schrefler, Probabilistic effective characteristics of cables for superconducting coils. Comput. Meth. Appl. Mech. Engrg. 188(1): 1-16, 2000. 

Author Response

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Reviewer 3 Report

A better explanation of different cracking paths in experiment and simulation (line 272 "Due to the randomness of cracking in nature... ") would be appreciated. Randomness could be proven with more specimens of same sort producing different cracks and only some comparable to simulation. On figure 8 there is some similarity on a and b while other results disagree. There might be some problem with material or machining of specimens or some setting in simulation need tuning. Also, crack paths should be presented more clearly on experiments figures (figure 8, first row).

In my opinion, it would be nicer if the results of the numerical analysis of different specimens would be shown at the same scale. In that way, only one legend per figure will suffice and results could be compared visually. This applies to figures 8, 10, 11, 12, 15, 16, 17, 19, 20, 21 and 23.

Author Response

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Round 2

Reviewer 2 Report

Equation (3) is still wrong - the left hand side includes dD[ini], while the comments around this equation do not include any comments on this particular parameter. Most probably it should be some derivative but this remains unclear and guessing is not a role of the reviewer. This paper does not include too many equations, so this is not a big problem to check them all. 

An information about the FEM discretization is still incomplete - the Authors postponed an information about the finite elements total number. It remarkably affects the correlation in-between experiment and numerical analysis; some sentence about numerical error should be also given, see: M. Kamiński, D. Sokołowski, Dual probabilistic homogenization of the rubber-based composite with random carbon black particle reinforcement. Compos. Struct. 140: 783-797, 2016.

A correlation has been completely left undefined in this paper, while many papers treat about the similar approach, see: M. Kamiński, P. Świta, Structural stability and reliability of the underground steel tanks with the Stochastic Finite Element Method. Arch. Civ. & Mech. Engrg. 15(2): 593-602, 2015.

Author Response

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Author Response File: Author Response.docx