Introduction to Macroscopic Optimal Design in the Mechanics of Composite Materials and Structures

Round 1

Reviewer 1 Report

The reviewer thanks the authors for the submission and the Editor for the invitation to review it. The reviewer feels that the paper is interesting, and it is within in the scope of the Journal, but please see the additional comments:

In the Abstract:

• On the first line of abstract, please, add another coma after the word priori, or remove the coma that is after appropriate
• Between lines 8-10: please improve the statement: the word properly appears too many times! Author can say for instance: Composite materials can be designed in a fashion away to meet some specific properties requirements, nevertheless, it is necessary to be careful about the orientation, placement and sizes of different types of reinforcement.
• In line 12, please replace kinematical by kinematic.

In section 1:

• In line 19, in the phrase: “The problems discussed in the paper concern with micro-composites” there is a lack of a verb! Please correct this and other similar write errors. The paragraph that starts at line 21 can be joined to the first paragraph.
• In line 23 and in line 38, it is important to give some book references. Moreover, in line 40-41, when authors say “The values of the material coefficients depend on the reference coordinate” it is important to clarify that the material coefficient matrix is a fourth order tensor and, therefore, their coefficients follow tensor transformation rules. Please add some book reference at line 45. There is a great number of books related with composite materials.
• In line 53, author can be more specific and say that the number of independent material parameters reduces from 81 to 9 engineering constants.

In section 2:

• In line 57, remove the first two words, “In fact”, there is no need for this statement!
• In lines 60-62, the main idea is that inhomogeneous composite materials can be macroscopically idealized as homogeneous and continuum. Nevertheless, in line 62 authors say that “Such idealisation can be realised over a representative sample (cell) of the composite material”, the term cell should be removed. In fact the word cell is used to identify the microstructure idealisation. For instance author can read the work of Neto et al. : “The homogenization theory is a mechanics based modelling scheme that transforms a body made with heterogeneous material into a constitutively equivalent body of homogeneous material. The transformation model is built on the base of the material microstructure, along with the relevant physical laws, enabling the definition of a set of effective properties for the equivalent homogeneous material.” (Maria Augusta Neto, Yu, Tang, & Leal, 2010)

Neto, M.A., Amaro, A., Luis, R., Cirne, J., & Leal, R. (2015). Engineering computation of structures: The finite element method. In Engineering Computation of Structures: The Finite Element Method. https://doi.org/10.1007/978-3-319-17710-6

Neto, Maria Augusta, Yu, W., Tang, T., & Leal, R. (2010). Analysis and optimization of heterogeneous materials using the variational asymptotic method for unit cell homogenization. Composite Structures, 92(12), 2946–2954. https://doi.org/10.1016/j.compstruct.2010.05.006

 

• In lines 84 and 88, please, give reference to these equations. Author should give more information about the x^loc, is a vector?
• All equations should be referenced as Eq., hence in line 91, the numbers (4) and (7) should have associated the word equation!
• In line 97, explain what the meaning of concentration matrices is. Moreover, in line 105, give more information about the definition of concentration matrices.
• In line 109, the designation of stiffness matrix is not appropriated, it should be material stiffness matrix.
• The space between lines 115 and 117 should be removed.
• In line 131, author says that Figure 4 shows a typical two-dimensional woven textile, the textile is a three-dimensional structure, but some simplifications modelling assumptions will allow to be considered as a two-dimensional structure. Hence, author should be more specific.
• In line 159, author should give more refences related with this kind of materials. The number of published works related with this issue is huge!
• The picture of figure 5 should be improved, for instance author can give different colours to the fiber and the matrix.
• Figure 6 should not be placed at the begin of section 2.2.
• In line 182, authors should be careful about the statement. The unidirectional lamina or laminate can be isotropic in one plane, meaning that in this plane the material has the same material properties on both directions and, therefore, the material stiffness matrix can be described by five independent elastic constants, instead of nine for fully orthotropic.
• Once more, it is necessary to give reference to equations (9) and (10).
• The statement of line 206 is not appropriated, in fact the evaluation of the transverse shear stresses can be done using the Reissner-Mindlin theory (or first order shear theory) and not the Kirchhoff theory.
• The text between lines 209-211 should be improved.
• The number of equation (14) should placed at the middle of all equations and it is important to add some references!
• The equations that are placed in section 2.3 (equations 17-20) relates the resultant forces/moment/curvatures with the membrane/generalized curvatures etc. hence a more careful presentation of this equations should be given, please read chapter 8 of Neto et al., 2015 (M.A. Neto, Amaro, Luis, Cirne, & Leal, 2015)

Neto, M.A., Amaro, A., Luis, R., Cirne, J., & Leal, R. (2015). Engineering computation of structures: The finite element method. In Engineering Computation of Structures: The Finite Element Method. https://doi.org/10.1007/978-3-319-17710-6

 

In section 3:

• In equation 27 it is necessary to use an integral over the volume, i.e. omega. So please correct this equation.
• In line 316, please verify where is the Lagrangian function in equation (25)!
• In lines 320-322 explain better what the integration domain is in 1-D, 2-D or 3-D nalysis.
• Figure 8 should not be placed in sub-section 3.1.
• The statement placed between lines 335-337 is not appropriated to define a shell structure, please refer for instance the Bathe K. J. book, Finite Element Procedure, 1996.
• The statement “… is a limit case…” is not appropriated, say for instance that is a special case.
• In line 347, when author speak about layerwise theory, some reference should be given to help the interested read.
• Reference to equation (31) should be added.
• In the reviewer opinion, this section should be presented just before section 2.3, because it gives the information that is needed to evaluate the generalized forces.
• In line 395, the reference of Muc is not correct.
• More information should be given about the notation used in equation (36).
• Some additional references should be given on section 4

Author Response

I corrected the text, figures and references

Reviewer 2 Report

There is need for an introduction to introduce why this work is important for industry, which are the challenges, what other was made in order to solve these challenges and what novel bring this work.

Otherwise section 1 presents some equations but not sure if is yours or from literature

It is possible to provides details of size of sample presented in Figures 4

I am not sure why you discuss 3D models (in page 6) while above was presented only 2D model

Please provide details of model in Figure 5..Also not clear why are the boundary condition in Figure 5

There is need to provide a case study to demonstrate the validity of this approach

Also a section of discussion and conclusion is required

How was determined the diagram from 9

The state of art is very brief and the references are quite old, therefore it is required some novel references

Author Response

I corrected the text, figures and references

Reviewer 3 Report

Given below are my comments to improvise upon the quality of the manuscript.

1. The manuscript is certainly an interesting read but gives an impression of more of a book chapter rather than a scientific paper. The manuscript desires some restructuring. For instance: The first section must be the introduction, highlighting the state of the art with work done in this paper.
2. I am unable to identify what is the goal of your work and what is the novelty involved?
3. Which type of micro-composites are you referring here (line 19). Please be specific.
4. Line 38: fur-ther or further.
5. Is figure 2 made by you or copied from elsewhere? Please mention citations necessary.
6. For all the equations used in the work, it is worth mentioning which of them are fundamental equations, which of them are adapted from other works and which of them are developed by the author.
7. Which optimization problem are you referring here (line 113)?
8. Which all models? (line 143-144)
9. Line 199: stress-stress or stress-strain?
10. Line 206: Kirch-hoff or Kirchoff?
11. Line 263: what does this mean ‘X denotes A or B or D or H’? Kindly explain.
12. Line 314: Which is the Heaviside’s function? 1(z-zj) or 1(z-zj+1) or both collectively?
13. Line 395: What is this referencing style ‘Muc [1.1]’? Do you mean section 1.1 from this paper, which by the way is not there in the paper?

Author Response

I corrected the text, figures and references

Round 2

Reviewer 1 Report

The number of references were significantly increased, but the self-citation is too huge.

In section 1:

• In line 26, the phrase: “The idea of composite materials arose from the need to combine different materials in order to overcome the shortcomings of this one, whose other properties are not useful to us.” Please improve this phrase, for instance: The idea of composite materials arose from the need to combine different materials in order to overcome the shortcomings of each one of them.
• In the second paragraph, authors should give references of published works wherein is possible to confirm that composites show heir mechanical characteristics! Moreover, this paragraph does not have correct punctuation.

In section 2:

• In line 77, improve the statement: “So far, human needs have been met by designing and producing constructions for which material has been selected.”
• In line 82, replace “…at present…” by nowadays
• In line 91, there is a reference to figure 1.1a, but the number of figure is 1 and there is no a) or b) in that Figure.
• In line 98-99, does not make sense the phrase: ”Usually, we intend to allow the tank to carry high pressures.” If author wants speak about high pressure tanks, then he should start the phrase introduction the issue as one possible application of designing materials.
• In Line 115, once more, the figure number is not correct.
• the idea between lines 118-122, needs to be careful review or removed.
• In line 125, please remove “…in order…”.
• In line 131, the number of Figure is not correct.
• Line 136, correct just after interactions.
• In line 187 there is a reference to figure 3, but the figure appears previously to this reference.
• In line 197, author write “in this book”, it should be in this work.

 

In Section 4

• The statement of line 405-406 is not appropriated, in fact the evaluation of the transverse shear stresses can be done using the Reissner-Mindlin theory (or first order shear theory) and not the Kirchhoff theory. Moreover, G13 and G23 are shear modulus.

Author Response

The corrections in the text are written in red

Author Response File: Author Response.docx

Reviewer 2 Report

.

Author Response

I corrected the text

Reviewer 3 Report

Please draft the paper again and resubmit. The author has not provided a detailed response to the comments I gave him the last time.

Author Response

The corrections in the text are written in green

Author Response File: Author Response.docx

Round 3

Reviewer 3 Report

Thank you for providing a response to my comments