Computation of Effective Elastic Properties Using a Three-Dimensional Semi-Analytical Approach for Transversely Isotropic Nanocomposites

Round 1

Reviewer 1 Report

The scope of this article is the estimation of the effective elastic properties of periodic reinforced nanocomposites. A three-dimensional semi-analytical approach (SAFEM-3D) is implemented as a combination of the asymptotic homogenization method and the finite element method. There is no experimental benchmark reported.

Comparisons with some methods reported in the literature are presented. But, the tables presented do not show any originality since there is no detailed discussion on novelty of the work, errors, and accuracies overall.

This journal is focused on applied sciences. But majority of this article is focused on deep derivations and mathematics. The core of the work could stay inside the article. But, the derivations should be given in appendix.

The work performed in this article is a better fit for the Journal of Composites Science. What is the reason of submitting this work to Applied Sciences?

There is no single paper cited from Applied Sciences in References. Why?

Author Response

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Reviewer 2 Report

This paper has been dedicated to present a semi-analytical finite element method to obtain the elastic properties of nsnocomposites reinforced with aligned and randomly distributed CNT fibers. The asymptotic homogenization method (AHM) and finite element method were employed for this purpose. Some numerical study has been implemented to investigate the effects of inclusion geometrical shape, volume fraction and inclusion length on the effective elastic properties of CNT based nanocomposites materials. The subject of the research is interesting. However, the manuscript requires a major revision according the following comments:  

1. The authors have stated that they have used finite element method for their study. There is question. Did you discretize the RVE? If yes, did you use solid element? Please clarify this subject in the abstract.
2. In title, the authors have stated that they have studied nanocomposites. This is general while in the abstract, they have said that only CNT reinforced composites have been analyzed. Please clarify this issue.
3. The keyword of SAFEM should be employed within the abstract. It is better to use it after “semi-analytical finite element method” in the first statement of the abstract.
4. The literature review of the paper is poor. There are many articles in which the elastic properties of the CNT based hybrid composite material has been studied. Especially, using the homogenization approaches for several three-phases materials can be useful for this part.
5. The authors should provide a flowchart in which the details of each step should be defined. Accordingly, the steps of calculating the elastic modulus should be presented by stating the equations used in each step in detail.
6. Some of the presented equations are not original. The reference of them should be discussed.
7. The conclusion should be improved. Some new and original results which have been only achieved from this study should be presented in this part.

Author Response

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Reviewer 3 Report

I enjoyed reading this paper and found the results interesting. The introduction is clear and frames the need for this research well. The literature review is clear. The methods used in the paper are semi-analytic finite element method. The methods are appropriate for the work and clearly described in 79 equations. The analysis of the results is sufficient. The authors report the outcomes and provide analysis of the results. Although there is no separate discussion section the article has the correct structure. English is generally correct, minor spell check required. Reference to figures and tables has been done correctly. The figures and tables are clear. To conclude: the article is interesting and valuable. It may be published in its present form.

Author Response

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Round 2

Reviewer 1 Report

All the questions were answered perfectly. Appreciated.

Author Response

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Reviewer 2 Report

The authors have attempted to respond to all comments as well. However, some more major clarifications are required:  

1. The authors should provide the model of RVE which has been discretized in ANSYS using Solid187 element.
2. The authors should explain how to reach the adequate number of elements which are required for discretizing the RVE in ANSYS.
3. The volume fraction of particles distributed in the RVE should be presented.
4. The authors should clarify which model of figure 1 has been studied in this paper. If all models have been investigated, the authors should provide a separate figure for each case in which the discretization of particle and base matrix should be depicted.
5. The authors should prove that the created RVE satisfies the two following conditions: (1) periodic boundaries, (2) intersection of particles.
6. The maximum value of volume fraction of particles that the authors could develop in this study should be clarified.
7. The authors should also explain how they generate the RVE and randomly distribute the particles throughout the base matrix. The procedure of RVE generation should be also discussed in detail.  

Author Response

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Round 3

Reviewer 2 Report

The reviewer thanks the authors to consider all comments as well in the revised version of the manuscript.