Exploring the Limits of Euler–Bernoulli Theory in Micromechanics

Round 1

Reviewer 1 Report

Seems the technology has been summarized in "H. Altenbach et al. (eds.), Generalized Continua as Models for Materials, Advanced Structured Materials 22, DOI: 10.1007/978-3-642-36394-8_14,© Springer-Verlag Berlin Heidelberg 2013," The Limits of the Euler-Bernoulli Theory of micro-beam have been studied and also in Micro-Raman Spectroscopy for Strain Measurement included AFM. This article may need to propose a novel way or explore their variations in other research.

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Reviewer 2 Report

Manuscript axioms-1537579 compares experimental results obtained by the Raman microscopy and numerical results according to the Bernoulli-Euler theory. It shows that this theory can successfully be applied for simulations at the microscopic level.

My comments and questions are listed below.

 

• The abstract is somehow confusing. It claims that Bernoulli-Euler theory is superior to other simulation techniques, however no any comparison with the alternative solutions is provided in order to support this conclusion. The results presented in the manuscript only show that Bernoulli-Euler theory can successfully be used for the modeling of structural elements at the microscopic level. There is no any evidence that this method is better than other theories. Please reformulate the abstract and the end of the introduction chapter (lines 56, 57).
• Comment: The theory presented in Chapter 2.4 is superfluous. Expression (11) for a cantilever beam is known (in the mechanical community) even without solving the differential equation for the bending of a beam. One can directly write it from the diagram of moments. However, you can let this chapter, it is not wrong.
• The explanation of the Raman test (page 6, lines 202-208) should be extended. What are wave numbers? What is the role of the peak wave number?
• Is the text in lines 204-205 conform to the caption in Fig. 2?
• Expression (10) has to be explained better. Which kind of constant is 1,4001? Is it a material parameter?
• Where do you take material parameters listed in Table 2? Which literature did you use?
• The study has been performed for a single length of the beam. Do you have date for other sample sizes? How many experiments have been performed?

Author Response

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Reviewer 3 Report

 

1. AFM is underfined in the abstract.
2. section 2.4 can be shortened it is very well known and there is no need of detailing Bernoulli-Euler beam theory in this context.
3. line 171: "according to the literature". I don't agree that is given by the energy principle if you carry out the principle of virtual work for Bernoulli-Euler theory. Once again very well-known (please see Reddy, Energy Principle and Variational Methods in Applied Mechanics, 3rd Ed, 2017, Wiley; among others)
4. Table 1 is also well known it the solution of the "elastica" (see Timoshenko, Theory of Elasticity; among others)
5. which kind of fitting has been used in figure 3? least-squares linear interpolation?
6. figure 4 demonstrates that the trend is linear (which was obvious since the beginning) but the error between the experiment and the theory is not indicated. Please compute the relative error.
7. The authors say that they demonstrated the validity of the present problem also by considering other nonlocal theories (which are not presented and not compared). Such comparison must be done.
8. If the present results demonstrated the validity of classical Bernoulli-Euler theory is strongly dependent on the material microstructure. Since it has been demonstrated by others in the literature that when the microstructure is orthotetragonal cosserat (nonlocal) continua are equivalent to Cauchy continua, thus the present study does not sufficiently prove the initial statement given by the title.
9. It is suggested to check the literature because the authors seem not to know many of the vast literature on nonlocal microbeams by considering explicit and implicit non locality which are very different in modelling the structural behavior of nano-scaled structures.

Author Response

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Round 2

Reviewer 1 Report

Thanks to the author for replying to my comments. I suggest that the reply suggestions be briefly described in the text, which can emphasize the progress and differences of the paper compared with other papers.

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Reviewer 2 Report

Authors have introduced necessary comments as required. The paper is now ready for the publication.

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Reviewer 3 Report

After carefully checking the reply by the authors the following comments are provided

1. There is no need to report Euler-Bernoulli beam theory everybody knows about it. Remove section 2.4 and simplify the paper. There is no need to write unnecessary long articles if strictly not needed to. No reader in this context would ever need to check Euler-Bernoulli theory.
2. Citations about this topic are still limited considering the vast literature available.

Author Response

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Round 3

Reviewer 3 Report

manuscript has been improved according to the comments provided. therefore the manuscript should be accepted for publication