On Symmetry Properties of Tensors for Electromagnetic Deformable Solids

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In this paper, we study the symmetry properties that arise in models describing the interactions between electromagnetic fields and mechanical deformations in solids. The study is a generalization of the known facts of the symmetry of the stress tensor in classical continuum mechanics to the case of bodies with electromagnetic fields changing in real time.

However, there are the following issues that should be clarified:

1. Need to expand the abstract in the paper and cite more results from this study.
2. The assumption of refutation of currents and charges (J and q) is not sufficiently substantiated. In what cases is this assumption justified, and in what cases is it not? How does this affect the accuracy of the results obtained?
3. A more detailed explanation of the physical meaning of the obtained symmetry conditions is necessary. What are the practical consequences of these conditions for the study and analysis of electromagnetic deformable bodies?
4. The proposed approach is discussed with a dissipative and heat-conducting medium, but other important factors such as nonlinear properties of materials, hysteresis, etc. are not taken into account. It is necessary to discuss the limitations of the proposed model and the possibility of its extension to take these factors into account.
5. It is necessary to more clearly define the designations of various tensors, vectors, and operators to facilitate the understanding of mathematical calculations.
6. In the conclusion, give examples and possibilities of practical application of the findings of this paper.

Author Response

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Reviewer 2 Report

Comments and Suggestions for Authors

The following corrections or additions can be made for the publication of the article:

- Nomenclature should be added to ensure that symbols and variables are defined and understood more clearly.

- The article is highly theoretical and sufficient information and references are not provided regarding the experimental verification or practical application of the derived symmetry conditions. In order to verify the theoretical findings obtained in the study and to show the practical applications of the theoretical results, verification with experimental studies should be provided.

- The innovative theoretical approach and comprehensive analysis presented in the article are valuable; however, broader applicability will be demonstrated with experimental verification.

- It would be appropriate to provide simplified explanations or appendixes for easier understanding of the complex mathematical derivations in the presented theoretical approach and for the results to be used in applications.

- Focusing on the effects in certain symmetry conditions may limit the generalization of the obtained results to other deformable solids or different electromagnetic interactions. In order to increase the generalization of the findings in the study, the applicability of the derived symmetry conditions to other deformable solids and different electromagnetic interactions should be discussed. 

Author Response

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Reviewer 3 Report

Comments and Suggestions for Authors

In this manuscript, the authors investigate symmetry properties in the modeling of magneto-/electro-mechanical interactions in deformable solids. It presents a rigorous mathematical formulation of balance equations and thermodynamic restrictions, deriving symmetry conditions for the total stress tensor. The work is mathematically well-structured and -presented, contributing to the field of continuum mechanics and electromagnetic interactions in solids. 

 

Major points:

 

1. The introduction does not make it clear why the contribution of this work is important. Indeed, they simply said it is just a "revisit" instead of being something new.

 

2. The entropic balance used in this work is only used in the near-to-equilibrium regime, where the equilibrium quantities as temperature are defined on time. This should be emphasized for clarity. Probably this would affect the interaction of the system with the electromagnetic field, which should be checked in the hypothesis of the problem as well.

 

3. The paper can emphasize that its discoveries help in modeling new systems by choosing constitutive tensors that respect the symmetry found, which I think it is a problem for experimentalists when dealing with a particular material.

 

Minor points:

 

1. In line 90 \rho_R is defined. Is it used afterward?

Author Response

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Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Overall, the authors have done a good job of improving the paper. The authors have refined the abstract and introduction, better explaining the role of symmetry in electromagnetic solids, and have added relevant references. Electric current and charge density have been added to the balance equations.
A new section on positive and negative magnetostriction models has been added. The behavior of magnets depending on the orientation of the magnetic field is described in detail.
Although the authors have added a section on nonlinear properties, it would have been useful to develop this topic in more detail, perhaps with specific examples or experimental data illustrating the effect of symmetry on material properties.
A more detailed discussion of the effect of the added electric current and charge density on the symmetry condition is needed.
It is necessary to clarify what they mean by “the non-monotone character of f”, which is claimed to change the sign of magnetostriction.

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The authors provided all the modifications I asked for previously. I recommend the publication now.

Author Response

Comments: The authors provided all the modifications I asked for previously. I recommend the publication now.

Response: We thank the reviewer for his stimulating comments.