A Creep Model with a Real Structural Parameter for Deformable Solidsâ€
Round 1
Reviewer 1 Report
Comments for author File: 
Comments.pdf
Author Response
Hello, kindly find my answer in the attachment.
Author Response File: Author Response.pdf
Reviewer 2 Report
Author Response
For the nickel alloy that with the chemical composition in Table 1, how to obtain this material information? How to obtain the creep curves by measurement or prediction should be elaborated.
The material region name is "ЖС3". The chemical composition of that material is regulated by the governmental standard 1-90126 - 85. I haven't found an analog and just put it here from the standard. For this particular article I used creep curves from the source [10] because my goal was to demonstrate usage of uncommon creep constitutive equations. I added information about that in the proper place.
What is the motivation for determining the creep time or hours (e.g., 200 hours) ?
If we look through the creep curves presented in [10] all experiments were done for 100 hours. All experiments are taken place under several values of temperature in a range up to melting point, and several stresses in a range up to yield stress at a given temperature. These type of curves usually consist of two creep stages, so it's easy to use them in finding constants to power law of creep, and then use the simplest power law of steady creep in calculations. I took 200 hours to be sure that the steady state creep has already started and wanted to show that transient creep stress distribution would approach the steady curved form within that time.
Most of figures should be improved for better reading and providing the corresponding legends.
I have added detailed captions.
Figure 7 shows the Stress relaxation and dislocation growth due to creep. The related discussion and further analysis should be supplemented.
I will check if there exist such initial values of dislocation density that give decreasing of immobile density and increasing of creep strains. I can only say that it's increasing because of positive values of creep strain and stress in the constitutive law, although I understand that we should probably observe decrease in a relaxation mode.
The main results from fig. 2 to Fig. 6 should be further discussed.
Conclusions or summary should be reorganized point-to-point. Some key quantitative results should be pointed out in Summary.
I attempted to provide the discussion in summary in a more organized manner.
Reviewer 3 Report
Author Response
Dear reviewer,
thank you for reading my article. I will try to clarify some your comments.
"The work fininshed by the authors should be placed in the last paragraph. It is necessary to emphasize the current problems, and make it clear."
Sorry, it's not clear here which work I should place. My actual work was to show briefly that such model exists in the frame of theory of Dr. Greshnov [3], and where it comes from, how such model can be combined with government equations of classical type, and to demonstrate that this with this model one can obtain similar solution as in classical solution in creep mechanics book with additional data (real structure parameter time evolution) which can lead to estimation of structure evolution after finishing calculation of stress state.
"The first few equations need to be numbered."
6.5 of Rules for authors says that I'm not obliged to number all equations. The first equations were provided for the reader to get familiar with its origin. They provide no help to do the next step, namely to use constitutive equation of that kind in mechanics. So I prefer to keep in unnumbered. If a new theory emerges that predicts structure in relation to the strain state, and provides new creep model of creep, we expect that the logic of following numbered steps will be the same.
"It is necessary to compare with existing models to show its superiority."
I prefer not to talk about superiority much. From mechanical perspective the model with a constitutive equation that helps to neatly be substituted in a government equation on the one hand, and with perfect catch of rheology without underlying physics on the other hand will be always superior. My idea was to show how constitutive equations of physical kind can be considered with standard mechanics problems. The advantage of this approach is that the output also yields functions of the structural parameter change. If the data from the theory providing the model are accurate, the resulting solutions provide information about the structure's evolution during deformation. I mentioned this in the article.
Could you please be more specific about desired changes in introduction, equations, and format?
Round 2 comments.
Dear reviewer,
Thank you for careful reading of my work.
I understand the importance of providing context for readers who might lack familiarity with certain aspects of the subject matter. As you may understand, my article focuses on a specific aspect of integrating one field of knowledge into another, assuming a basic understanding of all major areas. The reader of my profile expects practical instructions and implementation examples, not a historical overview or a detailed dive into the fundamentals of each discipline separately. To address your concerns regarding comprehensive introduction, I have supplemented the introduction with comments on the most key works in both fields and reworked the abstract, without overloading the material with historical digressions. My goal was to provide a specific methodology for integrating fields, not an in-depth review of existing work or historical information. I included sources with historical overview for both fields. I expect that the developer of similar physical theories, upon applying them to solid mechanics, may encounter discrepancies in formulation. These new approaches might initially appear incompatible with conventional methods commonly employed in phenomenological theories and standard mechanical problem-solving frameworks, even though the mechanical problems themselves are already known and solved with phenomenological constitutive equations. Thus, I anticipate that the steps described herein could facilitate physicists efforts seeking to combine their theories in solid mechanics.
As for formulas, equation and figures, perhaps we could discuss the specific points that caused difficulties in order to take your wishes into account most effectively.
Thank you for your cooperation,
Kind regards,
Author
Reviewer 4 Report
Author Response
Dear reviewer,
In addition to my last response, I have to add information about ε in equation (4). Yes, this is a strain from σ-ε curve. The author of [3] assumes that at a low temperature (room temperature experiment) the probability of overcoming barriers by dislocations under stress is equal to 1. So, he puts 1 instead of exp(0) in Eq. 1 and obtains a simple differential equation with respect to ρs. Since at a low temperature all exponential brackets are equal to exp(0), he also obtains the equation σ=βmGρ0.5, and substitutes derived ρs that he got earlier in the integration. So, after that he express λ from the last equation.
By this, author [3] argues that almost all necessary model constants could be obtained from room temperature elongation experiment with σ-ε curve output.
Kind regards,
author
Round 2
Reviewer 1 Report
Author Response
Dear reviewer,
I would like to thank you for significant contribution to my work. If my paper gets published, I would appreciate the opportunity to continue our dialogue. My contact details will be available following its publication (in case it will be accepted).
My further steps are to have an attempt to integrate this model into some planar problem (for instance, rotating discs). I also keep trying to search ways to combine weak form finite element formulation with the creep constitutive models of this kind. In case there would be any significant progress in solving these problems, I aim to contribute by presenting my findings at the upcoming NME2026 conference. While responding to the reviewer's comments, I've discovered a shorter way to write the model's equations. If these refinements lead to meaningful theoretical advances (especially in physics), they too will be included in future works.
Kind regards,
author
Reviewer 2 Report
Author Response
Dear reviewer,
I've rewritten the introduction to include references to key works by both phenomenological and structural scholars. I'd be grateful if you'd mention works that definitely should have been included in the overview section.
Kind regards,
author
