Review Reports

Round 1

Reviewer 1 Report

This work investigates the mechanical behavior of ultra-high-molecular-weight polyethylene (UHMWPE) by both viscoelastic and elastic-viscoplastic (modified Anand) models. While the viscoelastic model is not sufficient to capture multi-cycle loading conditions, the elastic-vicoplastic model is more representative. The elastic-viscoplastic model, including temperature-dependent parameters is a valuable contribution that enhances the model's applicability to general amorphous materials.

The experiments and modeling are clearly described and the paper is well organized. I would recommend to publish the paper if authors could address below issues.

1. Could author show the comparison between test and simulation for figure 10-12? So people can be more convinced by material parameters fitting
2. Could author provide experimental and simulation comparison through figure 13-17. There are only two models comparison, not sufficient enough to show which one is closed to reality.

And there is some minor things:

1. It is more common to validate viscoelastic or elastic-viscoplastic model by relaxation/creep test and uniaxial tension at different strain rate.
2. The author may try a nonlinear viscoelastic model like PRF to see if matches the test results well. If using plastic model, the author needs to prove there is permanent deformation by either load-unload or releasing the sample for long time.

Author Response

The experiments and modeling are clearly described and the paper is well organized. I would recommend to publish the paper if authors could address below issues.

1. Could author show the comparison between test and simulation for figure 10-12? So people can be more convinced by material parameters fitting

 

Answer: The figure numbers were changed upon responding to reviews. Experimental data have been added to Figures 11-12 (previously 10-11). These parameters allow for a comparison of the experiment and the numerical model. The parameter shown in Figure 13 (previously 12) cannot be determined directly using current experiments. The change in this parameter and the remaining empirical parameters are found by solving the inverse problem as part of the identification procedure.

 

2. Could author provide experimental and simulation comparison through figure 13-17. There are only two models comparison, not sufficient enough to show which one is closed to reality.

 

Answer: This type of experiment has not yet been conducted for a bearing with a flowing interlayer material. Current experiments with a real structure considered only low-cycle loading. The structure included an antifriction layer made of modified fluoroplastic. We plan to conduct a series of full-scale experiments under high-cycle loading on a real structure with small geometric parameters. We are currently looking for funding. This paper presents the parameter distributions within a first approximation. A comparative analysis of the plastic component of the model and its impact on the stress-strain state of the structure is also provided. A comparison of the numerical simulation results with those of other authors shows good agreement.

And there is some minor things:

1. It is more common to validate viscoelastic or elastic-viscoplastic model by relaxation/creep test and uniaxial tension at different strain rate.

 

Answer: Similar experiments have not been conducted. However, we plan to conduct a series of full-scale experiments on relaxation and creep at different temperatures, shear rates, and stress levels.

 

2. The author may try a nonlinear viscoelastic model like PRF to see if matches the test results well. If using plastic model, the author needs to prove there is permanent deformation by either load-unload or releasing the sample for long time.

Answer: Currently, there is no feasibility for implementing the proposed model. In future studies, we will attempt to conduct a comparative analysis with the proposed model.

Reviewer 2 Report

The paper shows detailed descrption of the experimental procedures of identifying the parameters for  Maxwell and Anand models. The application is the layer in the bridge bearings.

 My detailed comments are associated with the remarks  in answers to the questions above.

The finite element model is described in another paper, ref [57].

However, there should be given a table gathering all the constitutive parameters which are used in the Ansys input file.  Otherwise, the research is hard to repeat. A finite element mesh should be added as well. 

Author Response

1. The finite element model is practically not described. It is necessary to show the mesh, a table of all constitutive parameters. It is aimed at replicability of the results.

 

Answer: We've expanded the information about the finite element model. We hope this makes it clearer.

 

2. There are much earlier references concerning the Maxwel model than ref[48. Nearby the [48] should be cited, for example, the following reference Witold Nowacki, Theorie du fluage, Éditions Eyrolles, 1965, or another reference close to this date. It is possible that exists a Russian translation as well. I added a link to a library since the doi number is not available. I could not add it the recommede references. https://catalogue-bu.uca.fr/discovery/fulldisplay?vid=33CLERMONT_BCIU:33CLERMONT_VU1&tab=Everything&docid=alma991000155519704411&lang=fr&context=L&adaptor=Local%20Search%20Engine&query=sub,exact,Visco%C3%A9lasticit%C3%A9&offset=0&virtualBrowse=true

 

Answer: Thank you for bringing the importance of citing primary sources to our attention. We found this scholarly work. A translation into our native language exists. We have reviewed the material. It was very helpful. The link has been added to the work.

 

3. The existing figures and tables are well presented. However, more figures should be added. The figures and tables should illustrate the finite element model.

 

Answer: We have added more information about material and design models.

 

4. The finite element model is described in another paper, ref [57]. However, there should be given a table gathering all the constitutive parameters which are used in the Ansys input file. Otherwise, the research is hard to repeat. A finite element mesh should be added as well.

 

Answer: We have expanded information about the model.

Reviewer 3 Report

The manuscript proposes two constitutive models for UHMWPE in spherical bridge bearings—a Prony-based linear viscoelastic model and a temperature-dependent Anand viscoplastic model—calibrated using DMA, compression, and thermal expansion tests. These models are implemented in ANSYS to simulate multi-cycle loading, and the authors conclude that the viscoelastic model underestimates deformation while the modified Anand model more realistically captures irreversible behavior.

I recommend the following points to be considered:

The simulations lack experimental or literature validation, making the predictive capability of the models uncertain.

The viscoelastic Prony model is insufficiently identified, as temperature–frequency dependence is not properly characterized.

The modified Anand model is introduced without theoretical justification or polymer-specific references supporting its applicability.

The bearing FE model is oversimplified and omits critical 3D contact effects, frictional behavior, and mesh-sensitivity analysis.

Several conclusions are overstated because no quantitative comparison between model predictions and measured behavior is provided.

Essential parameters, derivations, and uncertainties are not reported clearly, reducing reproducibility; the authors should provide more detailed information on the FEM models.

Since the manuscript uses viscoelastic characterization via storage and loss moduli (DMA), the authors should cite recent studies on damping behavior in polymer composites, in particular https://doi.org/10.1088/1361-6528/ada6be.

Additionally, they should consider citing https://doi.org/10.1007/s00161-022-01111-w, which presents a closely related nonlinear constitutive framework for polymeric solids; its treatment of strain-energy formulation, volumetric response, and microstructure-driven nonlinear behavior aligns well with the modelling strategy of the present study.

 

I recommend the following points to be considered:

 

The simulations lack experimental or literature validation, making the predictive capability of the models uncertain.

 

The viscoelastic Prony model is insufficiently identified, as temperature–frequency dependence is not properly characterized.

 

The modified Anand model is introduced without theoretical justification or polymer-specific references supporting its applicability.

 

The bearing FE model is oversimplified and omits critical 3D contact effects, frictional behavior, and mesh-sensitivity analysis.

Several conclusions are overstated because no quantitative comparison between model predictions and measured behavior is provided.

Essential parameters, derivations, and uncertainties are not reported clearly, reducing reproducibility. tHE AUTHROS HSOULD GIVE MORE DETAILS ESPECIALLY REGARDING THE fem MODELS.

Since the manuscript uses viscoelastic characterization via storage and loss moduli (DMA), the authors should cite recent studies on damping behavior in polymer composites, in particular https://doi.org/10.1088/1361-6528/ada6be.

Additionally, they should consider citing https://doi.org/10.1007/s00161-022-01111-w, which presents a closely related nonlinear constitutive framework for polymeric solids; its treatment of strain-energy formulation, volumetric response, and microstructure-driven nonlinear behavior aligns well with the modelling strategy of the present study.

Some model equations are introduced without defining all parameters. Several terms in the Anand relations and temperature-dependent functions are not clearly explained in the text, and all parameters should be defined with units.

The temperature-dependent formulas require clearer justification. The manuscript presents exponential temperature relations without explaining why these specific forms were chosen or how they relate to polymer physics.

The Prony model is not reproducible because the actual relaxation parameters are not listed. The figures show trends, but the numerical values used in the simulations must be provided.

Key strain and stress measures are not explicitly stated. The manuscript should clearly define which equivalent stress and strain formulations are used and how they enter the constitutive models.

Important FEM modelling details are missing. Contact formulation, friction laws, boundary conditions, and element types should be described clearly so the FE implementation can be reproduced.

Author Response

1. The simulations lack experimental or literature validation, making the predictive capability of the models uncertain.

 

Answer: Data expanded.

 

2. The viscoelastic Prony model is insufficiently identified, as temperature–frequency dependence is not properly characterized.

 

Answer: Many researchers use temperature-time analogies to relate viscoelastic behavior to temperature; in this study, WLF is used. Model parameters have been added to the text of the article. Graphical visualization has been removed.

 

3. The modified Anand model is introduced without theoretical justification or polymer-specific references supporting its applicability.

 

Answer: Thank you for your comment! An earlier study demonstrated the limitations of the standard Anand model for describing amorphous solids. A link to the work is in the text of the article. The modification presented in this paper reduced the error between the experimental data and the numerical model.

 

4. The bearing FE model is oversimplified and omits critical 3D contact effects, frictional behavior, and mesh-sensitivity analysis.

 

Answer: The model description has been expanded. An axisymmetric model of the bearing is considered as a first approximation. This allows for a quick, qualitative assessment. Three-dimensional research is currently underway, including consideration of the lubricant present in the antifriction layer. We hope to present new material soon.

 

5. Several conclusions are overstated because no quantitative comparison between model predictions and measured behavior is provided.

 

Answer: Thank you for your comment! The findings presented relate to the first stage of the study. The work aims to evaluate the impact of plasticity on the structural behavior, using a numerical approach. Experiments on samples revealed the presence of plastic deformations, and we previously established that viscoelastic models provide a qualitative estimate (the results are underestimated). Our goal is to evaluate the influence of plasticity in the model on the bearing behavior. An experiment with a real structure is planned. Funding for its implementation is being sought.

 

6. Essential parameters, derivations, and uncertainties are not reported clearly, reducing reproducibility; the authors should provide more detailed information on the FEM models.

 

Answer: Data expanded.

 

7. Since the manuscript uses viscoelastic characterization via storage and loss moduli (DMA), the authors should cite recent studies on damping behavior in polymer composites, in particular https://doi.org/10.1088/1361-6528/ada6be.

Additionally, they should consider citing https://doi.org/10.1007/s00161-022-01111-w, which presents a closely related nonlinear constitutive framework for polymeric solids; its treatment of strain-energy formulation, volumetric response, and microstructure-driven nonlinear behavior aligns well with the modelling strategy of the present study.

 

Answer: Thank you for your recommendations. We have reviewed the material. It is very interesting and will be useful as we continue to develop our work. The directions for further development are reflected in the text of the article, with a link included.

 

8. Some model equations are introduced without defining all parameters. Several terms in the Anand relations and temperature-dependent functions are not clearly explained in the text, and all parameters should be defined with units.

 

Answer: Thanks for your comment! We've added the information.

 

9. The temperature-dependent formulas require clearer justification. The manuscript presents exponential temperature relations without explaining why these specific forms were chosen or how they relate to polymer physics.

 

Answer: Thank you for your comment! The presented dependence type was chosen based on experience with parameter approximation. The presented combination of exponential factors allows for the description of a wide range of functions. Its use was chosen for describing the temperature dependence of parameters. References to the sources that suggested this solution have been added.

 

10. The Prony model is not reproducible because the actual relaxation parameters are not listed. The figures show trends, but the numerical values used in the simulations must be provided.

 

Answer: Thanks for your comment! We've added the information.

 

11. Key strain and stress measures are not explicitly stated. The manuscript should clearly define which equivalent stress and strain formulations are used and how they enter the constitutive models.

 

Answer: The results show equivalent stress and strain von Mises.

 

12. Important FEM modelling details are missing. Contact formulation, friction laws, boundary conditions, and element types should be described clearly so the FE implementation can be reproduced.

 

Answer: Thanks for your comment! We've added the information.

Round 2

Reviewer 1 Report

it is okay for now that authors only conduct and give preliminary modeling results. looking forward to further study

N/A

Reviewer 2 Report

The authors improved the paper. In my opinion, the paper can be published.

The explanations concerning the model description  are introduced. 

Reviewer 3 Report

I believe that the manuscript is now appropriate for publication.

I believe that the manuscript is now appropriate for publication.