Calibration and Experimental Determination of Parameters for the Discrete Element Model of Shells

Round 1

Reviewer 1 Report

This article is devoted to studying the mechanisms of marine shell degradation using DEM. The authors have proposed an interesting manuscript structure, presenting the information in a reader-friendly manner. However, the authors need to answer a number of questions and develop a revised version of the manuscript based on them:

1. The introduction and conclusions lack a summary of the scientific and practical contributions of this work. There is no overall goal or objective of the study. The authors need to more clearly explain the answer to the question, "What is the point?"
2. The study lacks clear novelty. The only potentially new feature in this work is the use of calibrated DEM parameters for fracture modeling.
3. The limitations of the presented model are not addressed (e.g., "The model is validated for quasi-static bending conditions; its direct application to high-speed impact fracture modeling requires further verification").

1. I request the authors to check the density stated at the beginning of Chapter 2 and in the conclusion. There is likely a dimensional error: 2.2 kg/m^3.
2. The figures containing the captions are of poor quality and are not always clearly legible.
3. In Figure 12, the authors need to clarify the differences between the figures in the caption.
4. During the screening procedure, the authors fail to acknowledge the drawback of the Plackett-Burman method chosen, namely, that interactions between factors can be neglected. This is a rather serious assumption that requires substantiation.
5. There is an error in the title of Chapter 2.3.6.
6. The conclusions contain an odd dimension for the unit area normal stiffness.

Author Response

Major comments

This article is devoted to studying the mechanisms of marine shell degradation using DEM.The authors have proposed an interesting manuscript structure, presenting the information in a reader-friendly manner. However, the authors need to answer a number of questions and develop a revised version of the manuscript based on them:

Response:

We sincerely thank the reviewer for the careful evaluation of our manuscript and for the constructive and detailed comments. We appreciate the recognition that the manuscript is structured in a reader-friendly manner and that the topic DEM-based investigation of shell degradation and fracture mechanisms is of interest.

In response to the major comments, we have carried out a substantial and systematic revision of the manuscript. Specifically, the revised version addresses the reviewer’s concerns from the following key aspects:

Clarification of scientific motivation, novelty, and scope.

The Introduction and Conclusions have been revised to clearly articulate the overall objective of the study, its methodological novelty, and its practical relevance. Rather than proposing a new DEM contact law, this work is positioned as a fracture-oriented and experimentally validated parameter calibration framework for brittle shell materials, filling a gap in DEM modeling of shell fragmentation.

Improved physical interpretation and methodological rigor.

The physical meaning and calibration basis of critical Bonding parameters (e.g., bonding radius, stiffness ranges) have been clarified, and the initial parameter selection ranges are now explicitly linked to shell thickness, particle size, and effective bonded interaction scales. The calibration procedure is therefore framed as mechanism-informed rather than purely data-driven.

Explicit discussion of model assumptions and limitations.

Additional discussion has been added to address the effects of geometric simplification (spherical particles, homogeneous bonding) and the applicability limits of the calibrated parameters, particularly with respect to quasi-static bending versus dynamic or multi-scale crushing scenarios.

Enhanced experimental and statistical support.

The description of the three-point bending experiments has been strengthened by reporting specimen numbers, dispersion characteristics, and standard deviations, thereby improving the statistical reliability of the averaged load–displacement response used for DEM calibration.

Cleaner data presentation and improved readability.

Redundant and inconsistent descriptions (e.g., in the angle of repose test) have been removed, numerical values have been unified, figure captions clarified, and typographical or unit-related errors corrected to avoid ambiguity or misinterpretation.

Strengthened engineering relevance and transferability.

The Conclusions have been rewritten to emphasize how the calibrated DEM parameter set can be directly used for shell crushing equipment optimization, and how the proposed calibration framework can be transferred to other brittle shell-type or agricultural waste materials.

We believe that these revisions substantially improve the scientific clarity, physical interpretability, and practical value of the manuscript. All major concerns raised by the reviewer have been carefully considered and addressed point by point in the revised manuscript. We sincerely hope that the revised version meets the reviewer’s expectations and thank the reviewer again for their valuable guidance.

 

1. The introduction and conclusions lack a summary ofthe scientific and practical contibutions of this work. There is no overallgoal r objective of the study.The authors need to more clearly explain the answer to the question,"What is the point?"

Response:

Thank you for this valuable and constructive comment. We agree that clearly articulating the overall objective as well as the scientific and practical contributions is essential for improving the clarity and impact of the manuscript.

In response, we have revised the final paragraph of the Introduction to explicitly state the overall research objective, namely the development of a high-fidelity discrete element model for freshwater mussel shells and the establishment of a systematic parameter calibration framework for brittle shell materials.

In addition, we have expanded the Conclusions section by adding a dedicated summary paragraph that clearly highlights both the scientific contribution (i.e., a validated DEM calibration methodology for bonded brittle biological materials) and the practical contribution (i.e., providing a reliable numerical basis for shell fragmentation analysis and crushing equipment optimization).

These revisions directly address the question of “what is the point” of this study and strengthen the manuscript’s overall coherence and relevance.

 

2.The study lacks clear novelty. The only potentilly new feature in this work is the use of calibrated DEM parameters for fracture modeling.

Response:

Thank you for this insightful comment. We agree that the present study does not introduce a new DEM contact model or numerical formulation. However, we respectfully clarify that the novelty of this work is methodological and application-oriented rather than model-oriented.

Specifically, the novelty lies in the systematic, fracture-oriented calibration of bonded DEM parameters for brittle shell materials, which has rarely been reported in existing DEM studies. While calibrated DEM parameters have been applied to plant stems and soft biological materials, their extension to shell-like brittle structures with dominant bending fracture behavior remains limited.

In the revised manuscript, we have clarified this point by explicitly stating the methodological novelty in the Introduction, emphasizing the integration of mechanical testing, bonded-particle modeling, and multi-stage statistical optimization for fracture calibration. We have also strengthened the Conclusions section to clearly articulate how this work extends the application scope of calibrated DEM fracture modeling to shell materials and provides a transferable calibration framework for similar brittle biological materials.

We believe these revisions more clearly communicate the novelty and contribution of the study within its intended engineering context.

 

3. The limitations of the presented model are not adressed (e.g.,"The modelis validated for quasi-statc bending conditions; ts direct application to high-speed impact fracture modeling requires further verification").

Response:

Thank you for this important comment. We agree that clearly stating the limitations and applicability range of the proposed model is essential.

In response, we have added a dedicated discussion on model limitations in the revised manuscript. Specifically, we now explicitly state that the present DEM model and calibrated bonding parameters are validated under quasi-static three-point bending conditions, and that their direct application to high-speed or impact-driven fracture scenarios may require further experimental verification and possible recalibration.

In addition, we have discussed the simplifying assumptions adopted in the particle discretization strategy and clarified their potential influence on microstructural fracture representation. These additions clearly define the scope of applicability of the model while outlining directions for future research.

We believe these revisions improve the transparency and rigor of the manuscript.

 

Detailed comments

1.l request the authors to check the density stated at the beginning of Chapter2 and in the conclusion. There islikely a dimensional error:2.2kg/m^3.

Response:

Thank you for pointing out this important issue. We agree that the originally stated density value of 2.2 kg/m³ is incorrect due to a unit notation error.

In the revised manuscript, the density of the mussel shell has been corrected to 2.2 g/cm³, which corresponds to 2200 kg/m³ in SI units. This correction has been implemented consistently in Section 2.1 as well as in the Conclusions section. We would like to clarify that the correct density value was used in all DEM simulations, and the error was limited to the textual unit expression only. Therefore, this correction does not affect the numerical results or the conclusions of the study.

 

2.The figures containing the captions are of poor quality and are not always clearly legible.

Response:

We appreciate this comment and agree that figure clarity is essential for effective communication of the results. In response, we have carefully revised all figures in the manuscript to improve their visual quality and legibility. Specifically:

All figures have been replaced with higher-resolution versions.

Font sizes in axes labels, legends, and annotations have been increased to ensure readability.

Figure captions have been revised and expanded where necessary to clearly explain the content and distinctions between subfigures.

Redundant or unclear graphical elements have been removed to enhance visual clarity.

We believe these improvements significantly enhance the readability and presentation quality of the figures and meet the journal’s formatting and quality requirements.

 

3.In Figure 12,the authors need to clarify the differences between the figures in the caption.

Response:

Thank you for pointing this out. We agree that the original figure caption did not clearly distinguish the meanings of the two subfigures.

In the revised manuscript, the caption of Figure 12 has been updated to explicitly clarify that Figure 12(a) presents the Pareto chart for the effects of bonding parameters on the ultimate crushing load, while Figure 12(b) corresponds to the ultimate crushing displacement. Additional explanations of the significance reference lines have also been added for clarity.

We believe this revision improves the readability and interpretability of the figure.

 

4.During the screening procedure, the authors faito acknowledge the drawback of the lackett-Burman method chosen,namely, that interactions between factors can be neglected. This is a rather serious assumption that requires substantiation.

Response:

Thank you for this important methodological comment. We agree that the Plackett-Burman design inherently assumes that interaction effects between factors are negligible during the screening stage, and that this assumption should be explicitly acknowledged and justified.

In the revised manuscript, we have added a clarification in Section 2.3.3 stating that the P-B method was intentionally used only for preliminary screening of dominant factors, with the understanding that interaction effects are not resolved at this stage.

We further clarify that this assumption is subsequently relaxed by employing a steepest ascent test and a Box-Behnken response surface design, in which second-order interaction and quadratic terms are explicitly included and statistically analyzed. In this way, potential interaction effects are systematically addressed in the later stages of the calibration procedure, ensuring the reliability of the final parameter optimization.

We believe that this clarification improves the methodological transparency and rigor of the study.

 

5.There is an error in the title of Chapter 2.3.6.

Response:

Thank you for pointing out this error. The title of Section 2.3.6 has been corrected in the revised manuscript. The duplicated and incorrectly formatted heading has been revised to “2.3.6. Verification Test” to ensure clarity and consistency.

 

6.The conclusions contain an odd dimension for the unit area normal stiffness.

Response:

Thank you for pointing this out. We agree that the original wording in the Conclusions section may cause confusion regarding the dimensional definition of the stiffness parameter.

In the revised manuscript, we have clarified that this parameter refers to the normal stiffness per unit bonding area, as defined in the BondingV2 model. Accordingly, the unit N/m³ is a model-defined quantity rather than a bulk material elastic constant.

This clarification has been added to the Conclusions section to avoid misunderstanding and to improve the physical interpretation of the calibrated parameters.

Reviewer 2 Report

The paper establishes a discrete element model for freshwater mussel shells, systematically obtaining intrinsic and contact parameters and calibrating Bonding model parameters through Plackett–Burman screening, steepest ascent, and Box–Behnken response surface design. The main contribution lies in proposing a complete and reproducible parameter calibration workflow for brittle shell materials and achieving high agreement between simulation and physical bending tests.

Overall, the manuscript is clear and easy to understand, but the following issues should be addressed.

1. In Chapter 1, most references focus on works before or around 2024. The literature review lacks recent studies on DEM modeling of brittle multilayer shells and biomineral composites, as well as recent developments in Bonding models. Updating the background with 2023–2025 studies would strengthen the justification of the research gap.
2. In Section 2.1, the density of mussel shells is reported as 2.2 kg/m³, which is unrealistic by several orders of magnitude. The correct unit should be verified, since an incorrect density value undermines the validity of subsequent DEM calculations.
3. In Section 2.2.4, the angle of repose test contains repeated sentences, disordered phrasing, and inconsistent values for contact parameters. This affects readability and may mislead readers. The data presentation needs to be cleaned and unified, preferably in a clear table.
4. In Section 2.3, the three-point bending experiment provides only an average load–displacement curve. No standard deviation, error bars, or dispersion information is given. For brittle fracture studies, statistical support is necessary to confirm data reliability.
5. In Section 2.3.2, the simulation uses 1080 spherical particles of 1 mm diameter to represent the shell. The simplification may overlook the layered nacre structure and thickness gradient of shells. A discussion on how this geometric simplification affects fracture mode realism, or a sensitivity analysis, is needed.
6. In Sections 2.3.3–2.3.5, although the parameter optimization process is complete, the initial selection range of Bonding parameters lacks physical justification. The calibration process appears data-driven rather than mechanism-driven, weakening the scientific interpretation of the parameter meanings.
7. In Section 2.3.6, model verification relies solely on ultimate load error (3.8%). Without comparing displacement evolution, crack propagation paths, or energy dissipation, it is insufficient to claim that the model accurately reproduces the failure mechanism.
8. The conclusion restates experimental procedures rather than highlighting transferable value. The applicability of the proposed method to other shell-type or brittle agricultural waste materials should be clarified to improve the work’s broader significance.

Author Response

Major comments

The paper establishes a discrete element model for reshwater mussel shells, systematically obtaining intinsic and contact parameters and calilrating Bonding model parameters through Plackett-Burman screening, steepest ascent and Box-Behnken response surface design. The main contribution ies in proposing a complete and reproducible parameter calibration workflow for brttle shel materials and achieving high agreement between simulation and physical bending tests.

Response:

We sincerely thank the reviewer for the careful reading of the manuscript and for the constructive and insightful comments. We appreciate the reviewer’s positive evaluation of the manuscript structure and its reader-friendly presentation, as well as the recognition of the main contribution of this work.

In response to the major comments, we have conducted a comprehensive revision of the manuscript. Specifically:

Dimensional and parameter consistency

We carefully re-checked all physical parameters reported in the manuscript. The density of freshwater mussel shells has been corrected to 2.2 g/cm³ (2200 kg/m³) in both Chapter 2 and the Conclusions, clarifying that the previous issue was due to unit notation rather than experimental or modeling errors. This correction ensures consistency and reliability in subsequent DEM calculations.

Figure quality and caption clarity

All figures have been revised to improve resolution and legibility. Figure captions were rewritten to clearly distinguish subfigures and to provide sufficient explanatory information, ensuring that each figure is self-explanatory and accessible to readers.

Methodological rigor and physical interpretation

We have strengthened the methodological discussion by clarifying the assumptions and limitations of the Plackett–Burman screening design, explicitly acknowledging the neglect of interaction effects at the screening stage and explaining how these effects are subsequently addressed through steepest ascent and Box–Behnken response surface optimization. In addition, the physical basis and calibration logic of key Bonding parameters, including bonding radius and stiffness ranges, have been supplemented to reinforce the mechanism-driven interpretation of the calibration process.

Model simplification and validation scope

Additional discussion has been added to address the impact of geometric simplification (spherical particles, uniform size) on fracture realism, including limitations related to shell layering and anisotropy. The applicability range of the calibrated model has been clearly defined, emphasizing that it is validated under quasi-static bending conditions, while dynamic and impact-driven fracture scenarios require further investigation.

Statistical reliability and validation depth

Statistical dispersion of the three-point bending experiments has been clarified by reporting standard deviations of ultimate load and displacement, supporting the reliability of the averaged load–displacement response used for DEM calibration. The verification section has also been refined to avoid overclaiming and to better align numerical validation metrics with the experimental observations.

Engineering relevance and broader applicability

The Conclusions have been substantially rewritten to emphasize the engineering value of the calibrated parameter set for shell crushing equipment optimization and to outline future research directions, including dynamic crushing simulations and coupled analyses of equipment structure and particle fracture. Furthermore, we clarified the transferability of the proposed calibration framework to other shell types and brittle agricultural or biomineral waste materials.

Through these revisions, we believe that the manuscript has been significantly improved in terms of clarity, scientific rigor, and broader significance. The revised version now more clearly articulates the methodological contributions, physical interpretation, applicability limits, and engineering relevance of the proposed DEM calibration framework.

We sincerely thank the reviewer for the valuable comments, which have helped us substantially enhance the quality of the manuscript.

 

Detailed comments

 

Overall, the manuscript is clear and easy to understand,but the following issues should be addressed.

1.In Chapter1, most references focus on works before or around 2024.The literature review lacks recent studies on DEM modeling of bittle multiayer shelle and biomineral composites, as wellas recent developments in Bonding models.Updating the background with2023-2025 studies would strengthen the justification of the research gap.

Response:

Thank you for this constructive suggestion. We agree that incorporating more recent literature (2023–2025) is important to better position the study and strengthen the justification of the research gap. In the revised manuscript, we have updated Chapter 1 by adding a new paragraph that summarizes recent progress in DEM-based fracture modeling for brittle shell/biomineral-like composites, and highlights recent developments in bonded/contact models, including multi-bonding and damage/softening formulations as well as fracture-mode-dependent bond breaking strategies. We have also revised the end of the background section to explicitly link these advances to the remaining gap in fracture-oriented, experimentally validated parameter calibration for shell-like brittle materials under bending-dominated conditions, thereby clarifying the motivation and contribution of the present work.

 

2.In Section2.1,the density of mussel shell is reported as2.2 kg/m, which is unrealistic by several orders of magnitude. The correct unit should be verified, since an incorrect density value undermines the validity of subsequent DEM calculations.

Response:

 

Thank you for pointing out this important issue. We agree that the density value as originally written was incorrect due to a unit error.

In the revised manuscript, we have corrected the density of the mussel shell to 2.2 g/cm³(equivalent to 2200 kg/m³), which is consistent with the drainage-method measurement and with reported values for biomineral shells.

We would like to clarify that the correct density value was used consistently in all DEM simulations, and the error was limited to unit notation in the text only. This correction does not affect the validity of the simulation results or the conclusions of the study.

 

3.In Section 2.2.4, the angle ofrepose test contains repeated sentences, disordered phrasing,and inconsistent values for contact parameters. This affects readability and may mislead readers.The data presentation needs to be cleaned and unified,preferably ina clear table.

Response:

Thank you for this helpful comment. We agree that the original presentation of Section 2.2.4 contained redundant sentences and unclear phrasing, which reduced readability and could potentially cause confusion.

In the revised manuscript, Section 2.2.4 has been completely rewritten to remove repetitive statements and to present the angle of repose test procedure and results in a clear and consistent manner. The contact parameters for shell–shell and shell–304 stainless steel interactions are now explicitly stated once with unified values, and the validation results are described concisely using averaged experimental and simulation outcomes.

These revisions improve clarity and readability while preserving the original data and referenced sources.

 

4.In Section2.3,the three-point bending experiment provides onl an average load-displacement curve. No standard deviation, fror bars, or dispersion information is given.For brittle fracture studies, statistical supportis necessary to confrm data reliabiiy,

Response:

Thank you for this important comment. We agree that statistical information is necessary to support the reliability of brittle fracture experiments.

In the revised manuscript, we have added quantitative dispersion information to Section 2.3. Specifically, thirty specimens were tested under identical three-point bending conditions. The average ultimate load was 100 N with a standard deviation of ±4.1 N, and the ultimate displacement exhibited a standard deviation of ±0.02 mm.

The relatively small dispersion confirms the good repeatability and deterministic nature of shell fracture under quasi-static bending and supports the use of the averaged load-displacement curve for subsequent DEM parameter calibration.

 

5.In Section 2.3.2,the simulation uses 1080 spherical particles of 1 mm diameter to represent the shell. The simplification may overlook the layered nacre structure and thickness gradient of shell.A discussion on how this geometric simplification affects fracture mode realism,or a sensitivity analysis,is needed.

Response:

Thank you for this important comment. We agree that representing the shell using spherical particles with a uniform diameter is a geometric simplification that does not explicitly capture the layered nacre structure and thickness gradients of real shells.

In the revised manuscript, we have added a dedicated discussion in Section 2.3.2 addressing the implications of this simplification. We clarify that the objective of the present DEM model is to reproduce the global bending-dominated fracture response, including ultimate load and macroscopic failure mode, rather than micro-scale crack evolution within individual nacre layers.

We further explain that, under quasi-static bending conditions, the dominant fracture behavior is governed by overall stiffness and bond failure across the section, which can be reasonably captured by a bonded spherical-particle representation. The revised text also outlines potential future extensions, such as layered or non-spherical particle modeling, to improve local fracture realism.

These additions clarify the scope, limitations, and physical interpretation of the adopted modeling strategy.

 

6.In Sections 2.3.3-2.3.5, although the parameter optimization process is complete, the initial selection range of Bonding parameters lacks physical justifcation.The calibration process appears data-driven rather than mechanism-driven, weakening the scientfic interpretation of the parameter meanings.

Response:

Thank you for this insightful comment. We agree that the physical basis of the initial Bonding parameter ranges should be explicitly clarified to avoid the impression of a purely data-driven calibration process.

In the revised manuscript, we have added a detailed explanation of the physical rationale behind the initial parameter range selection. Specifically, the ranges of unit normal and tangential stiffness were linked to the experimentally measured elastic and shear moduli of the shell material, while the critical normal and tangential stresses were constrained by the brittle fracture behavior observed in the three-point bending tests. In addition, the bonding radius range was justified based on particle size, shell thickness, and effective inter-particle bonding representation.

These additions clarify that the calibration strategy follows a physics-informed, experiment-constrained approach, with statistical methods used only to refine parameters within physically meaningful bounds. We believe this revision strengthens the scientific interpretation and methodological rigor of the parameter calibration process.

 

7.In Section 2.3.6,model verfication relies solely on ultimate load error (3.8%). Without comparing displacement evolution, crack propagation paths, or energy dissipation,it is insufficient to claim that the model accurately reproduces the failure mechanism.

Response:

Thank you for this important comment. We agree that model verification should not rely solely on the ultimate load error and that additional indicators related to deformation evolution and fracture behavior are necessary to support the validity of the failure mechanism.

In the revised manuscript, we have expanded Section 2.3.6 to include a qualitative comparison of the load–displacement evolution, fracture initiation location, and crack propagation characteristics between the simulation and the physical three-point bending experiments. We further discuss the energy-release behavior associated with brittle shell fracture to demonstrate consistency in the dominant failure mechanism.

While a fully quantitative analysis of crack paths and energy dissipation under dynamic conditions is beyond the scope of the present study, the added discussion clarifies that the calibrated BondingV2 model reproduces not only the ultimate load but also the key deformation and fracture features under quasi-static bending. This revision strengthens the validation of the proposed model.

 

8.The conclusion restates experimental procedures rather than highighting transferable value.The applicability of the proposed method to other shelltype or brite agricultural waste materials should be clarifed to improve the work's broader significance.

Response:

Thank you for this insightful comment. We agree that the original conclusion placed excessive emphasis on summarizing experimental procedures and calibration steps, while the broader applicability and transferable value of the proposed methodology were not sufficiently highlighted.

In the revised manuscript, we have restructured the Conclusions section to shift the focus from procedural repetition to methodological transferability and engineering relevance. Specifically, we now clarify that the proposed fracture-oriented DEM parameter calibration framework, which integrates mechanical testing with hierarchical statistical optimization, is not limited to freshwater mussel shells. Instead, it is directly applicable to other shell-type and brittle agricultural waste materials, such as oyster shells, clam shells, eggshells, and similar biomineral composites that exhibit bonded microstructures and bending-dominated brittle fracture behavior.

Furthermore, we emphasize that the calibrated modeling strategy can serve as a general reference for DEM-based crushing and fragmentation analysis, enabling researchers and engineers to adapt the workflow to different material systems by adjusting material-specific intrinsic and contact parameters. These revisions enhance the broader significance of the study and clearly articulate its transferable value beyond the specific case investigated.

Reviewer 3 Report

This manuscript conducted systematic experimental and numerical investigations to address the parameter calibration issue in the discrete element model of seashells, aiming to establish a high-fidelity numerical model that accurately characterizes their macroscopic mechanical behavior, thereby providing a basis for optimizing parameters of seashell crushing equipment. The work is relatively interesting, and the structure and language are well prepared. Some comments below need to be addressed or considered to improve the technical depth of the manuscript:

(1) The parameter calibration process does not adequately explain the impact of model simplification on the results. The manuscript models seashells as spherical particles with a diameter of 1 mm and uses the BondingV2 model to simulate bending failure. However, actual seashells possess a layered structure and anisotropy. Could this simplified modeling affect the authenticity of fracture patterns and load response? A supplementary discussion on the limitations of the model is needed.

(2) The statistical methods used are relatively conventional and lack in-depth analysis of interaction effects. The manuscript employs Plackett-Burman design, steepest ascent method, and Box-Behnken design for parameter screening and optimization, which is reasonable but common practice. The response surface analysis indicates that interaction effects on ultimate load are not significant, but the manuscript does not delve into whether this is due to parameter range settings or model assumptions.

(3) The conclusion section could further refine the value for engineering application and future research directions. The current conclusion primarily summarizes the experimental and calibration results, without fully elaborating on how the calibrated parameter set can be specifically used for "seashell crushing equipment optimization." Clear suggestions for follow-up research, such as dynamic crushing simulation and coupled analysis of equipment structure, are also lacking.

(4) The preparation method and property description of the "seashell powder bonded plate" are insufficient in the sample preparation section. For measuring the rolling friction coefficient, a plate made of "seashell powder mixed and cured with epoxy resin" was used. However, the type of epoxy resin, mixing ratio, curing conditions, and whether its surface characteristics are consistent with real seashell surfaces were not specified. This may introduce systematic error in the measured "seashell-seashell" friction coefficient.

(5) The physical meaning and calibration basis of the "bonding radius" are not clearly explained. In the Bonding model, "bonding radius" is a key parameter, but the manuscript does not explain its correlation with the microstructure of seashells (e.g., the distribution width of the organic matrix), nor does it justify why it was fixed within the range of 0.95–1.05 mm for screening. It is recommended to supplement the physical basis and calibration logic for this parameter.

(6) The "cross-scale applicability" of the parameter calibration results is not discussed. This study calibrated bonding parameters for millimeter-scale particles (1 mm). However, actual seashell crushing processes may involve the mechanical behavior of larger particles (shell fragments) or smaller particles (powder). Are the calibrated parameters applicable to simulations at different scales? It is recommended to address this in the discussion.

This manuscript conducted systematic experimental and numerical investigations to address the parameter calibration issue in the discrete element model of seashells, aiming to establish a high-fidelity numerical model that accurately characterizes their macroscopic mechanical behavior, thereby providing a basis for optimizing parameters of seashell crushing equipment. The work is relatively interesting, and the structure and language are well prepared. Some comments below need to be addressed or considered to improve the technical depth of the manuscript:

(1) The parameter calibration process does not adequately explain the impact of model simplification on the results. The manuscript models seashells as spherical particles with a diameter of 1 mm and uses the BondingV2 model to simulate bending failure. However, actual seashells possess a layered structure and anisotropy. Could this simplified modeling affect the authenticity of fracture patterns and load response? A supplementary discussion on the limitations of the model is needed.

(2) The statistical methods used are relatively conventional and lack in-depth analysis of interaction effects. The manuscript employs Plackett-Burman design, steepest ascent method, and Box-Behnken design for parameter screening and optimization, which is reasonable but common practice. The response surface analysis indicates that interaction effects on ultimate load are not significant, but the manuscript does not delve into whether this is due to parameter range settings or model assumptions.

(3) The conclusion section could further refine the value for engineering application and future research directions. The current conclusion primarily summarizes the experimental and calibration results, without fully elaborating on how the calibrated parameter set can be specifically used for "seashell crushing equipment optimization." Clear suggestions for follow-up research, such as dynamic crushing simulation and coupled analysis of equipment structure, are also lacking.

(4) The preparation method and property description of the "seashell powder bonded plate" are insufficient in the sample preparation section. For measuring the rolling friction coefficient, a plate made of "seashell powder mixed and cured with epoxy resin" was used. However, the type of epoxy resin, mixing ratio, curing conditions, and whether its surface characteristics are consistent with real seashell surfaces were not specified. This may introduce systematic error in the measured "seashell-seashell" friction coefficient.

(5) The physical meaning and calibration basis of the "bonding radius" are not clearly explained. In the Bonding model, "bonding radius" is a key parameter, but the manuscript does not explain its correlation with the microstructure of seashells (e.g., the distribution width of the organic matrix), nor does it justify why it was fixed within the range of 0.95–1.05 mm for screening. It is recommended to supplement the physical basis and calibration logic for this parameter.

(6) The "cross-scale applicability" of the parameter calibration results is not discussed. This study calibrated bonding parameters for millimeter-scale particles (1 mm). However, actual seashell crushing processes may involve the mechanical behavior of larger particles (shell fragments) or smaller particles (powder). Are the calibrated parameters applicable to simulations at different scales? It is recommended to address this in the discussion.

Author Response

Detailed comments

 

This manuscript conducted systematic experimental and numerical investigations to adres the parameter calibrationisue in the discrete element modei f seashell, aiming to estabiish a high-fideliy numerical model hat accurately characterizes their macroscopic mechanical behavior, thereby providing a basis for optimizing parameters of seashellcrushing qupment.The work is relatvely

interesting,and the structure and language are well repared.Some comments below need t be adressed orconsidered toimprove the technical depth of the manuscript:

(1)The parameter calibration process does not adequately explain the impact ofmodel simplification on the results.The manuscript models seashells as spherical articles with a diameter of 1 mm and uses the BondingV2 model to simulate bending fllure.However, actual seashell possess a layered structure and anisotropy.Could this simplified modeling atfect the authenticiy of fracture patterns and load response? A supplementary discussion on the limitations of the model is needed.

Response:

Thank you for this important comment. We agree that modeling seashells as spherical particles represents a simplification of their naturally layered and anisotropic structure. In the revised manuscript, we have added a dedicated discussion clarifying that the present DEM model focuses on reproducing macroscopic bending response and fracture load rather than microstructural crack mechanisms. We also explicitly acknowledge the limitations introduced by particle shape simplification and outline potential future extensions using layered or anisotropic representations.

(2)The statistical methods used are relatively conventional and lack in-depth analysis of interaction effects.The manuscrpt employs Placket-urman design, steepest ascent method, and Box-Behnken design for parameter screening and optimization, which is reasonable but common preactice.The response surace anaysis indicates tat interaction effectsontimate lad arenot signilicant,but the manuscript does not delve into whether this is due to parameter range settings or model assumptions.

Response:

Thank you for this insightful comment. We agree that the adopted statistical framework represents a commonly used calibration strategy. In the revised manuscript, we have clarified that the limited interaction effects observed in the response surface analysis are closely related to the physically constrained parameter ranges defined based on experimental measurements and preliminary screening.

We further emphasize that the hierarchical design (Plackett–Burman→steepest ascent→Box-Behnken) was intentionally chosen to efficiently isolate dominant parameters while maintaining physical realism. A discussion has been added to clarify that stronger interaction effects may arise under wider parameter ranges or different loading regimes, which could be explored in future work.

 

(3)The conclusion section could furtherefine the value for engineering application and future researchdirections.The curent conclusion primarly summarizes the experimental and calbration results, without fullyelaborating on how the callbrated parameter set can be specifically used for "seashell crushing equipment optimization."Clear sugestions for follow-up research,such as dynamic crushing simulation and coupled analysis of equipment structure,are also lacking

Response:

Thank you for this constructive comment. We agree that the original Conclusions section focused mainly on summarizing experimental and calibration results and did not sufficiently emphasize the engineering applicability and future research directions.

In the revised manuscript, the Conclusions section has been substantially rewritten to explicitly clarify the engineering value of the calibrated DEM parameter set for seashell crushing equipment optimization. In particular, we now describe how the calibrated bonding parameters can be directly applied to DEM-based simulations of shell crushing processes to support the optimization of crusher structural parameters, loading conditions, and operating modes, thereby reducing reliance on extensive trial-and-error experiments.

Furthermore, we have added clear directions for future research, including (i) extending the calibrated model to dynamic and high-speed crushing simulations, (ii) investigating the scale applicability of the parameters for shell fragments and powder-level particles, and (iii) performing coupled DEM–equipment structural analyses to evaluate the interaction between shell fracture behavior and crusher components.

We believe these revisions significantly enhance the practical relevance of the Conclusions section and clearly position the present work as a foundation for subsequent engineering-scale simulations and equipment optimization studies.

 

(4) The preparation method and property desciption of the "seashellpowder bondd late"are nsutficlet th smple preparatilo section.For measuring the rolling friction coeficient, a plate made of "seashellpowder mixed and cured with epoxy resin"was used. However, the type of epoxy resin,mixing ratio.curing conditions, and whether its surface characteristics are consistet withrl sahl surfaces were not specified.This may introduce systematic error in the measured "seashellseashellfriction coeficient.

Response:

Thank you for this valuable comment. We agree that the preparation method of the seashell powder bonded plate should be more clearly described.

In the revised manuscript, we have added detailed information regarding the type of epoxy resin, mixing ratio, curing conditions, and surface treatment of the bonded plate in Section 2.2.2. We also clarified that the surface friction behavior is primarily governed by exposed shell particles rather than the epoxy binder itself.

These additions improve transparency and help readers better assess the reliability of the rolling friction coefficient measurement.

 

(5) The physicel meaning and calibration basis of the "bonding radis"are not clearty xplained.In the Bonding model,"bonding radius" Is a key parameter,buthe manuscript does not xplain its corelation withthe micrstructure of seashell e..thdetbution with f the organic matrix), nor doesit ustfy why itws fxed within the rne f0.5-1.5mm for screning ts recommended to supplement the physical basis and calibration logic for this parameter.

Response:

Thank you for this important comment. We agree that the physical meaning and calibration rationale of the bonding radius should be more clearly explained.

In the revised manuscript, we have added a dedicated explanation in Section 2.3 clarifying that the bonding radius represents an effective cohesive interaction zone between particles rather than a direct geometric feature. We further relate this parameter to the biomineral composite nature of seashells, in which load transfer occurs through mineral–organic interfacial regions.

In addition, we now justify the selected screening range (0.5-1.5 mm) based on the adopted particle size (1 mm) and preliminary numerical stability considerations, explaining why this range provides physically meaningful and numerically stable fracture behavior under bending loads.

We believe these additions clarify the physical basis and calibration logic of the bonding radius parameter.

 

(6)The"ro-cle applcabilty"of the rmeter alirtionresut is t dsusse.s stuy calirted boding rmeter fr mietercae tcles (1m.oweerctulsehelluhing processesmyve teecanichavirfargser ties(shell ragments) or smaller particles (powder).Are the calbrated parameters applicable to simulations atdiferent scaes?ts recommended to address this in the discussion

Response:

Thank you for this important comment. We agree that the applicability of calibrated DEM bonding parameters across different particle size scales should be explicitly discussed.

In the revised manuscript, we have added a dedicated discussion on the scale applicability of the calibrated parameters. We clarify that the present bonding parameters are calibrated and validated for a particle discretization scale of approximately 1 mm under quasi-static bending conditions, and that their direct transfer to significantly larger fragments or finer powder-scale particles may not be strictly scale-invariant.

We further discuss how particle size, bond density, and effective contact area influence bonded DEM behavior, and explain under which conditions the current parameter set may remain applicable or require re-calibration. These additions clearly define the scope and limitations of the calibrated parameters while outlining future research directions toward multi-scale DEM calibration.

Round 2

Reviewer 1 Report

I express my gratitude to the authors for comprehensive answers to my questions.

There are no questions anymore

Author Response

Thank you for your final feedback and for confirming that you have no further questions regarding our revisions. We sincerely appreciate the time and effort you have dedicated to reviewing our manuscript and providing valuable comments throughout the process.

We are pleased to hear that our responses have addressed your previous concerns satisfactorily. Your constructive input has undoubtedly helped improve the quality of our work.

Reviewer 2 Report

After reviewing the revised manuscript, it is evident that the authors have adequately addressed the previous review comments, and the overall quality of the paper has been clearly improved in terms of background, methodology, statistical support, and model applicability.

1. In Section 2.2.3, the description of the collision restitution coefficient test still contains repeated sentences and minor editorial issues. While the experimental method is correct, the text should be carefully edited to remove redundancy and improve readability before final publication.
2. In Section 2.3.6, the added discussion on deformation evolution and fracture behavior strengthens the validation, but it remains largely qualitative. If possible, including one simple quantitative indicator would further enhance the credibility of the model, although this is not a critical issue.

Author Response

Thank you for your careful and thorough review of our manuscript, as well as for your constructive feedback throughout the process. We sincerely appreciate the time and expertise you have dedicated to improving our work.

Below, we provide point-by-point responses to the specific comments you raised:

Comment 1: Regarding the repeated sentences and editorial issues in Section 2.2.3 (collision restitution coefficient test).
We have taken this comment very seriously. In the revised manuscript, we have carefully refined this section by removing redundant expressions and improving sentence structure to enhance clarity and readability. The corresponding modifications have been updated in the text.

Comment 2: Regarding the suggestion to add a simple quantitative indicator to the discussion on deformation evolution and fracture behavior in Section 2.3.6.
We have incorporated a clear quantitative comparison in the relevant paragraph. Specifically, we have added the simulated versus experimentally measured fracture initiation displacement along with the calculated percentage deviation. This addition provides a concrete numerical metric that strengthens the model validation while preserving the original discussion’s flow and focus. The revised text can be found in Section 2.3.6.

We believe these amendments address your comments effectively and have improved the overall quality and clarity of the manuscript. Thank you once again for your valuable input.

Reviewer 3 Report

I have read the revised version of manuscript and found the authors have explained all the issues and comments I made in my first revision. 

I have read the revised version of manuscript and found the authors have explained all the issues and comments I made in my first revision. 

Author Response

Thank you for your final feedback and for confirming that you have no further questions regarding our revisions. We sincerely appreciate the time and effort you have dedicated to reviewing our manuscript and providing valuable comments throughout the process.

We are pleased to hear that our responses have addressed your previous concerns satisfactorily. Your constructive input has undoubtedly helped improve the quality of our work.

Round 3

Reviewer 2 Report

Overall, the revised manuscript is scientifically sound, logically coherent, and relevant to engineering applications. The added references are up to date, the methodology is clearly presented, and the conclusions are appropriately cautious while retaining transferable value.

After carefully reading the latest revised manuscript, it is evident that the authors have largely and effectively addressed the comments raised in the previous review. Substantial improvements have been made in updating the background, clarifying the physical meaning of parameters, strengthening statistical support, and defining the applicability range of the model.