Mass Spring Models of Amorphous Solids
Round 1
Reviewer 1 Report
The author presented techniques of tuning spring parameters to address high variance of properties of a disordered mass spring model at the global scale. Overall, the paper is well organized and well written. Following comments need to be addressed.
- In the introduction, the author talked about the effect of ordered lattice network on the crack propagation and claim disordered MSMs would be beneficial. Recent work by Chen et al. (Chen, H., Lin, E., Jiao, Y. et al. A generalized 2D non-local lattice spring model for fracture simulation. Comput Mech 54, 1541–1558 (2014).) has systematically studied the lattice network effect on crack propagation and proposed remedy for such problem by introducing nonlocal interactions. The author should clarify this point in the introduction.
- As to achieve varying values of Poisson’s ratio, another way is to consider the volume change of a mass point in the potential energy. The approach proposed by Chen has found a lot of application for mechanical problem, such as Chen et al., (2014). A novel Volume-Compensated Particle method for 2D elasticity and plasticity analysis, IJSS, 51(9), 1819-1833, and Chen and Liu, (2016). A non-local 3D lattice particle framework for elastic solids, IJSS, 81, 411-420. The author should acknowledge these works.
- The symmetry of the elasticity tensor is also a result of the material lattice structure, in addition to stress and strain tensor. The author should clarify this point.
- The symbols used in Equation (4) should be explained.
- Detailed proofreading is needed, such as line 23-24, “and on paper”, line 38-39, “we also we”.
Author Response
> In the introduction, the author talked about the effect of ordered lattice network on the crack propagation and claim disordered MSMs would be beneficial. Recent work by Chen et al. (Chen, H., Lin, E., Jiao, Y. et al. A generalized 2D non-local lattice spring model for fracture simulation. Comput Mech 54, 1541–1558 (2014).) has systematically studied the lattice network effect on crack propagation and proposed remedy for such problem by introducing nonlocal interactions. The author should clarify this point in the introduction.
Thank you for pointing that out. I'm including the suggested references.
Some more comments on this point -- not to be shared publicly (in case the review discussion gets published)
I must mention however, that the study presented in that article is not exhaustive. The article suggests that the presented technique eliminates lattice artefacts from the simulation, whereas in reality, there is no hope of achieving that in general case.
Conditions studied in Chen et al. involve cracking fronts which are determined by well directed forces (such as mode 1 cracking which produces straight-line cracks).
There is however a whole class of problems, where this technique won't work. For example if the cracking is induced by a shrinkage front progressing through a material, such as in the case of drying or cooling materials.
This follows simply form translational symmetry of the problem. Lattice based MSM also has a translational symmetry therefore if the cracking is progressing together with the shrinkage front the same error is made at each cracking step and nothing ever changes.
The stress profile is set, it should cause a crack tip to move forward in a direction which just slightly diverges from the current crack direction. Normally the crack should turn possibly producing e.g. a parabola shape discontinuity. However if the initial incentive to turn is not strong enough, it will not cause the spring on the side of the cell to break, but rather the one in front of the tip. Then the contraction front progresses and a few seconds later we will have exactly the same physical situation, only shifted by one cell in the network - in effect the crack will never turn, resulting in a straight line cracking instead of parabolic one. No amount of extra connections (etc) can solve that, since the system by definition has a translational symmetry and the turn/angle that a crack can take is discretised.
I have somewhat explained this in the introduction. This also serves as a good example why disordered MSM may be preferred for certain applications.
> As to achieve varying values of Poisson’s ratio, another way is to consider the volume change of a mass point in the potential energy. The approach proposed by Chen has found a lot of application for mechanical problem, such as Chen et al., (2014). A novel Volume-Compensated Particle method for 2D elasticity and plasticity analysis, IJSS, 51(9), 1819-1833, and Chen and Liu, (2016). A non-local 3D lattice particle framework for elastic solids, IJSS, 81, 411-420. The author should acknowledge these works.
Acknowledged.
> The symmetry of the elasticity tensor is also a result of the material lattice structure, in addition to stress and strain tensor. The author should clarify this point.
It is true that the symmetry does depend on the underlying structure, however the place in the text where elasticity tensor is discussed does not deal with numerical models. It simply starts with continuous material case, where such things are not taken under considerations yet.
I'm afraid that mentioning lattice topology there would confuse the reader.
> The symbols used in Equation (4) should be explained.
Explanations added.
> Detailed proofreading is needed, such as line 23-24, “and on paper”, line 38-39, “we also we”.
Thank you. This part was rewritten.
Reviewer 2 Report
This paper presents techniques for improving the performances of randomized mass spring models for non-crystalline materials. The study appear to be sound, while the presentation is sufficiently clear. Here follow a few comments/suggestions to be considered in a revision.
- The line before eqn (2): the Author considers "a small deformation from a stress-free configuration", a comment can be added on the fact that such a configuration might not exist in some cases (e.g., for load-free prestressed configurations), and it can be stated if/how such cases can be fit into the presented framework.
- Lines 139-140, "The stress was measured by averaging forces present in the radius 1.5⟨L⟩ around the point of interest": a formula for the stress measurement should be added in the text for better clarity. It should be discussed how the present stress measurement compares with the virial stress at zero Kelvin, if different.
- Consider adding, or referencing, one case study regarding a real material in order to show the practical implications of the presented results on disordered MSMs.
- Line 38-39: remove the extra "we".
Author Response
> The line before eqn (2): the Author considers "a small deformation from a stress-free configuration", a comment can be added on the fact that such a configuration might not exist in some cases (e.g., for load-free prestressed configurations), and it can be stated if/how such cases can be fit into the presented framework.
Thank you for the comment. I changed the "stress-free configuration" to "a reference configuration", which makes this statement more accurate.
> Lines 139-140, "The stress was measured by averaging forces present in the radius 1.5⟨L⟩ around the point of interest": a formula for the stress measurement should be added in the text for better clarity. It should be discussed how the present stress measurement compares with the virial stress at zero Kelvin, if different.
A proper explanation with the formula has been added as well as citations to papers which explain the stress measurement procedure in full detail.
> Consider adding, or referencing, one case study regarding a real material in order to show the practical implications of the presented results on disordered MSMs.
This is now somewhat done in the introduction.
>Line 38-39: remove the extra "we".
thank you
Reviewer 3 Report
I think the article would fit more into a journal on physical modeling than a chemistry one.
It is not clear from the article for what purpose the presented procedure was developed, where it will be used. The introduction does not adequately present state-of-the-art, it does not adequately place the area under study within the field of science. There is a great lack of explanatory figures, e.g. a crystal (lattice) based and disordered network.
"It should not come as a surprise" => not an objective statement
"because such MSM is typically easier to set up and on paper and it gives much better accuracy than random models" etc. => makes statements without a source
"Real materials are not perfect." => How does this relate to the context? The fact that some procedures are "based on statistical estimates" does not mean that a procedure works well for structural errors. The whole paragraph is inconsistent. The author responds to problems that he does not explain in sufficient depth.
The paragraph tries to compare the crystal based and disordered model, but I don’t think that would be appropriate here. Here, in the introduction, you should rather describe the purpose and application areas of mass spring modeling, what shortcomings are still there, what research is underway. In a next section, you could illustrate the existing MSM methods and advantages and disadvantages in detail with figures.
The example presented in Section 4 is not justified. Some parameters are selected, but why exactly? The article talks about measurement in many places while it is all about simulation. It does not write what software the simulation was made with. The section seems more educational than scientific.
Section 5 is also full of random, unreasonable values, but this section is at least fundamentally scientific.
192 our fist attempt => first
The article looks clashed. Since the author has already published good quality scientific publications, this paper cannot be saved by making it a beginner’s first attempt, and that’s all what was succeeded. I suggest that the author withdraw the article, think carefully about what he or she wants to communicate, rework his or her work accordingly, and expand the background information accordingly, then resubmit it to a journal.
Author Response
> It is not clear from the article for what purpose the presented procedure was developed, where it will be used. The introduction does not adequately present state-of-the-art, it does not adequately place the area under study within the field of science. There is a great lack of explanatory figures, e.g. a crystal (lattice) based and disordered network.
The requested figures have been added. As stated in the introduction, this article is a follow up to two previously published papers on this topic. I serves little purpose to repeat the whole introduction with detailed explanations and literature reviews once again. Instead, recommendations of review articles are given, so that a reader who feels that he is missing the context can refer to them.
An article does not need to be clearly classifiable to a field of science, to contain knowledge useful to other researchers. This problem was however addressed to an extend -- the introduction was reworked to contain more direct references to problems which may benefit form the contents of this paper. State-of-the-art articles suggested by Reviewer 1 were added as well.
> "It should not come as a surprise" => not an objective statement
"because such MSM is typically easier to set up and on paper and it gives much better accuracy than random models" etc. => makes statements without a source
"Real materials are not perfect." => How does this relate to the context? The fact that some procedures are "based on statistical estimates" does not mean that a procedure works well for structural errors. The whole paragraph is inconsistent. The author responds to problems that he does not explain in sufficient depth.
(...)
This paragraph has been reworked to address these issues. Now it discusses more deeply a concrete example of where disorderd networks provide a good utility.
> The example presented in Section 4 is not justified. Some parameters are selected, but why exactly? The article talks about measurement in many places while it is all about simulation. It does not write what software the simulation was made with. The section seems more educational than scientific.
This section serves as an introduction to the tests and study that follows. It is meant to be educational.
Most of the parameters listed in this section are not critical or do not need to be set to any specific values.
As long as their values are in a reasonable range, the results of the described procedures will be qualitatively the same. E.g. we expand the cube by 1%. There is no specific reason for that. We could do it for 0.1% or 2% and expect analogous results. Simirarly dimentions of the cube, or a value of K. It only sets the scale on the graphs that follow. Or we could use a ball or a cylinder instead of a cube - the choice is rather arbitrary.
I provide the values of these parameters to allow for reproducability in case someone wants to verify the presented results. Most papers don't do that, and simply don't even mention all the hidden knobs which affect the experiment.
There is however one aspect here, which if fact was not discussed properly -- the stress measurement procedure. That part have been revised and properly explained.
> The article talks about measurement in many places while it is all about simulation.
This is mentioned in the introduction:
"It should be noted, that we investigate only the static properties of MSMs. We do not address here the question of how these systems evolve over time or what are the most efficient numerical schemes to track their dynamics."
The simulation in this context means that we construct a numerical representation of a given material and investigate its mechanical response to various stress/displacement conditions.
> Section 5 is also full of random, unreasonable values, but this section is at least fundamentally scientific
Some values present in this section are in fact partially heuristic, such as a minimal change in the progress of an algorithm at which we stop. Such paremeters are present in all numerical algorithms, regardles of whether researchers chose to disclose them or not.
E.g.
https://www.gnu.org/software/gsl/doc/html/multimin.html
"The accuracy of the line minimization is specified by tol. (...) A tol value of 0.1 is suitable for most purposes..."
Moreover the section does not claim to be providing the best numerical algorithms to perform the described tasks, but rather aims at showng a working example of a well defined procedure together with results which can be obtained from it. (It is more about what is being minimized, and not how to carry out the minimization)
Should the results be insufficient for someone's application, he/she is free to improve on the presented algorithms.
This is in fact stated in the article "the implementation details are of a lesser importance, than the effects each tuning procedure has on the MSM quality (as mentioned one might simply use linear solvers)."
> 192 our fist attempt => first
thank you
> The article looks clashed. Since the author has already published good quality scientific publications, this paper cannot be saved by making it a beginner’s first attempt, and that’s all what was succeeded. I suggest that the author withdraw the article, think carefully about what he or she wants to communicate, rework his or her work accordingly, and expand the background information accordingly, then resubmit it to a journal.
> I think the article would fit more into a journal on physical modeling than a chemistry one.
There is not enough time to rework the article completely, however it seems that the rest of the comments, which were not addressed, refer mostly to the introduction being inadequate and motivation towards the work being insufficient, and do not address the scientific correctness of the contents of the paper.
Judgement of adequacy of the contents of paragraphs such as introduction, or the one section which "seems more educational than scientific" is rather subjective - some people may like them, some may not, some may want them to be structured differently. This does not affect the correctness or usefulness of the scientific sections.
As to whether the motivation behind the work is sufficient, or if the article fits into the scope of the journal is best left to be judged by the editors.
Round 2
Reviewer 3 Report
The author understood the criticisms contained in the first review and revised the article accordingly. The introduction thus clearly presents the place of the results included in the article in the field and the novelty content of the results. The less objective contents were reworked, making the article a good quality scientific work. The revised article is in order both in form and content, of publishable quality.
