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Updated: 12 hours 35 min ago

by the way, I forgot to check if my BAM model works fine

Sat, 2018-02-17 15:19

In reply to a "contact sport" between academics

By the way, this imechanica discussion makes me wonder why I did not check if my BAM model

works fine with the "Contact Challenge" surface. One reason may be that I developed BAM after the contact challenge results were collected.

It should be easy to do it, except to find the time!

Anyone willing to do it?

Interested in the position

Sat, 2018-02-17 05:41

In reply to Master/ PhD/ PDF positions in mass timber construction research at the University of Alberta, Edmonton, Canada

Dear Jianhui,

I have sent my resume to Prof. Chui. Looking forward to his response.

Kind regards,

Aleem Ullah

the big review paper with my good friend Muser has appeared!

Sat, 2018-02-17 04:56

In reply to a "contact sport" between academics

Modeling and simulation in tribology across scales: An overviewTribology International

Available online 12 February 2018

In Press, Accepted Manuscript — Note to users


 Modeling and simulation in tribology across scales: An overview 

  • a Advanced Production Engineering, Engineering and Technology Institute Groningen, Faculty of Science and Engineering, University of Groningen, Nijenborg 4, 9747 AG Groningen, The Netherlands
  • b MINES ParisTech, PSL Research University, Centre des Matériaux, CNRS UMR 7633, BP 87, F 91003 Evry, France
  • c Univ Lyon, Ecole Centrale de Lyon, ENISE, ENTPE, CNRS, Laboratoire de Tribologie et Dynamique des Systèmes LTDS, UMR 5513, F-69134, Ecully, France
  • d Department of Materials Science and Engineering, Delft University of Technology, Mekelweg 2, 2628 CD Delft, The Netherlands
  • e Department of Industrial Engineering, University of Padova, Via Venezia 1, 35015 Padua, Italy
  • f Tribology Group, Department of Mechanical Engineering, Imperial College London, South Kensington Campus, Exhibition Road, London SW7 2AZ, UK
  • g Division of Machine Elements, Luleå University of Technology, Luleå, Sweden
  • h IMT School for Advanced Studies Lucca, Multi-scale Analysis of Materials Research Unit, Piazza San Francesco 19, 55100 Lucca, Italy
  • i Department of Mechanical Engineering, Technical University of Denmark, DK-2800, Kgs. Lyngby, Denmark
  • j National Centre for Advanced Tribology at Southampton (nCATS), Bioengineering Science Research Group, Faculty of Engineering and the Environment, University of Southampton, Southampton SO17 1BJ, UK
  • k Biomechanics and Mechanobiology Laboratory, Biomedical Engineering Division, Department of Human Biology, Faculty of Health Sciences, University of Cape Town, Anzio Road, Observatory, 7925, South Africa
  • l LSMS, ENAC, Swiss Federal Institute of Technology (EPFL), CH-1015 Lausanne, Switzerland
  • m Department of Engineering, Aarhus University, Inge Lehmanns Gade 10, 8000 Aarhus C, Denmark
  • n SKF Engineering & Research Centre (ERC), SKF B.V., Nieuwegein, The Netherlands
  • o Department of Physics, King's College London, Strand, London WC2R 2LS, England, UK
  • p Hamburg University of Technology, Department of Mechanical Engineering, Am Schwarzenberg-Campus 1, 21073 Hamburg, Germany
  • q Department of Control Engineering, Faculty of Electrical Engineering, Czech Technical University in Prague, Karlovo Namesti 13, 12135, Prague 2, Czech Republic
  • r Politecnico di Bari, V. le Gentile 182, 70125 Bari, Italy
  • s Institute of Fundamental Technological Research, Polish Academy of Sciences, Pawinskiego 5B, 02-106 Warsaw, Poland
  • t Department of Physics and Nanostructured Interfaces and Surfaces Centre, University of Torino, Via Pietro Giuria 1, 10125 Torino, Italy
  • u Laboratory of Bio-Inspired & Graphene Nanomechanics, Department of Civil, Environmental and Mechanical Engineering, University of Trento, Via Mesiano 77, 38123 Trento, Italy
  • v Ket Lab, Edoardo Amaldi Foundation, Italian Space Agency, Via del Politecnico snc, 00133 Rome, Italy
  • w School of Engineering and Materials Science, Queen Mary University of London, Mile End Road, E1-4NS London, United Kingdom
  • x Department of Materials Science and Engineering, Saarland University, 66123 Saarbrücken, Germany


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some more clarifications

Fri, 2018-02-16 06:15

In reply to a "contact sport" between academics

I would specify that my statements are general and do not mean to say that Muser was in any way dishonest or falsifying any of the process of the "contact mechanics" challenge.

But the situation is simply that I raise points, also in my "comment" to the "contact challenge", which are difficult questions and do not necessarily pertain to the contact-mechanics challenge.

In a sense, it may look misleading and too much an attack to Muser that I raise these questions.

Muser is a very strong scientist, with very strong honest behaviour, and I have no intention to claim otherwise.

These questions are purely scientific debates.  Unfortunately the way the "contact challenge" is organized, being Persson's theory, for that specific case, very well organized, makes all other theories less strong.

Muser was not in a good position to answer all my questions.  His reply is a very interesting scientific paper.

The fact that we collaborated on a review paper shows that we are very good collegues and friends!

Future directions in tribology require more discussion. 


You should make clear these things clear in an extra blog. I am seriously concerned about the damage your blog did and I want damage control to the largest possible degree. You are the only person who can fix this right now. 



I apologize for one of the questions to Muser -- 9

Fri, 2018-02-16 05:37

In reply to a "contact sport" between academics


I must apologize for one point 9 in my questions to Muser.  It is not true that he did not permit me to partecipate.  I apologize and corrected.

in the commercial site of Persson surfaces are non Gaussian!!!

Fri, 2018-02-16 03:48

In reply to a "contact sport" between academics

The influence of roughness on the adhesion and frictional properties is mainly determined by the surface roughness power spectrum C(q) (or power spectral density) which is the most important quantity characterizing roughness. The surface roughness power spectrum fully characterizes all statistical properties of a measured surface. This means that all available information on the roughness is uniquely preserved in this quantity. It can be calculated directly from nearly any measured topography using our power spectrum software. This means that the power spectrum software is the perfect tool to further analyze your topography files and to calculate the input files necessary for our contact mechanics and rubber friction software. Note that while the root mean square roughness is usually dominated by the longest wavelength surface roughness components, higher order moments of the power spectrum such as the average slope or the average surface curvature are dominated by the shorter wavelength components. All these roughness parameters have therefore one thing in common, they do not describe the surface properties on different length scales. However it has been found that this is necessary to understand the true contact area between a tire with the road surface. It is hence not enough to gather information about a measured topography by only calculating the standard roughness parameters which exist for a long time already. The surface roughness power spectrum is the only statistical quantity which covers roughness properties over all length scales without loosing information over the surface measured. This is actually very important because practically all macroscopic bodies have surfaces with roughness on many different length scales. When two bodies with nominally flat surfaces are brought into contact, real (atomic) contact will only occur in small randomly distributed areas, and the area of real contact is usually an extremely small fraction of the nominal contact area. The contact regions can be visualized as small areas where asperities from one solid are squeezed against asperities of the other solid; depending on the conditions the asperities may deform elastically or plastically. How large is the area of real contact between a solid block and a substrate? This fundamental question has extremely important practical implications. For example, it determines the contact resistivity and the heat transfer between the solids. It is also of direct importance for wear and sliding friction, e.g., the rubber friction between a tyre and a road surface, and has a major influence on the adhesive force between two solid blocks in direct contact. The power spectrum calculator offers a quick, intuitive and hence easy to use software for calculating the surface roughness power spectrum of all kinds of different input formats.The figure below shows the latest Windows version of the program. After specifying the format type and some other important information about the topography file, like how many points in x and y-direction or the lattice constant between two points, one can choose between calculating the full, top or bottom power spectrum. Windows Version of the power spectrum software 

When the calculation is finished successfully it is possible to directly check the power spectrum as shown below. The power spectrum software will give you in addition to the power spectrum many other important parameters. This includes different roughness parameters as for example the rms roughness value or the rms slope.


The surface roughness power spectrum


Here we show two other quantities which can be very to check after the power spectrum has been calculated as they contain very useful information. On the left is the height probability distribution while on the right we show the slope probability distribution. It is recommended to check these two curves after the calculation is finished to make sure that the results are reasonable and consistent with the power spectrum.


Thanks for your feedback on the HASEL technology!

Thu, 2018-02-15 23:17

In reply to Dear Christoph,

Dear Tongqing,

thank you very much for your positive comment!

Yes, Zhigang mentioned some still unpublished efforts on GEO in an earlier comment; I am curious to see this when the papers go online. GEO is without doubt a great combination of materials that is exceptionally rich in mechanics and materials innovation. As for GEO, I would suggest that you maybe consider making your analysis even broader. We have had some very nice results with Peano-HASELs, which do not rely on elastomers and can also be made with thin metal films as electrodes -- and still, Peano-HASELs can serve as very good electrohydraulic artificial muscles. Maybe some of the mechanics concepts you are working on related to GEO could be generalized and made broader to also apply to systems, that consist of a liquid dielectric, thin polymer films (including but not limited to elastomers) and conductors (hydrogels, but also thin metal films or other types of stretchable conductors). Of course, you would have to adapt the beautiful name of GEO which you might not want to do. In some sense GEO can be viewed as a specific case of HASEL, using elastomers and hydrogels. I look forward to seeing your results and a discussion in iMechanica!

Here are answers to your questions:

1) Self-healing is only one advantage of using liquid dielectrics. I think what might be even more or equally important is the ability to have direct electrical control over soft hydraulic actuators, which are incredibly versatile and can achieve a lot of different actuation modes. We are still exploring what we can do with different types of oil with high values of permittivity or dielectric strength, both of which influence Maxwell stress. It is also a nice feature that HASEL actuators can be optimized for a specific application by making use of hydraulic amplification, as we have shown with donut HASEL actuators.

2) We have shown that donut HASEL actuators undergo a pull-in transition, which can be clearly seen from our experimental data. Whether this is a desired feature or not depends on the specific application. Some applications might benefit from bistable behavior (maybe soft mechanical switches or triggers, maybe also valves), other applications do not benefit from pull-in. The design of HASEL actuators is very versatile and we already have versions of these actuators that do not show this type of highly nonlinear response, but react with monotonic, almost linear behavior (which can be a simplifying feature for controls in robotics applications).

Happy new year of the dog!




A new article in national press in Corriere della Sera!

Thu, 2018-02-15 13:49

In reply to Corriere della Sera: recruitment in Italian Academia

See here.  How petition has collected almost 13 000 signatures, including prestigeous names. See the link here

Position Closed

Thu, 2018-02-15 05:05

In reply to Post-doc position (Closed)

Position closed.

Unable to find the job link

Mon, 2018-02-12 17:32

In reply to Postdoctoral Position in FEM Flow Modeling


I am trying to apply for this position but unable to find this job in all job section. Could you please share the application link.



The contact APP received 200 visits in one day, and was fixed

Mon, 2018-02-12 15:44

In reply to A web site APP for rough contact adhesion from simple Ciavarella BAM model

There were some errors in the earlier version, that some people noticed, thank you for help.


Now the APP finds the pull-off force also, and is corrected.

my reply to Dr. Bo Persson

Mon, 2018-02-12 06:58

In reply to a "contact sport" between academics


and Bo, when I say "fractals" are not important, I do NOT mean only the power law PSD, but all multiscale effects are not important, as far as I can see.


It is a pollution in the literature to invade with many articles raising hopes that these multiscale effects have anything predictive at all...But this is just my humble opinion, you certainly now agree on power-law PSD are not relevant, but I do not see why the NON-power law PSD are relevant also!

I understand of course you have valid reasons to promote your nice solutions, also commercially, with which, paradoxically, contains information and diagrams that surfaces are NOT gaussian, so your theory cannot be used anyway.....





Cabboi, Carbone, Persson

Mon, 2018-02-12 02:50

In reply to The debate between me and Bo Persson continues on Researchgate

Michele Ciavarella

  • 39.97
  • Politecnico di Bari

dear Bo I agree your theory is an improvement over GW in some respects, which appear important only when we deal with indeed "fractals", or broad multiscale surfaces. But this doesn't improve our understanding of friction. My main points are (i) that Muser did not answer any of my question, which you can find listed as "12 questions" in ----- please answer. And that your theory does not change anything in terms of actual "prediction" of friction coefficient. Please provide examples where your theory, especially since you have a commercial operation (and this can be considered by many as "pollution" in science and conflict of interest), and therefore you should be able to explain where you solved any real problem with including roughness ----------- this has NOT to include arbitrary cutoff in the fractal description, such as the ridicoulos choice of truncating the spectrum to h' rms=1.3 which you do with viscoelastic friction. RegardsMike

  • 6m ago
  • Delete
  • Edit

Bo Persson

  • 46.66
  • Forschungszentrum Jülich

Hi, I do not like fractals very much either and my theory has really nothing to do with fractals, it only require roughness on many length scales which is true for all surfaces in nature and engineering. In my theory I read in the surface roughness power spectra numerically and I do not care if it is a power low in the wavenumber or not! Still many surfaces is a power low in the wavenumber and can be usefully classified with the exponent! The GW theory does NOT predict the linearity between contact area and normal force and my theory was the first one to do so and even the first version of this theory gives the contact area to within ~ 20% of the exact numerical result. Taking into account all the complications in real life situations (e.g. elastic non-linearity) there is no point in trying to do better! As I have stated before, most articles and comment of Ciavarella are scientific pollution and what he wrote above is a typical example of this.I have only one interest in science: the truth!

  • 2h ago
  • Recommended

Michele Ciavarella

  • 39.97
  • Politecnico di Bari

Alessandro,you are quite rigth to keep at far distance from this useless academic area. My good friend and father of fracture mechanics, Jim Rice of Harvard University, told me that he was sharing the corridor with Benoit Mandelbrot and made friend with him. Only years later did he found that Benoit had published a well known paper in Nature where he claimed that fracture surfaes are fractals!Jim Rice has never used fractals, yet he has dominated the field of fracture mechanics. If fracture surfaces were fractals, or if this were important, Jim Rice would have noticed.Similarly, if the fractality of surfaces were anything like important in tribology, all these speculations about Persson's theory being better than GW, would have produced some progress. And they have.Another big, Ken Johnson, never really got involved into the GW problem, because he mentioned the qualitative results about linearity of contact area and load, in his book, and that was enough for him!Thanks for your interest. You are a promising and clever scientist, don't get the smoke in your eyes, think with your own brain.Mike

The debate between me and Bo Persson continues on Researchgate

Mon, 2018-02-12 02:46

In reply to a "contact sport" between academics

See at this link

6d ago Giuseppe Carboneadded a commentThe reply is also interesting:

  • 1 Recommendation

 5d ago Michele Ciavarellaadded a commentsee also why Muser did not really reply here with 12 questions re explained to Muser who avoided them.....Reply 3d ago Alessandro Cabboiadded a commentHi Michele, I read your comment on Muser's paper and Muser's reply as well. The debate is interesting, and I was wondering if it is still going on. Unfortunately, I cannot give a constructive feedback on both letters since I am keeping myself at a "safe" distance from the topic concerning "fractal…RecommendedReply

  • 3 Replies
  • 2 Recommendations



Dear Christoph,

Sat, 2018-02-10 04:04

In reply to Journal Club for February 2018: HASEL artificial muscles for high-speed, electrically powered, self-healing soft robots

Dear Christoph,

Congrulations on your excellent work. As Zhigang mentioned, you are our admire to push the idea so far!

A few students of Zhigang in China are working on the combination of gel, elastomer and liquid. I'm also involved. Zhigang gave it a beautiful name of GEO. We have been playing with it for quite a while.  I have  two questions:

1. When you add oil in, the advantage you presented is the self-healing property. The idea is really neat. I'm curious that becasue oil can take a much higher value of permittivity than elastomer, so are you able to output a much higher force using oil compared with tranditional dielectric elastomers, such as VHB?

2. We have done some analysis about the pull-in in GEO, although our configuration is not quite similar with yours. So do you think pull-in is an essential feature in your design and why? We mechanics peaple are quite interested at this.




Fri, 2018-02-09 16:06

In reply to Congratulations, Christoph!

Hi Xuanhe,

thank you very much for your positive comments!

I am also very excited that the field of soft active materials is so active and productive now. I think it is important to note that HASEL actuators significantly draw from the advances in soft fluidic actuators. In particular, the Peano-HASEL actuators directly build on the great papers on Peano fluidic actuators [16-18]. Also, in contrast to DEAs, HASEL actuators do not have to rely on elastomers (Peano-HASELs use a thin flexible polymer shell), and the fundamental principles of actuation do not work without the use of hydraulic liquids. Therefore, I think HASEL actuators are best described to synergize the activation mechanism of dielectric elastomers (Maxwell stress) with the versatility and ease of fabrication of soft fluidic actuators, and thus form a new direction of research for artificial muscles.

I am answering your questions below:

1) At the moment we measure energy efficiency of around 20-30% for HASEL actuators (see figure S4 of the Science paper, where we report a cycle with 21%, for an actuator lifting a weight of 100g for >>10% strain). It is important to note that this number is based on a rigorous analysis of electromechanical conversion efficiency of a full cycle in work conjugate planes of force-displacement and voltage-charge (a lot of work in the field of artificial muscles does not consider full cycles when stating efficiency, and it is thus very important to compare numbers with care). The measured efficiency of HASEL actuators is comparable to typical experimental values for DE actuators -- whereas DE actuators have potentially high efficiencies (based on estimates up to 80%) experimentally measured efficiency ranges from 10 to 30%.

A number that is even more important for untethered operation of soft robots is system efficiency (this includes everything coming from the main energy source (such as battery pack), through amplifiers and switches, and finally resulting in mechanical work). In an upcoming paper, we analyze system efficiency of HASEL actuators that are driven by miniature HV electronics. The results will be very important for some practical applications.

2) Yes, high voltage could potentially be a concern for practical applications that are not designed well. I am personally not too worried about the safety aspect; after all, we constantly carry lithium ion batteries with us that can explode -- I think the risk with well insulated and shielded HV actuators is lower than that. As far as practical applications are concerned, we have been very positively surprised by the strong reaction to our papers from a range of different industries, and from companies representing several hundred thousand employees. We are already funded by a large car manufacturer to explore active surfaces based on HASELs, which could find use both inside and outside of the car. Peano-HASELs are attractive for robotic applications, due to their ability to linearly contract upon application of voltage without relying on stacked configurations or prestretch. Additionally, HASELs will find use in various types of haptic interfaces, life-like prosthesis, valves, pumps, vibration control, positioning systems and basically everything else that requires silent, efficient, lightweight, soft, inexpensive and high-speed actuators.

Yes, we made direct use of your invention in the area of tough bonding of hydrogels -- It feels great to build upon groudbreaking work from friends!

Thank you!



A new book in Contact Mechanics

Fri, 2018-02-09 14:03

In reply to a "contact sport" between academics

The topic of Contact Mechanics and also rough surfaces is covered in this book by J R Barber about to appear.



The references for the excellent works of Molinari at EFPL

Fri, 2018-02-09 13:12

In reply to a "contact sport" between academics


 you should mention that we strongly refer to recent excellent work of the group of J. F. Molinari at EPFL in top journals.


 Critical length scale controls adhesive wear mechanismsR AghababaeiDH Warner, JF Molinari - Nature communications, 2016 - [CITATION] Achard got it right: insights from a cohesive model (invited workshop)JF MolinariR Aghababaei… - CECAM Workshop, he …, 2016 - On the debris-level origins of adhesive wear…, DH Warner, JF Molinari - Proceedings of the …, 2017 - National Acad Sciences Mechanics of surfaces: a new look at the old problem of wear…, DH Warner, JF Molinari - Tribology & Lubrication …, 2017 -  and some more recent papers which JF Molinari kindly gave us in advance, as they are still under review.

The adhesion paradox in wear law

Fri, 2018-02-09 12:59

In reply to a "contact sport" between academics

A very debated topic nowadays is wear, which still remains one of the major unsolved problems in tribology. We are almost stuck at the Reye's hypothesis (1860) as also the more recent Archard's law seems to be in contradiction with recent experiments. Recently some attention has been paid to the Rabinowicz criterion, which is based on the competition between plasticity and adhesion. Unfortunately, the most of the papers on "adhesive wear" do not consider adhesion for determining the actual contact size!

We have addressed this problem here:

Abstract:In a recent paper in Science, namely, “The Contact Sport of Rough Surfaces”, Carpick summarizes recent efforts in a “contact challenge” to predict in detail an elastic contact between the mathematically defined fractal rough surfaces under (very little) adhesion. He also suggests the next steps that are needed to “fulfill da Vinci’s dream of understanding what causes friction”. However, this is disappointing as friction has been studied since the times of Leonardo and in 500 years, no predictive model has emerged, nor any significant improvement from rough contact models. Similarly, a very large effort we have spent on the “sport” of studying rough surfaces has not made us any closer to being able to predict the coefficient of proportionality between wear loss and friction dissipation which was already observed by Reye in 1860. Recent nice simulations by Aghababaei, Warner and Molinari have confirmed the criterion for the formation of debris of a single particle, proposed in 1958 by Rabinowicz, as well as Reye’s assumption for the proportionality with frictional loss, which is very close to Archard anyway. More recent investigations under variable loads suggest that Reye’s assumption is probably much more general than Archard’s law. The attempts to obtain exact coefficients with rough surfaces models are very far from predictive, essentially because for fractals most authors fail to recognize that resolution-dependence of the contact area makes the models very ill-defined. We also suggest that in the models of wear, rough contacts should be considered “plastic” and “adhesive” and introduce a new length scale in the problem.

See an example review of the Kassapoglou paper

Thu, 2018-02-08 12:37

In reply to Mike, as I said previously, I


 see an example of the reviews I get for the Kassapoglou paper.  They are not to the point, and innovation is needed on this aspect, more than on the aspect you suggest.


Commenting on literature models can be of some interest, however criticisms without suggesting a better alternative is not of much help to improve the knowledge of the scientific community.
The Kassapoglou model under scrutiny is proposed to derive the cycles to failure, as a function of R, for composites under fatigue loading. This may be indeed meaningless and not helpful for the (safe) design of composite structures. The final failure of a composite laminate is typically related to the failure of load bearing plies. However, this is only the last catastrophic event of the damage evolution into the material, which begins very early in the fatigue life with the formation of transverse cracks followed by delamination. Damage evolution is associated with a dramatic stiffness loss, which is indeed in most of the cases the reason why the component is not responding anymore to the design requirements and has to be considered “failed”. This scenario is known since the 80s thanks to the pioneering studies of Jamison, Schulte, Reifsnider and Stinchcomb at Virginia Tech, however neither the Kassapoglou model not the comments included in this paper account for this evidence.
In view of the point above, this reviewer sees a very limited value and interest for both the Kassapoglou model itself and the scrutiny discussed in this paper. The extensive discussion on the limits of the statistical analysis of the K model and the reliability of predictions based on static strength values loose significance because the prediction is not considering at all the damage evolution and the associated stiffness loss which may be indeed very different depending on a number of parameters. Just to name a few, one should consider the effects on fatigue response of reinforcing fibers, lay-up, type of loading, load ratio, environment, defects and so on.
After the research program at Virginia Tech,  (see, as a representative example, Jamison, R. D., Schulte, K., Reifsnider, K. L., and Stinchcomb, W. W.,. "Characterization and Analysis of Damage Mechanisms in Tension-Tension Fatigue of Graphite/Epoxy Laminates," Effects of Defects in Composite Materials, ASTM STP. 836, American Society for Testing and Materials, 1984, pp. 21-55.) huge experimental efforts were devoted to understand the mechanics of the fatigue damage evolution. The outcomes are rather clear and conclusive and the literature available on the subject is endless.
Based on this body of knowledge, very recently interesting attempts have been made to develop physics – based design approaches to fatigue oriented to predict the formation of damage and its evolution , see for instance:
Hosoi, Sakuma, Fujita , Kawada, Prediction of initiation of transverse cracks in cross-ply CFRP laminates under fatigue loading by fatigue properties of unidirectional CFRP in 90_direction. Composites: Part A 68 (2015) 398–405
J. Montesano, H. Chu, C.V. Singh , Development of a physics-based multi-scale progressive damage model for assessing the durability of wind turbine blades. Composite Structures 141 (2016) 50–62
J.A. Glud , J.M. Dulieu-Barton , O.T. Thomsen, L.C.T. Overgaard , A stochastic multiaxial fatigue model for off-axis cracking in FRP laminates. International Journal of Fatigue 103 (2017) 576–590
R.D.B. Sevenois , D. Garoz , F.A. Gilabert , S.W.F. Spronk, W. Van Paepegem, Microscale based prediction of matrix crack initiation in UD composite plies subjected to multiaxial fatigue for all stress ratios and load levels. Composites Science and Technology 142 (2017) 124-138
Several methods have been also made available to quantify the stiffness change based on a certain damage state, quantitatively measured by the crack density and delaminated area. Few examples are:
Junqian Zhanga, K. P. Herrmann, Stiffness degradation induced by multilayer intralaminar cracking in composite laminates. Composites: Part A 30 (1999) 683–706
L.N. McCartney, Model to predict effects of triaxial loading on ply cracking in general symmetric laminates. Composites Science and Technology 60 (2000) 2255-2279
P. Lundmark, J. Varna,  Constitutive Relationships for Laminates with Ply Cracks in In-plane Loading. International Journal of damage mechanics, 14 (2005) 235-259
C. V. Singh, R. Talreja , A synergistic damage mechanics approach for composite laminates with matrix cracks in multiple orientations. Mechanics of Materials 41 (2009) 954–968
As a final comment, the physics – based methods are much more reliable and promising than those cited by the authors in refs. [21-23] and this is the approach the community and the industry should follow rather than base the design on phenomenological fittings which are by definition not reliable and most of all not of general validity!


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