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Pastewka and Robbins criterion is found clearly wrong at last

Mon, 2021-02-22 01:01

In reply to On Pastewka and Robbins' Criterion for Macroscopic Adhesion of Rough Surfaces

We recently found that Pastewka and Robbins criterion, on which we were always suspicious about the "fractal limit", is indeed wrong, as the numerical observations are limited to very narrow surface roughness spectra, and PR criterion is in contrast with results of BAM of Ciavarella, Persson-Scaraggi, and Persson Tosatti.

See here:


Universal features in “stickiness” criteria for soft adhesion with rough surfacesAuthor links open overlay panelM.CiavarellaShow moreAdd to MendeleyShareCite rights and content Highlights


We derive a stickiness criterion from the simple Persson and Tosatti theory of adhesion of rough solids.

We derive another stickiness criterion from the BAM (Bearing Area Model) theory of Ciavarella.

We compare the two derived new criteria with that Violano et al., and Pastewka and Robbins and Muser.

We find Persson–Tosatti, BAM, and Violano criteria give very close results, and are mainly dependent on macroscopic quantities, while Pastewka and Robbins and Muser criteria differ from the previous three in that they depend on the truncation of the spectrum of roughness.


On cavitation

Tue, 2021-02-16 14:18

In reply to The poker-chip experiments of Gent and Lindley (1959) explained

Dear Oscar,

This is an interesting paper yet the idea of cavitation as a damage (rather than purely elastic) phenomenon is not that new. Here are papers on the topic, which were published quite a few years ago:

Volokh KY (2011) Cavitation instability in rubber. International Journal of Applied Mechanics 3:29311

Lev Y, Volokh KY (2016) On cavitation in rubberlike materials. Journal of Applied Mechanics 83:044501

Faye A, Rodríguez-Martínez JA, Volokh KY (2017) Spherical void expansion in rubber-like materials: the stabilizing effects of viscosity and inertia. International Journal of Non-Linear Mechanics 92:118-126

Best regards,


to be connected to the Ferrari Formula 1 seminar, declarations!

Sun, 2021-02-14 13:26

In reply to world first ONLINE webinar of Ferrari Formula 1 Head of Stress unit - Politecnico di BARI


Tomorrow there is large request to access the Ferrari formula 1 seminar, you are invited, but you are requested to declare that you will not take pictures, photos, videos or interviews.


Sat, 2021-02-13 21:42

In reply to Re: Dynamic solid-liquid interaction


Glad you like this discussion topic. Thanks much for raising these two excellent questions, and my thoughts are below

1. Yes, there might be a size effect when the thickness of film is down to several nanometers due to surface strain/stress of nanofilm. This size effect could influence both the calculation of mechanical energy such as bending and elongation energies and the measurement of contact angle between solid-liquid. However, it is not expected to affect the application of the energy balance theory between film and substrate at the steady state of transfer because of the associated constant bended configuration of film and the stable contact status with liquid at the transfer front.  In our experiments, we demonstrated the transfer of film with thickness as small as 1 um, and the transfer forces for both push-down and pull-up transfer directions showed good agreement with both theoretical predictions and FEA. For a very large film, this proposed transfer technology and mechanics theory are also expected to be applicable, but you need to ensure first that film floats on the surface of liquid before the start of transfer. 

From the theoretical point of view, when the film is extremely soft, the solid-liquid interaction at the transfer front is expected to lead to local mechanical deformation in film along its thickness direction, similar to the discussion in the cited literatures in our paper such as Phys. Rev. Lett. 122, 248004 (2019); Phys. Rev. Lett. 106, 186103 (2011); Nat. Commun. 6, 7891 (2015). This local deformation will also affect the measurement of contact angle that is one of important parameter for our transfer technology. Taking account of these local deformation of extreme soft films in theory will be helpful for broader applications of the proposed transfer technology, but could be minimized by selecting the most suitable liquid phase as a partner. 

In addition, a strong size effect is expected for solid-liquid interactions in a nanoconfined environment such as nanofluidics where the double layer structures are largely overlapped. This size effect is closely associated with nanoconfinemental environments and is usually independent of either solid or liquid phase. How to leverage this intrinsic size effect of solid-liquid interactions for future design and manufacturing of materials and structures is crucial.

2. Yes, gas phase is critical, for example, as the evaporation continues, the 2D sheets will be mitigated to the surface of droplet and are exposed to vapor, which leads to the appearance of capillary force at the solid-vapor-liquid interface. The evaporation also results in a recoil force at the liquid-vapor interface squeezing the interface toward the liquid side. In our mechanics analysis, because the capillary force changes its direction dynamically with the free motion of 2D sheets in droplet, along with other forces/pressures led by such as capillary flow, vapor recoil and vapor pressure, we developed a unified equivalent evaporation pressure model to describe their contributions to crumpling and assembling of 2D sheets.

The assembling process reflects the competition between solid-solid and solid-liquid interactions. For example, for multiple 2D solid sheets, at the early stage of evaporation, solid sheets are far from each other, and the assembling process is dominated by solid-liquid interactions. As the evaporation goes on, the solid sheets become closer, and the solid-solid interaction between 2D sheets (crumpled 2D sheets) will appear, i.e. the intra-layer slider in our rotational spring-mechanical slider model needs be to included. With the further evaporation of liquid, solid-solid interactions will become dominative for the assembling until a dry assembled solid particle forms after the complete evaporation of liquid where only solid-solid interactions exist. The competition between solid-solid and solid-liquid interactions and their dominative role can be determined by comparing the energies between rotational springs and mechanical sliders, as we did in the paper. Also note this assembling process is similar to that of rigid particles in traditional colloidal science, but our mechanical model takes into account mechanical deformation of particles (here 2D sheets) and can easily reduce to classic assembly theory when deformation is allowed (i.e. the constant of rotational spring in the spring model is sufficiently large) which we have demonstrated in our paper.    

Hope these explanations are helpful. Feel free to share your work, especially your work in solid-liquid interactions in nanoconfinements, by posting your relevant publications here if I forgot to cite them in the above references.  



Re: Dynamic solid-liquid interaction

Thu, 2021-02-11 10:31

In reply to Journal Club for February 2021: Deformation, instability, and assembly of materials by dynamic solid-liquid interactions

Yue, Qingchang, and Baoxing,

Great work on this important topic. Your findings are of great importance for the understanding of the interaction between dissimilar materials/components at the solid-liquid interface and will benefit the development of advanced materials and structures. I have two follow up questions and seek your insight.  

1. Is there any size effect on the energy balance between the soft film and the substrate? The fabrication example is at mm scale. Are your findings applicable to film transfer at a much larger or smaller sacle?

2. Does gas-phase play a role in the crumpling process? At the solid-liquid interface, all three phases, i.e. the gas, liquid, and solid phases, exist. Is this assembling process dominated by solid-liquid interaction only?

I look forward to reading your future works and your valuable comments. Thank you for sharing the journal club with us. 





prof. Rob McMeeking, Timoshenko Medal, signs the online petition

Wed, 2021-02-10 01:23

In reply to online petition for basic research funding in Italy

Thanks to Rob for being one of the original promoters of this initiative.  Ad Maiora.

Chiara Daraio signs the online petition for italy

Tue, 2021-02-09 01:30

In reply to online petition for basic research funding in Italy

Thanks to Chiara for being one of the original promoters of this initiative.  Ad Maiora.

Abaqus Built-in materials

Sun, 2021-02-07 05:22

In reply to ABAQUS built-in material models

You can find all the files with a step-by-step training video here:


Youtube link to the talk

Fri, 2021-02-05 20:34

In reply to Special webinar by Professor Davide Bigoni

The recorded video of the talk can be watched here:

The meeting has moved to the

Wed, 2021-02-03 12:40

In reply to Special webinar by Professor Davide Bigoni

The meeting has moved to the below zoom link:

ID riunione: 938 6994 8764

Passcode: 831229 

regarding Damage model

Wed, 2021-01-27 10:35

In reply to UMAT subroutine in ABAQUS for elasto-plastic cyclic loadings

Dear Bojan,

I am also working on a damage model and if you get this UMAT, I'd really appreciate it if you share it with me as well.


Programming the Finite Element Method in English & Chinese

Wed, 2021-01-20 06:38

In reply to Free Finite Element Programs in Fortran 95

Just a note to advise that this book was updated to the 5th Edition a few years ago and has also been translated to simple Chinese.,+5th+Edition-p-9781119973348

Last update on this thread...

Wed, 2021-01-13 15:52

In reply to A preliminary document on my fresh new approach to QM

1. Check out this one status at:

2. No, I'm not currently in a mood to update this one, updated last year, on 25 May 2020:

I am still jobless. You should LOVE Indian IT industry. No, You MUST! The way you ALWAYS did!

3. Check the MONEY you made last year.

4. Bye for now.






Dear Mohammed,

Sun, 2021-01-10 22:47

In reply to Fourth dimension

Dear Mohammed,

Thanks for your great question and sorry for my delayed reply!

First of all, I want to clarify that the example I present here about 3D printing with liquid crystal elastomer is not 4D printing. We demonstrate an example about harnessing the energy dissipation behavior of LCE during the phase transition between the monodomain state and the polydomain state [1]  to print 3D lattice structures that could absorb energy upon impacts. Therefore, in our printed 3D structures, the LCE mesogens are randomly arranged as organized liquid-crystalline domains with varying alignments.

Besides 3D printing energy absorbing structures, LCEs have also been widely used to print soft actuators and robots. The pioneering works include 4D printing with LCEs presented by Prof. Taylor Ware’s group [2, 3] and untethered soft robots by 3D printing LCEs from Prof. Jennifer Lewis’ group [3]. The printed actuators and soft robots exhibit free-standing actuation due to the phase transition between the monodomain state and the isotropic state. Therefore, aligning the mesogens into monodomain is the key to realizing the free-standing actuation of the printed structures. So far, the 4D printed structures made of LCEs are mainly printed using DIW-based 3D printing which aligns the mesogens through the shear force during the extrusion-based printing process. 


Hope my reply helps.






[2] Ambulo, C. P.;  Burroughs, J. J.;  Boothby, J. M.;  Kim, H.;  Shankar, M. R.; Ware, T. H., Four-dimensional Printing of Liquid Crystal Elastomers. ACS Applied Materials & Interfaces 2017, 9 (42), 37332-37339.

[3] Saed, M. O.;  Ambulo, C. P.;  Kim, H.;  De, R.;  Raval, V.;  Searles, K.;  Siddiqui, D. A.;  Cue, J. M. O.;  Stefan, M. C.;  Shankar, M. R.; Ware, T. H., Molecularly-Engineered, 4D-Printed Liquid Crystal Elastomer Actuators. 2019, 29 (3), 1806412.

[4] Kotikian, A.;  McMahan, C.;  Davidson, E. C.;  Muhammad, J. M.;  Weeks, R. D.;  Daraio, C.; Lewis, J. A., Untethered soft robotic matter with passive control of shape morphing and propulsion. 2019, 4 (33), eaax7044.


Timoshenko Cantilever Beam Free vibration

Thu, 2021-01-07 13:33

In reply to Timoshenko beam free vibration analysis

is anyone know about Timoshenko Beam Free vibration MATLAB programe

Fourth dimension

Wed, 2021-01-06 16:17

In reply to Journal Club for January 2021: 3D Printing of Soft Materials

Dear Kevin,

Thank you for this valuable work.

Is the fourth dimension information introduced randomly in the 3D printer like you have cited for Lattice configutations in liquid cristal elastomers for the 4D printing ? We can get unexpected resulting structures in this case.




Dear Kevin,

Wed, 2021-01-06 11:02

In reply to Dear Zhijian,

Dear Kevin,


Thank you for such a helpful reply!




An update concerning the development of my new approach to QM

Wed, 2021-01-06 06:00

In reply to A preliminary document on my fresh new approach to QM

Hi all:

Just an update. It's perhaps too detailed, but guess it's good to leave a record of where things stand, as of today...

1. Theoretical development for the spinless massive particles is over:

I think that, by last night (India time), I had satisfactorily resolved all major theoretical issues pertaining to understanding a quantum system of two spinless electrons, using my new approach to QM. This included the tricky issues such as: (1) quantitative predictions for the motions of particles, and (2) the issue of how the system wavefunction, defined as it is over the $3N$-dimensional configuration space, relates to the physical fields I have posited as existing only in the $3D$ physical space.

2. There are significant changes from the above document:

There are considerable changes and revisions to be made to the theoretical positions/explanations mentioned in the above-mentioned PDF document (attached to the main post here).

Indeed, rather than revising the above document, I now plan to write, completely fresh, a set of two new documents, and to upload their initial versions here at iMechanica. The two documents will be posted in separate posts (and not right in this thread, though I will provide a link from here).

The first of the two planned documents will address the spinless, massive elementary particles (electrons &/or protons). The second document will then add the considerations arising due to the quantum spin, and further modify the description as necessary. As of today, I do not plan to address detailed theory/computational modelling for photons at all.

Although there are a lot of changes necessitating a completely fresh write-up for my new approach, many of the points mentioned in the above documents are found to hold well. Some of these have been of crucial importance too.

3. Time estimates:

The estimate for completing the new planned document on the spinless particles, together with its accompanying Python code, is about two months, i.e., by February 2021-end. As of today, I am not clear when the second (i.e. spin-related document) may get completed, though I do already have a lot of material ready for it too.

As to the spinless particles:

I've already implemented the hydrogen atom in a 3D box, but the helium atom will be the first important test for my new approach. I can only hope that the results turn out to be satisfactory. One of the important reasons I say "hope" is because there are certain tricky issues, discussed below.

4. A problem area:

Although the theory of the new approach is now quite fully clear (at least for the spinless particles), I've noticed that a lot of subtle issues come up in computationally modeling and solving the eigenvalue equations.

For eigenvalue computations, I use the SciPy sparse-array functions, and sometimes also verify these results using LinAlg's dense-array functions (which is only feasible for very small systems).

While modelling the hydrogen atom in a 3D box using these libraries, I have observed that the reported eigenvalues are unduly sensitive to the mesh size.

One important reason may be that while the Coulombic field is theoretically singular, the finite difference approximation can work only with a finite depth for the potential energy well.

The relative coarseness of the mesh also should be an issue, simply because there must be discontinuities even in the first-order spatial derivatives in FDM, and if the discrete jumps in the gradients are too high, the eigenvalue solver wouldn't be able to respond very well. For instance, I have observed that with even small changes in the mesh count, e.g., just from 50 nodes per side of the simulation cube to 52 nodes, the ground-state eigenvalue changes a great deal: from about -0.48 hartree to -0.21 hartree or so, a difference of more than 200 %! For comparison, the analytical solution is available; it's -0.5 hartree, exactly. The physical side of the box in all cases was 1 nm (i.e. almost 18.7+ Bohr radii).

So, the FDM may not be the idea method to use for this problem, in this regime of mesh refinement. On the other hand, my laptop doesn't have capacity to handle adequately refined mesh (say 500, 1000, or 2000 nodes per side).

5. My planned course of action:

My current plan is to pursue the simplest possible numerical techniques, so that I can better focus attention on showing how the new approach can at all be used. The objective is to make the theoretical structure of the new approach clear, even if the numerical results aren't all that satisfactory.

This means continuing to use FDM and the readymade Python libraries, at least until the first of the new planned documents is completed.

For the same reason, I am postponing any studies/implementation of the mainstream QM techniques, esp. the variational method.

6. Other factors:

Much of the uncertainty concerning this entire project arises from the aforementioned kind of computational aspects alone.

Any other major issues, if they become "show-stoppers", will be noted via a further comment at this thread. (Such things can also include RSI (repetitive injury syndrome) which has affected me for the last 3--4 months. It has reduced a lot by now, but if it aggravates once again, there will be further delays.)

7. I am taking this up on priority:

I am now getting going with computational implementation for modelling the helium (He) atom in 1D and 3D boxes, using my new approach, starting right today.

(However, potential employers need not wait for its completion. I would be able to implement everything on a part-time basis, say purely on week-ends, and still be able to keep the schedule mentioned in this update.)

8. Request to you:

If you know of any 1D or 3D implementations (esp. in Python or C/C++) for the He atom, then kindly alert me to them. I could use perhaps use them for benchmarking purposes.

Otherwise, kindly hold your comments, questions etc., until the initial version of the first document is uploaded. Thanks in advance. (You won't have to wait for any more than two months now! Contrast: The above document was uploaded almost two years ago.)

Wish you all a very happy, productive, and prosperous new year!



Dear Zhijian,

Tue, 2021-01-05 22:31

In reply to 4D printing of shape memory polymers

Dear Zhijian,

Thank you very much for raising this challenging but important question. As you mentioned, the shape memory polymers can be classified into two types: (1) one-way SMP which requires an external stimulation to reprogram the shape memory effect (SME) again after the SMP return the original shape from the temporary shape. One-way SMP is the main type that has been applied to 4D printing, but its disadvantage is obvious since it also requires the external load to reprogram the SME. (2) The two-way SMP (2W-SMP) which can switch the original and temporary shapes cyclically upon heating-cooling without reprograming.

In the last two decades, many efforts have been made to develop 2W-SMP [1, 2]. However, in the early years, the 2W-SMP requires a constant external force to realize the 2W-SME, and the 2W-SME cannot be completed after the removal of external force. This is called the quasi two-way SMP. The applied external force greatly limits the application of quasi two-way SMPs in various fields. Therefore, more researches focus on the study of 2W-SMP under stress-free conditions. The free-standing 2W-SMP is realized mainly through the idea of defining the orientation of the crystallization induce elongation (CIE) [3-6]. However, so far, I haven’t seen any work that reports 4D printing of 2W-SMP. I think that the key challenges include (i) how to make the 2W-SMP printable. For DLP based 3D printing, how to make the 2W-SMP precursor UV curable while maintaining relatively low viscosity (less than 10 Pa·S) is the key; for DIW based 3D printing, how the make the 2W-SMP precursor have the shear-thinning effect is the key. (ii) How to define the orientation of the CIE . Although the free-standing 2W-SMP does not need external load during actuation, it still requires the application of an external load to define the orientation of CIE. Then, the question is how and when to apply this external load when we print 2W-SMP?

To realize 4D printing of 2W-SMP isn’t easy but would be very impactful, we are looking forward to the breakthrough in the near future.





1. Chung, T.;  Romo-Uribe, A.; Mather, P. T., Two-Way Reversible Shape Memory in a Semicrystalline Network. Macromolecules 2008, 41 (1), 184-192.

2. Zhao, Q.;  Qi, H. J.; Xie, T., Recent progress in shape memory polymer: New behavior, enabling materials, and mechanistic understanding. Progress in Polymer Science 2015, 49-50, 79-120.

3. Behl, M.;  Kratz, K.;  Zotzmann, J.;  Nöchel, U.; Lendlein, A., Reversible Bidirectional Shape-Memory Polymers. Advanced Materials 2013, 25 (32), 4466-4469.

4. Yang, G.;  Liu, X.;  Tok, A. I. Y.; Lipik, V., Body temperature-responsive two-way and moisture-responsive one-way shape memory behaviors of poly(ethylene glycol)-based networks. Polymer Chemistry 2017, 8 (25), 3833-3840.

5. Zhou, J.;  Turner, S. A.;  Brosnan, S. M.;  Li, Q.;  Carrillo, J.-M. Y.;  Nykypanchuk, D.;  Gang, O.;  Ashby, V. S.;  Dobrynin, A. V.; Sheiko, S. S., Shapeshifting: Reversible Shape Memory in Semicrystalline Elastomers. Macromolecules 2014, 47 (5), 1768-1776.

6. Jin, B.;  Song, H.;  Jiang, R.;  Song, J.;  Zhao, Q.; Xie, T., Programming a crystalline shape memory polymer network with thermo- and photo-reversible bonds toward a single-component soft robot. Sci Adv 2018, 4 (1), eaao3865.


4D printing of shape memory polymers

Tue, 2021-01-05 00:36

In reply to Journal Club for January 2021: 3D Printing of Soft Materials

Dear Qi,

Thanks for your summary. Fantastic work! Now, in 4D printing of shape memory polymers, we still need to apply external force to make the printed structure memorize the shape. I am curious whether it is possible to print a structure of two-way shape memory polymer which can deform immediately under external stimuli. Just like the work that have been done in hydrogels and liquid crystal elastomers. 




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