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Updated: 22 hours 48 min ago

Please notice change in Zoom link

Thu, 2020-05-28 18:43

In reply to Northwestern University - TAM Webinar



To enable a larger number of attendees, this webinar has been moved to:


Zoom Webinar Link:





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Tendons and Ligaments, Nonlinear Hereditariness

Sun, 2020-05-24 10:47

In reply to Fractional-order nonlinear hereditariness of tendons and ligaments of the human knee

In this paper, the authors pointed out the main features of a wide experimental campaign devoted to investigate the mechanical behaviour of knee tendons subjected to long-standing loads. The results of the experimental campaign show that creep and relaxation behaviour of the tendons may be well captured by power laws in the ranges of strain (1–5%) and stress (0–16 Mpa) considered.

The order of the power law proved to be different between creep and relaxation proving that some form of nonlinearity is involved in the micromechanics of the tissue so that no linear theory of fractional hereditariness may be used to capture the mechanics of tendons. Moreover, it has been observed that the material parameters are significative dependent on the applied stress in creep tests as well as on the applied strain during relaxation.

These features, already observed in other mechanical tests in the last 20 years, have never been conducted in combination on human tendons, yielding one to conclude that the finding relaxation runs faster than creep is valid also on human knee patellar and hamstring tendons.

Based on this observation, the paper was devoted to the introduction of an analytical model to describe creep and relaxation showing that some closed-form expression relating creep and relaxation parameters could be established.

Direct comparison among results of such expressions and the measured values showed excellent matches with slight coefficient of variations and, in order to show that such relations hold whatever kind of test is considered, a numerical validation has been introduced with other than constant value of the applied strain (stress), namely linear and harmonically varying strain (stress).

The obtained results showed excellent match among the initial and the recovered values of the applied stress (strain) leading one to conclude that the proposed relations may be a benchmark to provide clinical support to the surgeons that apply pre-stress to the tendons before surgical replacement to reconstruct anterior cruciate ligaments functionality.

Hi Tongqing, Congratulations

Thu, 2020-05-21 21:38

In reply to Mechanics of Dielectric Elastomer Structures: A review

Hi Tongqing, Congratulations on the timely and informative review! 


Thu, 2020-05-21 14:13

In reply to How can I calculate "Transverse Shear Stiffness" for shell and beam elements?

 G shear modulus

t thickness

Congratulations, Tongqing!

Thu, 2020-05-21 13:05

In reply to Mechanics of Dielectric Elastomer Structures: A review

The review collects new developements. Timesly!

Reply to Qi

Thu, 2020-05-21 09:28

In reply to Dear Ajit,

Dear Qi,

Thanks for your reply.

Following the best-practices advice, so far, I had always used the odd-sized kernels---except for the last layer (which fact I had figured out on my own). For yet another reference, I in the meanwhile recollected what Dr. Adrian Rosebrock said here [^].

That's why, it was a bit interesting to note that you didn't actually see aliasing effects.

To figure out why, I decided to take a fresh look at the maths involved.

Looks like, contrary to the received opinion, as far as the strictly sequential models go, the difference between the odd- vs. even-sized kernels should not make a substantial difference, provided that the number of convolutional parameters stay comparable (between purely convolutional models employing odd- vs. even-sized kernels). That's what the maths seems to say. In the strictly sequential models of machine learning, the issue of symmetry vs. asymmtry should not arise. Of course, I haven't put this implication to an empirical test yet. (No time at hand.) But it does seem to justify what you say, though, of course, this again is a justification after the fact!

What about the non-sequential models like those with, say, the skip-connections? (Or, even just with concatenating layers?) Here, the rough-and-ready maths suggests that the odd-sized (symmetrical) kernels should learn better than the even-sized ones, provided that the image size stays the same. To what extent should the learning be better? The rough-and-ready maths offers no rough-and-ready answer! But a good hypothesis, this one should make for. Of course, once again, empirical evidence is required. (There was no reason why 'ReLU's should have worked better than the tanh or the sigmoid, until they figured it out how it actually works! That is, after the fact!) Hope some UG/PG student of CS decides to take a systematic look at it.

Anyway, this has been a definitely useful discussion for me. Threw light on something I had not separately looked into. So, thanks for sharing your observations and all.


Dear Ajit,

Mon, 2020-05-18 20:53

In reply to Re: GAN for designing complex architectured materials

Dear Ajit,


Thanks for your comments! Great points. The hyperparameters of the convolutional neural networks are highly dependent on the designers. The main point here is to illustrate GAN's idea in architectured materials' design instead of benchmark for machine learning performance. For our case, the even kernel size works well, and aliasing effects did not happen. However, we do believe that it would achieve a better result with a more complex network, i.e., symmetric kernels, VGGNet, ResNet-50, or even ResNeXt. We will try them in our future works to see whether there are any differences. Thank you for your advice. The methodology here is general and applicable to other properties. 




VAM Related Query

Sun, 2020-05-17 16:34

In reply to VABS, A Unique Tool for Modeling Composite Beams

Respected Professor,

I know i am bit late to add to this discussion but Please reply if possible as i am knew to VAM and really want to learn.

While going through your papers (''Asymptotic construction of Reissner-like composite plate theory with accurate strain recovery'' and few others) ,I noticed that you ususally do some transformation into reissner model although in the Neoclassical plate theory by Hodges ("Application of the Variational-Asymptotical Method to Laminated Composite Plates") they included the shear strain in the 3-D strain term itself ,In the similar manner 3-D elasticity formulation is done in a paper by Peereswera of inter-laminar stresses in composite honeycomb sandwich panels under mechanical loading using Variational Asymptotic Method) 

So i just want to understand are these two different theories or the same ,if same then why do we need to go through transformation part. 

also some links in above discussion doesn't work any more if possible plase provide updated links.

Re: GAN for designing complex architectured materials

Fri, 2020-05-15 15:02

In reply to Designing complex architectured materials with generative adversarial networks

Dear Xuanhe,

1. Interesting! A great deal of work seems to have gone into it!!

2. I mostly skipped on the materials/mechanics side (the topic isn't familiar to me). However, there is a bit of an oddity which I spotted on the neural networks' side.

3. For the discriminator, your first and second convolutional layers have the kernel size of 4 X 4. Using an even number for the kernel seemed a bit odd to me!

If you use even numbers for the kernel size, it leads to asymmetric kernels. These can potentially introduce aliasing effects. (For some explanation, see, for instance, this Q&A at the Data Science StackExchange [^].)

Within the odd-sized kernels, for general-purpose image recognition (say CIFAR and all), it seems that the recent trend is to go in for deeper architectures and smaller kernels, like 3 X 3 or 5 X 5.

So, it might be worth running a few trials with such odd-sized kernels.

4. Another point. If your initial convolutional and pooling operations go on reducing the image size in such a way that your last Conv layer happens to have a 4 X 4 input size, then it's OK to go in for a 4 X 4 kernel too. Such a Conv layer is going to produce just 1 pixel, and so, the considerations of symmetry vs. asymmetry cease to apply. I don't know for sure, but I do think that symmetry and all should be important only if another Conv layer is going follow a given Conv layer.

5. But yes, all in all, highly inter-disciplinary, nah, multi-disciplinary work. I appreciate it.



PS: Can't resist! A fun thought occurred to me. Why not try Penrose tiles and see if anything interesting gets thrown up---whether during the learning phase or for the predictions---or for properties (Schachtman)? ... Just an idle musing...



Thu, 2020-05-14 17:50

In reply to NEWFRAC ITN Consortium on Fracture Mechanics



Thu, 2020-05-14 17:48

In reply to NEWFRAC ITN Consortium on Fracture Mechanics


Available immediately

Thu, 2020-05-14 07:32

In reply to Fully funded MS/ PhD position

Available immediately

The deadline for applications

Tue, 2020-05-12 16:35

In reply to Call for Associate Editors for the first Overlay Journal in Mechanics

The deadline for applications has been postponed to the 1st of June 2020.
We are looking forward to receiving your applications!

Thanks for sharing

Tue, 2020-05-05 12:26

In reply to Northwestern University - TAM Webinar

Dear Horacio, 

Thanks for the sharing this. I am looking forward to the webinar. 



Tue, 2020-05-05 09:58

In reply to Bioinspired Materials with Self‐Adaptable Mechanical Properties

Dear Santiago,

   Wonderful idea. Thank you very much for the detail answer. I don't have further questions.


Best Regards,


Thank you!

Mon, 2020-05-04 19:50

In reply to Congrats on the new job,

Thank you, Xueju! Also congratulations to your start of a successful career at Mizzou. I look forward to knowing more about your new research!

Congrats on the new job,

Mon, 2020-05-04 19:37

In reply to PhD Openings in Data-driven Multiscale Modeling

Congrats on the new job, Haoran!

Dear Lixiang,

Mon, 2020-05-04 19:10

In reply to Interesting

Dear Lixiang,

Thank you for your interesting question, and for reading our work.

Yes, bone becomes stiffer with increase of external load. The general principles of bone adaptation to mechanical stress apply to both cortical and trabecular bone. The law that describes this behavoir is called Wolf's Law. Bone remodels on regions of high mechanical stress. Clinically, this has been observed as increased in BMD.

In our experiments, we did not test bone samples. We used a piezoelectric polymer serving as scaffold that generated signal (charges) for mineral formation. We showed that the higher electrical charged at the surface (produce by higher external mechanical load) the more mineral will form.  The change of modulus occurrs due tto the increased formation of mineral in proportion to the external force.


Feel free to let us know whether you have additional comments/questions.

Stay well,


Sun, 2020-05-03 22:22

In reply to Bioinspired Materials with Self‐Adaptable Mechanical Properties

Hello Dear All,

    Thank you for sharing your interesting work. I am trying to understand your paper.  Can I ask you a question?

    You mentioned bone gets stiffer under external loading. Will mineral substance inside bone change under external loading? How?  In your experiments, is there an assumption that bone is tested as  the piezoelectric beam?  Is Young's modulus change of piezoelectric beam or bone related to more mineral substance on the beam surface or inside?

Thank you very much.



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