Tag Archives: science

About Tsai-Wu failure criterion

Predicting material failure is always a challenge, especially when it comes to composites and advanced materials. There are plenty of theories that try to provide a numerical approach to solve this complex problem, such as Maximum Stress/Strain Theories,¬† Hashin, Tsai-Hill or Tsai-Wu. Although all of them brought something valuable to the table, some of them don’t seem to be that precise when accurate results are needed. In these terms, Tsai-Wu is my least favourite criterion and I’ll explain the reasons for that.


First of all, Tsai-Wu is an interactive failure criterion for composite materials. This means that the theory takes into account the interaction of different stress components in order to predict failure. Basically, the criterion uses equation 1 (subjected to the condition given by equation 2) to calculate an index and, if its value is one, then it means the material is failing. Please note that i,j=1,2,…,6, where subindices 1 to 3 represent normal stress components and 4 to 6 are shear stress components. In the original publication, authors explain how the different coefficient can be determined through experimental tests (e.g. compression, tension, biaxial…). So far, so good.

01

Equation 1

02

Equation 2

Problems start when people adapt this approach to introduce failure in Finite Element (FE) analyses. This theory does not include any damage evolution, so if you define failure as soon as the index reaches 1, then elements will be deleted from the model straight away. To be fair, if you are just trying to get estimations for composites, this is not that bad, since they are supposed to fail as soon as they reach a certain level of stress. The main issue is when users use this interactive failure criterion for other materials. For example, for a three dimensional case, equation 1 can be rewritten as follows:

06

Equation 3

Now consider a material which has similar strengths in the 3-principal axes and assume that the positive and negative shear strengths are equal. Then, using the expressions from equation 4 (where the parameters represent the tensile, compressive and shear strengths), we know that: F1=F2=F3; F11=F22=F33; F4=F5=F6=0; F44=F55=F66.

03

Equation 4

There are an infinite number of ways to determine the interactive coefficients so, how do we solve this problem? Some people suggests biaxial tests but another effective way to overcome this issue is to make the following assumption (as suggested in literature):

04

Equation 5

Firstly, this assumption satisfies the stability condition (equation 2) and secondly, it proves to be quite satisfactory for composite materials. Generalising this idea, we find the following:

05

Equation 6

Okay, so now consider that our material exhibits an elastic-perfectly plastic behaviour in compression. This would mean that the specimen should keep deforming under constant load after the yield (or maximum) compressive stress was reached. Hence, the criterion would predict failure once that value was reached, and no plastification prior to failure would be considered. For instance, consider uniaxial compression once the yield stress is reached, as shown in Figure 1:

Capture

Figure 1

Using all the equations which were introduced before, we have:

07

Equation 7

Therefore, in FEA elements would be deleted after that point, whereas in reality we would expect the material to keep deforming. That being said, more problems appear in cases where the structure is subjected to mixed loading conditions, since the criterion would then predict premature failure.

This post does not intend to state categorically that this theory is useless, that is not what I mean at all! But lately I have seen companies offering FE services using this type of approach, not taking into account that the material under consideration might not be compatible with the assumptions made for this criterion. I just needed to highlight this bad practice that I’ve noticed, so sorry if I’ve offended anyone!

Spanish university to collaborate with the development of intelligent materials

The University of Alicante (Spain) is taking part in a project that will develop intelligent materials for aerospace, automotive and transportation industries. The main aim will be to improve the safety of occupants and the durability of the components.


Researchers from the Department of Civil Engineering from the University of Alicante and the tech company Applynano Solutions are carrying out this project known as MASTRO, which stands for Intelligent Bulk Materials for Smart Transport Industries. The project is part of the Horizon 2020 programme, which is the biggest investment system for R&D in Europe.

Their goal is to develop intelligent materials for the transportation sector. In particular, the aerospace and automotive industries will be the main targets. Amongst other innovations, ¬†these materials will be able to monitor their own deformations and they will also be capable of heating and defrosting their surfaces. Besides, thanks to their capability to repair and protect themselves from damage, they will improve their efficiency, their durability and users’ safety. At the same time, manufacturing and maintenance costs will be reduced, as well as emissions.

In order to develop these materials, different matrices will be used, including polymers, concrete and carbon nanomaterials. Their functions will be based on three processes: the variation of electric resistivity when a material is subjected to a mechanical load, the relation between the heat that is generated and the electric flux, and electrostatic discharge.

One the one hand, the Spanish university will work on the development of the function related to perception of strain and damage on structures made of reinforced concrete. In addition, the previously mentioned institution will also focus on the heating of surfaces made of asphalt and concrete in order to avoid the formation of ice.

On the other hand, Applynano Solutions will work on the development of the carbon nanomaterials, the manufacturing of composites and the production of prototypes.

These are exciting news for the European research community, since not only Spain but also institutions from United Kingdom, Portugal, Italy, France, Germany and Sweden will collaborate with the MASTRO project. Hopefully, we’ll see encouraging results in the near future! I’ll keep you updated!

The Secret Science of Superheroes

Do you like science? Are you a comic geek? If your answer to both questions is “yes”, then “The Secret Science of Superheroes” is your book!


Last August I got myself an autographed copy of “The Secret Sicence of Superheroes”, thanks to Dr David Jesson and Dr Mark Whiting (University of Surrey) and I must say I don’t regret it at all! The book is distributed by the Royal Society of Chemistry and it was edited by Mark Lorch and Andy Miah. When I first heard about this book, Dr David Jesson told me that the whole thing was completed in just one weekend during an event in Manchester and that each chapter was written by a different author and it related a specific superheroe topic with the author’s field of expertise. Interesting, right?

I would review every single chapter, I really would, but… then you wouldn’t read the book! So, I’m just going to talk very briefly about the things I enjoyed the most. Basically, the text is written for a general audience, introducing the scientific concepts as the authors try to make their point. Read more