If this is a gentle poke at the seriousness of science, I welcome it.

In which case I suggest a connection between honeycomb and boiling miso soup.

Also between galactic dynamics and the act of adding cream to stirred coffee.

And as the strength/deformation curve for polyisocyanurate foams almost exactly matches the curve of my enthusiasm levels throughout the day, I conclude that my mind has a similar cellular-foam like nature and deforms through exposure to questions like this.

Yours, deformedly;

TLDR: Correlation is not necessarily causation - in *either* direction.

Here is the creep diagram:

Have to learn the fundamentals of universe inflation theory. I considered that the cosmic ray (Speed of Light) will change certain period of time, possibly billion years. I believe, there is certain mathematical relation to hold cosmology, gravity and time factors, but those diagrams correlation may quite differ from our prediction of universe inflation theory. Still it is unclear how E=Mc2 reduced when it overwhelm in black hole. Even there is suspect behind the global warming reflect through weather cosmic rays intensity variation at certain time / green house gases. If the diagram is possible to predict, then we can predict the 5 decades global warming exact reason.

Well I haven't learned about fracture mechanics, but I have this theory that one day our universe will reach thermodynamic equilibrium (/maybe crystallize), fracture, condense, and restart.

Even if I'm wrong, it makes for a cool mind image.

I am unsure if a mere similar graph suffices. I think it would be important to compare the conditions under which the graphs have been produced. Especially since the universe is not solid body, which would be used for fracture mechanics as a model. But maybe there are certain analogue structures in some equations?

If this is a gentle poke at the seriousness of science, I welcome it.

In which case I suggest a connection between honeycomb and boiling miso soup.

Also between galactic dynamics and the act of adding cream to stirred coffee.

And as the strength/deformation curve for polyisocyanurate foams almost exactly matches the curve of my enthusiasm levels throughout the day, I conclude that my mind has a similar cellular-foam like nature and deforms through exposure to questions like this.

Yours, deformedly;

TLDR: Correlation is not necessarily causation - in *either* direction.

Surely I must say that such correlation is rather nice and bold.

Of course, at the tertiary stage the micro-voids start to appear in material and they increase the stress concentration around material, hence creep deformation enhances. Now what could be a void equivalent in case of spacetime problem,... could it be blackhole (a singularity in space time fabric). The more you form, black holes, the more discontinuous a fabric become and that could have appear as a tendency of dark energy. I assume somebody thought about that already.

Fracture mechanics is a theory that explains the fracture procesos un en eucledian scale. It considera that the material es continuos, linear elastic and isotropic. Un this case, there es only pone fisure. Sin e muy point of view, it es not valor por the universe.

Dear Faysal,

Thanks, very inspiring analysis. Self-similarity (Fractals) on all scales may be the secret key to understanding the complex phenomena. This obvious example of self-similarity on rather different scale, that you mentioned, is another proof of fractal nature of cosmology.. Multi-scale modeling of physical phenomena and matter-materials response on different length scale represent powerful tool in modeling.

This approach presents a breakthrough in the phenomenological analysis of complex phenomena. The fractal nature of the fracture process and the geometry of a crack is well described in the literature.

I recently published. post on LinkedIn - "Fractals & Microstructural Disorder", about research of the great mathematician Prof. Benoît B. Mandelbrot, founder of Fractal Geometry and pioneer of Complex Systems Mathematics.:

"Fractals & Microstructural Disorder" - LinkedIn post by Milos Djukic:

http://www.linkedin.com/today/post/article/20140408234122-248021126-fractals-microstructural-disorder?trk=prof-post

Prof. Mandelbrot paved the way for the attainment of fundamental results such as the definition of the role of microstructural disorder and the scale effects on the fracture energy of materials.

This es a general approach. Fractals can take pintó account di verse aspectos of the materials

Thank you Luis and Milos for your comments.

Milos, this is a great post: http://www.linkedin.com/today/post/article/20140408234122-248021126-fractals-microstructural-disorder?trk=prof-post

Thank you very much.

Faysal, You are welcome. It seems to me that we think in a similar way. Also, thanks for this discussion.

As I mentioned fractales can consider diverse physical aspectos. In this case es advisasable to read the work of Prof. Mandelbrot. This es fundamental research.

You mean cavitate or boil: planets are mainly gases and liquid droplets, black holes are condensate liquid phases. So the Universe is a fluid continuum, not a solid continuum. :-)

Fracture mechanics deals with the separation of two parts of a material body. Creep concerns the deformation of a body under a constant load. Both are processes that occur on matter that is *in* space.

The expansion of the universe is caused by the expansion of *space itself*. Whatever space is, it is certainly not matter, and thus it seems to me unlikely that the superficial similarity between the expansion of the universe and a creep curve is particularly meaningful.

I'm also unsure what I should imagine when it comes to ' fracturing of the universe'; i.e space itself. I doubt it is a meaningful concept.

Hi,

Can fracture mechanics predict when the whole Universe will fracture? No. Fracture mechanics is the field of mechanics concerned with the study of the propagation of cracks in materials and the question may be flowed in that the big bang may never have happened and the universe is in simple dynamic equilibrium expanding and contracting in a cycle. A limit of expansion if achieved result in a phagocytosis with a parallel universe.

Fracture mechanics is mainly focuse on materials

I am pretty sure that the fracture mechanics CAN predict when the Universum will fracture, but under one condition: this just should be the special kind of - the Universum Fracture Mechanics, probably not invented yet :)

IMHO the main problem of such mechanics will be the distinction between the elastic strain of the Space (reversible) and the plastic one (irreversible). Very useful will be as well the Universum Fatique Theory, to answer the question, if the Space is undergoing the high-cycle fatique, or it is just a a tensile test made by God on the Specimen.

It is well known for engineers, that fracture type strongly depends on the number of cycles!

I recently published post on LinkedIn: Fractals, Beauty of Complexity.

http://www.linkedin.com/today/post/article/20140511020021-248021126-fractals-beauty-of-complexity?trk=prof-post

I invite your dear colleagues to participate in discussion.

Quite funny and intriguing question at the same time Faysal :)

Giving the physical meaning of the "cracking" aside, if two different phenomena appear to behave similarly (similar data trends), one should rather be careful with interpretation (imho). The curve “A” in the image appears to be similar to data trends observed in the da/dN-versus-dK plots that describe general FCGR behavior (on the log-log scale, that is).

Therefore, if your question would be further entertained (lets have some fun), what should be taken as the “dK” equivalent for the plot of the universe expansion (assuming that expansion itself is something like dV/dt = da/dN)? Should be “t” itself be used as in the cited plot or should be something like t^1/2 be used? How would be the whole formula look like (stress based rather than strain based?) ? Directly measured crack growth data curves (“a” versus “N”) look very different from discussed “S” shaped curve.

Anybody any idea? :)

Cheers,

MK

Hello Faysal,

are you elaborating on your idea? just out of curiosity ...

cheers,

mk

The evolution with time (or the life) can be seen that way for many systems :      

Dear Faysal,

Your interesting question should be redesigned from «  Can fracture mechanics predict when the whole Universe will fracture? » into « Can the Universe be seen as an evolving complex system, and, if yes, can one predict the instability time of its evolution ? ».

Indeed, complex systems (with many positive and negative feedback loops of several orders between their components) evolve in three stages when subject to stress : (1) a first stage of initial adaptation ; (2) a second stage of steady evolution (which could be called its “true life”) ; (3) a third stage of exhaustion up to collapse.

• Mechanical devices : engines, turbines, cars, …. : there is a first stage of “youth illnesses” (see “learning curve” of Duane), a second stage of “actual life” and a third stage of exhaustion where the defective behaviors cumulate up to collapse (see “bathtub curve” and “reliability curve”).
• Living entities (many biological systems) : there is a first learning stage (childhood and teenagers for humans), a second stage of steady life (adulthood for humans) and a third stage of senescence (where the capacities are impairing and the risks of illnesses are increasing) up to death (see “mortality curve” as equivalent to “bathtub curve” and “survival curve” as equivalent to “reliability curve”). This is also seen at several other levels : life of cells, bacteria, organs, systems (neural, digestive, …).
• Higher systems, like computers, industrial plants, ecological systems, …. can also be seen to evolve that way.
• ………………………

The curve has usually a shape roughly given as follows : (1) power law increase with time (concave from below), (2) linear increase and (3) exponential increase (convex from below). This curve could be called the “evolution curve” or the “aging curve”.

This is also a typical creep curve. The same 3-stages are seen in a creep curve of metals (if the temperature is above a threshold temperature 0.3 to 0.5 the melting temperature in K). The strain of metals subject to constant load (stress) and temperature evolves in a 3 stage sequence : 1ary creep (“learning”, adaptation), 2ary “steady state” creep and 3ary creep (exhaustion) up to rupture.

Why is this curve called the "creep curve” although the curve reflects a more general phenomenon (evolution of complex systems with time, or life) ?   Because the 3 stages (power law, linear, exponential) are especially neat for metals. Metals are very ordered and regular 3-D crystals and the only ones exhibiting the “metallic bounding”: peripheral electrons don’t belong to a given atom, which gives an homogeneous macroscopic behavior. Moreover, during creep tests they are subject to carefully maintained laboratory conditions (constant stress/load, constant temperature, humidity, …). Therefore the curve develops nicely according to the 3 stages above.

However, this behavior is not proper to creep. It is the more general “evolution or aging curve” that appears so nicely and clear during creep tests because the characteristic of metals and the laboratory testing conditions for creep allow it.

The « evolution or aging curve » can be simply expressed by following equations :  

E (t) = k.exp(α.t).tβ   (1)

Or after derivation :

(1/E).dE/dt = α + β/t   (2)

With E(t) an evolution marker for the system under study (e.g. strain for creep) , α=1/ti ≥0 (the evolution is stopped after the 1st stage if α=0) , 0 β/t during the inflationary era and β/t >> α during the radiation – and matter – dominated era’s (provided of course there are transition periods between era’s).

Equation (3) is exactly equation (2).

Therefore, using Equation (3) with the most recent available data from measurements, one finds that the expansion of the Universe started to accelerate around 7.1 Gyears after the big bang and that the instablity time ti is : t i = 47.6 Gyears after the big bang thus within 33.8 Gyears from present time.

Thus under this kind of assessment, we can consider that there is still plenty of time left before the Universe would « collapse ». Answer to the redesigned question !