## The meshing dilema

Some times we use the default mesh and get happy with the result,s others we don’t. It is hard to develop a test setup or expensive to buy the test setup equipment to calibrate the model. On these cases that we can’t compare results we have to take simulation results as final. This presents a few chalenges since how do we know the model is good enough for our purpose? Normally I follow two paths either by analytically calculating a rough value or by carefully analysing mesh sensitivty, analysing energy balances and whatnot. Although it is tempting to take a rough model as final, bad consequences can come from that decision, since we can end up with divergent results that relate more to model deficiencies than to the actual physics in hand.
Look at this example where I have 3 result set’s for varying thicknesses, however with different meshing strategies.

Which of the lines is the truth? Just a small change and such a big difference. You have to trust me on this, there is a big difference 200MPa from bottom blue to top grey.

## The mystery of the train seat uncovered

Will the train seat withstand 120Kg? was I seeing things? Maybe the weight was more since the person had a backpack. But the load was extreme.

I calculated 5 mm deformation on the cushion. Could I have seen it? Well maybe. Stresses were far away from the plasticity limit, however the structure feels loaded.

From my analysis the structure could take even more load and wobble even more. Maybe the squeaking sound over exaggerated my notion of wobbling.

The light blue image is the deformed state, we can see the deformation direction, which moves in a expected direction.

In this close up we can see a slight displacement. But very small.

So my conclusions:

The heavy train traveller was safe, the seat could stand a few extra Kg’s of weight with some more camping equipment.

The design seems fairly robust, however it actually wobbles.

## Train seat analysing

Finally I got time to mesh and solve my imaginary problem. I will not dive into meshing since it is a chapter on its own. I used a tetrahedron mesh as standard as it gets. The work flow is simple; get a CAD model, get material data, mesh it, add supports and loads and finally get some results, either by stresses or displacements.

My results for a small load of 1.2Kg shows that the T tube element will suffer most when we sit on it. I would say that if it breaks it will be there. Ok this case is more then evident since the only thing holding my weight is this connection.

But will it wobble with 120Kg weight?

## Free Body Diagram

In order to build up my model some boundary conditions need to be defined. For this a free body diagram is helpful. With it it’s possible to visualise what is interacting with my target body.

With this in mind we have two fixed supports that constrain (X, Y, Z and fixation null torque in all directions Mx, My and Mz).

I will continue more in-depth since im am curious regarding tubular meshing and to actually know if the seat can take a 120Kg weight on top.

## Will it hold?

My today’s train trip is being quite interesting. As someone sat on a seat it wobbled. It made me think “how much would it hold”. Well, I enjoyed the seat design with it’s tubular shape and table attached to it.

This made me think also. How would I model this?

I have a few inputs/assumptions I already can imagine:

• Assuming a 120Kg (more or less 250 pounds) person
• Isotropic behaviour structural steel
• Perfect welding connections (I know I know but it’s just a rough analysis)

Maybe these boundary conditions, hold the seat in place. I will also assume only one seat is present instead of the hole bundle.

On my next post I will follow up on the model building.

## So why hair? Is it simple enough?

We see hair type filaments everywhere! We have them, insects have them and even plants have them (trichomes). Although very different in composition all of them have in common a thin filament shape that serves many purposes. They can be microscopic or very long in length.

Is a hair filament simple to model? I don’t know. I searched the web as I decided to first understand what is the basic geometry of an hair filament and what’s it made of. I also decided to focus on human hair. I started my search on wikipedia and discovered that hair isn’t homogeneous! ðŸ™‚ Well that was expected. So if hair isn’t made an homogenous material, how do I define it’s behaviour? See figure below.

An important step in modelling things is that we need to simplify, and start making some assumptions, some will be accurate others at least will let us move on to another stage even if wrong. In my professional life I guide my self through papers and extensive experimental work closely bonded to my customer expectations. Models are always directly linked to calibration data that gives us information of how far we are from our target result.

I should make clear that I am not focusing on the purely technical and accuracy side but to embark in journey to model mother nature and all of it’s creations and build up models through mind experiments resorting to numerical simulation tools.

Continuing. The easy way out, would definitely be to consider hair as homogeneous and isotropic material. However from the picture above it is clear that hair isn’t homogenous although it has radial symmetry and probably instead of Isotropic it is anisotropic like wood I would guess. Isotropic is a material which behaves similarly in all X, Y, Z directions, an anisotropic material behaves differently in two directions, meaning X-Y and Z. Since hair looks like it has radial symmetry I think it is fair to say that we have axial behaviour and radial behaviour.

But what is hair essentially made of? It’s made of alpha-keratin protein.

Some hair types are curled, is the structure prestressed in any way? Well we could stay a good while looking at specific hair type behaviour.

The more questions we make the more accurate the model gets, however the more complex the model gets also and harder it is to reach an end.

Going back to the beginning, hair is not that simple to model when we consider it’s real complexity. Maybe an Isotropic simplification is enough and when not more effort has to be done to reach the final goal analysing the anisotropic behaviour. There is always a balance between accuracy and effort. At to what purpose we need the model for. An example is an uniaxial stress test where axial properties are very important comparing to radial behaviour.

All of this just to say hair can be challenge or very simple.

## A world of opportunities in nature

Natures beauty in many ways shadows man’s work, its intricate complexity and detail has no rival. Representing natures many manifestations can be some what challenging. It is difficult not to get amazed with what nature offers us to discover.

However as in most of my life experiences I really need to adjust my expectations of the problem I have in hands to what I am actually able to do. So instead of taking the hole complexity of a certain problem , it is better to focus on simple parts. Like JuJu’s hair for instance! How would we model hair instead of modelling a complete spider? I have no clue but this looks like it will be quite an adventure. No clue how I would do it, and why I would need it in the first place.