## 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! 🙂 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.

For more information see Wikipedia Isotropic article and Wikipedia Anisotropic article.

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.

## What is a model?

What is a model?

According to google it is “a thing used as an example to follow or imitate” and or a “three-dimensional representation of a person or thing or of a proposed structure, typically on a smaller scale than the original”.

For Merriam the definition is more explored where in point 12 we get a more compatible definition of modelling. “a system of postulates, data, and inferences presented as a mathematical description of an entity or state of affairs; also :  a computer simulation based on such a system” Merriam dictionary

Representing our world objects, processes, states as mathematical expressions. These can be developed, visualised and used in CAD, CAE, Excel, Matlab, any capable programable environment software. A good day to day example offered in Merriam dictionary is the Weather model. There are a set of mathematical equations that are calibrated through many real life weather stations that deliver predictions of what the weather will be in the future and what occurred in the past which we did not measure. So basically a model is a means to study a future state or recap a past state through a lot of math. Looks simple.