A small comment for Mori-Tanaka's micro mechanics, composite material and disturbance observer

Note that Mori-Tanaka's Micro Mechanics is not sold on both amazon.co.jp and amazon.com. Hence, this part of thesis is written based on what I remember.

Text book of Mori-Tanaka is thick. There are several hundred pages. The question is, Mori-Tanaka is difficult and complex theory of material? Author thinks the answer is no.

An original journal paper of Mori-Tanaka is started from disturbance. Disturbance for material? What is it? See my core M.Phil thesis. My Disturbance Observer (K-Disturbance Observer) is started from combination of nominal system matrix A and disturbance. If disturbance is modelled by some dynamics and coefficient, it could be combined with original system matrix A which is deltaA.

So, what is system matrix A for material engineering? That is stiffness of a material. That means that if reinforced material is modelled as disturbance which is deltaA, its effect can be modelled with stiffness A.

As a physics side, there are many cell in material. A cell is fiber, a cell is plastic. Then, combine a effect with cell by cell. That is A + deltaA.

It is simple, isn't it? That is all for basic of Mori-Tanaka.

Then, why the text book of Mori-Tanaka is so thick? Just thick for thick? The prototype of K-Disturbance Observer is simple. That is started from just 3 or 5 pages which is composed by some simple analysis and numerical calculation. Then, it becomes about 160 pages. Similar thing is occurred in Web company as well. That is, a prototype is simple. But by year gets past, a web system gets complex and large.

The interesting point of Mori-Tanaka is its accuracy. In theory of composite material, there are several way of modelling material with micro mechanics. Each method has modelling error according to class room lesson note. However, Mori-Tanaka is very best theory against experimental result.

Why? Author thinks that which is because it is cell. And it is too small cell. If one think about system or stiffness matrix A, it is obvious.

Another interesting topic is when I was undergrad student and joined to CFRP research team. There is master's student who researched about micro mechanics. Its theory is relatively simple. Just think about cell of a material. What? That is the same as Mori-Tanaka, isn't it? But my supervisor may not found that fact. Me as well. I found that they may be the same several year after my undergrad.

Moreover, a theory of robust controll is coneected to a theory of micor mechanics which is Mori-Tanaka. Both of them are involved by author.

This section is from control engineer or applied mathematician. Author would wait the response from specialists of material engineering.