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Micropolar material constants

Can someone help me to give the numerical values for micropolar elastic solids and micropolar fluids so that i can study the behaviour of such materials numericaly?  Also suggest me some references and books regarding Micropolar Elasticity. 


Dilbag Singh Kahlon

Senior Research Fellow- CSIR

Center for Advanced Study in Mathematics

Panjab University

Chandigarh -160 014




Pradeep Sharma's picture

Dear Dilbag,

Far as I know the most comprehensive work on micropolar constants was done by Youping Chen and James Lee. You can check their papers as well as references cited by them. Also, recently, my student published a paper on strain gradient elasticity constans for various materials. That particular theory includes as a special case the so-called couple stress theory (which in turn is a special case of micropolar theory). It will give you some idea about the characteristic length scales. You can download my papers from my website. I should caution you however that micropolar constants are negligible for most common crystalline metals and ceramic. Only for composites, amorphous metals/ceramics and polymers are they of significance.

Roozbeh Sanaei's picture

Micropolar materials have different models

each model have its corresponding constants.

which model do you use?

I have material constants for some models.

you can simulate micropolar materials with particle methods and calculate their constants numerically in order to study this model.

professor "Rod Lakes" in U.S have measured this constants for some cases. you can contact him too.





Hi! Roozbeh Sanaei

Thanks for you. I will check the information of Prof "Rod Lakes".  From my view, I did not think the computation to be the good method. I like the experimental method to get these constants. 


I heve checked his infromation . But, I did not find his information. Would you like provide much more information about him ? Such as, his address, the department and the university.

Go to his webpage at the University of Wisconsin. His negative Poisson's ratio stuff and the viscoelasticity experiments are particularly interesting.

MichelleLOyen's picture

Lakes has a downloadable pdf review paper on the subject posted on his website at this link:

Lakes, R. S., "Experimental methods for study of Cosserat elastic solids and other generalized continua", in Continuum models for materials with micro-structure, ed. H. Muhlhaus, J. Wiley, N. Y. Ch. 1, p. 1-22, (1995).

He's done some really interesting work on this subject in the context of bone. 

Hi! MichelleLOyen

Thanks for your information. Very glad to know that Prof Lakes had researched the biomechanics of bone. My researching interesting was also the biomechanics of hard tissue and soft tissue.

Henry Tan's picture

Links to:

An introduction to the Cosserat theory of elasticity (from Lakes)

microstructure theory of elasticity (from д.ф.-м.н., проф. И.Н.Шардаков)

Hi! Biswajit Banerjee

Thanks for your information. I am very interesting at the negative Poisson's ratio effect and the viscoelastic behavior.

As I know, the measure on the material constants of micropolar was not found. Many years ago, I inquire how to measur these constants. Someone told me that I may get a prize if I find a mean to measure these constants. But, I did not get any methods. So, I think your problem is very difficult.

Will you please give me contacts of some of well known persons in micropolar elastic constants?


Roozbeh Sanaei's picture

i think i mentioned proffesor ROD LAKES ,proff Eringen is one of najor researchers in this field. if you tell which model do you use i can say you some constants, but i am not so well-known

The energetically preferred graphitic van der Waals gap is aproximately 0.34nm, which means the effective interiour lumen inside a 1.4nm diameter nanotube is about 0.7nm. Nevertheless, it has proved possible to insert C80 fullerenes, which are nominally 0.8nm in diameter, inside such SWCNTs. How can this be the case?

Dear Roozbeh Sanaei,

I have contacted Prof. Eringen. I hope that i must get some hint regarding these material constants.

I use to discuss the problems wave propagations and reflection and reflections of plane waves at the interfaces of micropolar elastic solids and fluis. For that purpose in numerical discussions i need these values so that the results are obtained for realistic model.


Who can explain where are from I can find numerical values of bending or cuvature modulus for different materials?

Mindlin R.D. Influence of couple stresses on stress concwentrations//experimental mechanics.

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