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Micro Analysis of Composites in ansys

 Hi everybody, i am Ravikumar doing M. Tech. project on multi scale analysis of composites.

I gave the input as nodal displacements and different material properties for glass and resin. I applied all the normal stresses and shear stresses on the micro scale model which is of hexagonal array  structure. (i.e., one circular fiber at the centre and quarter fibers at the four corners of the model and the remaining portion is filled up by resin).

My aim is to findout all the engineering constants in the compliance matrix by knowing the stresses which i will get from Ansys and Strains (as i am giving as the input).

But, i dont know how can i get the average stress over an element. Because in the paper what i am refering, author mentioned as average stress.

I know stresses at each node and elemental stresses along the perticular direction. From any of these, can i get average stress on perticular element?

  The paper states that for average stress, the following equation is used.

  Avge. σij-- = (1/V)∫(σ)ij dV  

What does the above equation means ?

 I thought to multiply the stress of the element in perticular direction with volume of the element and to sum those values for all the elements and devide the result by the total volume of the structure (micro RUC)

Here, i am attaching the reference paper also. Can any one explain me what equation 5 exactly means?

Please help me and Thanks in advance



PDF icon Periodicity boundary conditions.pdf553.4 KB


Lianhua Ma's picture

σij--   denotes average stress tensor of the RVE(unit cell). For the calculation of the average stress, please see

Dear Lianhua Ma,

Thank you very much for your help. I proceed in the way as you told by taking the reactional forces and devide those by the area, it worked well for finding out the normal stresses.

Can you tell me how to solve it for shear stress calculation?

I am applying positive displacement on the top and right planes (strain*lenghts of planes respectively) of RUC (Representative Unit Cell) and negative dispalcement on the left and bottom planes of RUC for finding out the average shear stress on XY plane. (as YZ plane in reference paper. Fig8)

Is it the way to apply the boundary conditions for that?

After solving, i am getting the same deformation mode  as in reference as in Fig9.

I tried with multiplying the elemental shear stress (Sxy) with volume of the elements and sum all these values and finally devided the result by the volume of RUC. But, i am getting higher value. I think, it may not be correct.

Can you tell me how to calculate the shear stress?

Once again thank you for your help.......

Lianhua Ma's picture

Hi Ravikumar,

This approach mentioned above is suitable for both  normal and shear deformation.  Please check the prescribed displacement on every edge of your RVE.

For the calcultion of shear stress in x-y plane:

Assuming  a, b and c are the edge lengths of your RVE along x,y and z direction,  the applied positive displacement on the top edge should be 1/4*b, whereas the displacement prescribed on the right edge should be 1/4*a. Similarly, the displacement applied on the left and bottom edges should be -1/4*a ,-1/4*b, respectively.

Hope this helps  



Hello Lianhua Ma,

 I am applying the shear load as you mentioned. But, how can i get the average shear stress over the plane.OR how can i get the average shear stress on XY plane by knowing reaction forces of X and Y on the edges?


 Thank you....

Lianhua Ma's picture

As noted in your post. Average shear stress over the domain of RVE=  "multiplying the elemental shear stress (Sxy) with volume of the elements and sum
all these values and finally devided the result by the volume of RUC."

Yes....Exactly i am doing in the same way..... But my results are not matching. I am getting higher values than the author what he mentioned in the paper.

I dont know may be any other method is available to solve for that. If you have any idea  please let me know.

Thnak you......

Lianhua Ma's picture

You can try another method to solve the x-y shear stress.

Firstly extract the reaction force of every node in a face.

Secondly, sum them together.

And finally divide the result by the area of the face. 

Wenbin Yu's picture

If you use VAMUCH , a general-purpose micromechanics analysis code, you don't have to worry about how to apply loads and boundary conditions. What you need as inputs are the geometry of the unit cell and the constitutive properties of each phases. The 6x6 stiffness and compliance matrices are generated within one analysis. An interface is also developed for ANSYS users to take advantage of its powerful pre/post processing capabilities.

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