Is Mori-Tanaka scheme independent of the number of inclusions?

In summary, the Mori-Tanaka scheme only takes into account the volume fraction of inclusions due to its direct impact on the homogenized modulus.
  • #1
Galbi
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When we homogenize composite materials by using Mori-Tanaka scheme, we only consider the volume fraction of each inclusions. Why don't we need to consider the number of inclusions?
Let's assume both of picture above has same volume fraction of the inclusions. If we use Mori-Tanaka scheme, they have same homogenized modulus, don't they? However, I think they should have different modulus.

what do you think?
 

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  • #2
The Mori-Tanaka scheme does not consider the number of inclusions because the volume fraction is considered to be the most important factor in determining the homogenized modulus. The number of inclusions, although important, is secondary as it does not directly affect the volume fraction. The volume fraction, on the other hand, does have a direct effect on the homogenized modulus. Thus, when using the Mori-Tanaka scheme, only the volume fraction of the inclusions needs to be considered.
 

Related to Is Mori-Tanaka scheme independent of the number of inclusions?

1. What is the Mori-Tanaka scheme?

The Mori-Tanaka scheme is a method used in materials science to predict the mechanical properties of composite materials. It takes into account the properties of both the matrix material and the dispersed inclusions within the composite.

2. How does the Mori-Tanaka scheme work?

The Mori-Tanaka scheme uses a series of equations to calculate the overall mechanical properties of a composite material based on the properties of the constituent materials and the geometry of the inclusions.

3. Is the Mori-Tanaka scheme applicable to any type of composite material?

Yes, the Mori-Tanaka scheme can be used for any type of composite material, as long as the properties of the matrix material and the inclusions are known.

4. Does the Mori-Tanaka scheme take into account the number of inclusions in the composite material?

Yes, the Mori-Tanaka scheme does take into account the number of inclusions in the composite material. The equations used in the scheme are modified based on the number and arrangement of inclusions.

5. Is the Mori-Tanaka scheme independent of the number of inclusions?

No, the Mori-Tanaka scheme is not completely independent of the number of inclusions in the composite material. While it does take the number of inclusions into account, the effects of large numbers of inclusions may not be accurately captured by the equations used in the scheme.

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