How to calculate the elastic modulus of a three-component composites, reinforcements, including a particle component and a component fiber?
You could use homogenization theory. If your composite is linear elastic here are different possibilities, like use two time Voigt and Reuss bounds or even more refined bounds like Hashing-Striklin. My suggestion first compute matrix and fiber effective modulus and then use this result and add the particles or vice versa. Otherwise you could model the composite using fem (3d) and use homogenization theory to computed the effective moduli.
You could use homogenization theory. If your composite is linear elastic here are different possibilities, like use two time Voigt and Reuss bounds or even more refined bounds like Hashing-Striklin. My suggestion first compute matrix and fiber effective modulus and then use this result and add the particles or vice versa. Otherwise you could model the composite using fem (3d) and use homogenization theory to computed the effective moduli.
There are a lot of model in literature concerning the calculus of elastic moduli of different types of composite. Homogenization method is a very nice theory but you must to have some knowledge in the domain and is not an easy task. The proposal of Peter Wriggers to use FEM can be the best way to solve the problem.
The problem is that, dependig on the properties of inclusions and their alignment, the macroscopic properties don't need to be isotropic nor linear. Therefore, there won't be a single and constant elastic modulus, in general.
Yes, Jakub is completely right. In case of fibers, especially when they have a distinct direction there will be anisotropic material behavior leading to a more complex behavior. If you want to get all possible constants, the attached procedure can be used together with a finite element analysis. There are also many papers that relate to this subject. I have added one of my own which shows the way how it it has to be done, but there are many.
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