# Prof. Yu's Research Group in the Cloud

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## Descriptions

In this wiki tutorial, you will learn about how to obtain effective properties of composites possessing four microstructures, including

1. hexagonal packed fibers
2. square packed fibers with interphase layer between fiber and matrix
3. 0/90 laminate
4. two spheres included in matrix

Geometric dimensions and material properties are taken from Challenge Problems for the Benchmarking of Micromechanics Analysis. Apart from how to calculate effective material properties of these four microstructures, you will also learn about

• how to extract and plot local stress values along a line after dehomogenization (in Case 2)
• how to draw a sphere and assign material properties by editing command files (in Case 4)

## Case 1. Hexagonal Pack Microstructure

The hex pack microstructure describes a continuous fiber reinforced composite. Figure 1 shows the cross-section. Dark portion represents fiber. Volume fraction of fiber is 60%. Material properties are given in Figure 2.  ### Video

You may refer to the YouTube video for hex pack micromechanics analysis.

## Case 2. Square Pack Microstructure

Cross section of a square pack composite with an interphase layer is given in Figure 12. Volume fraction of fiber and interphase is 60% and 1% respectively. Material properties are given in Figure 13.  ## Case 3. 0/90 Laminate

Figure 33 shows the microstructure of a 0/90 laminate. The fiber volume fraction is 60%. Diameter of the fiber is 5 microns. Fiber and matrix properties are the same as given in Figure 2 for Case 1.
We first calculate the effective properties of lamina using square pack geometry, then input lamina properties to calculate the laminate properties.

## Case 4. Double spherical inclusion

Reinforcing particles or voids in composites are represented by spheres inside a box. The double spherical inclusion microstructure is shown in Figure 46. The box is 2*2*2 microns. Diameter of the two spheres are 1 and 0.5 microns. The larger sphere is centered at (0.6, 0.6, 0.6) and the smaller sphere is centered at (1.5, 1.7, 1.3). Material properties are given in Figure 47.  ## References

1. Andrew J Ritchey; Hamsasew Sertse; Johnathan Goodsell; Wenbin Yu; Byron Pipes (2015), “Micromechanics Simulation Challenge Level I Results,” https://cdmhub.org/resources/948.