Volume fraction and rule of mixtures in Matlab.

Hello!! I need help with creating a code for volume fraction and rule of mixtures in Matlab for any given finite element structure. By using power law the ceramic and metal phase is considered and E value should be between 10 to 210 GPA respectively and the m values controlling the gradation should range from 1 to 10 where less than 1 is for ceramic phase and more than 1 for metal phase. I only need the code for any fem structure and hence I am not providing the file here.

Thank you for your kind help.

Answer 1

[Rohit Kulkarni]

Hi Adeline,

I understand that you want to create code for volume fraction and rule of mixtures in MATLAB.

The following code provides a general outline for implementing the volume fraction and rule of mixtures for composite materials.

Rand() function has been used to generate random values for E for the range 10 to 210 and m values from 1 to 10.

% Define the material properties
E_ceramic = rand() * (210 - 10) + 10; % Random value between 10 and 210 GPA
E_metal = rand() * (210 - 10) + 10; % Random value between 10 and 210 GPA
m_ceramic = rand() * 9 + 1; % Random value between 1 and 10 for ceramic phase
m_metal = rand() * 9 + 1; % Random value between 1 and 10 for metal phase

% Load your finite element structure data here (you need to implement this part)

% Calculate the volume fraction
Vf_ceramic = (E_metal / E_ceramic)^(-1 / (m_metal - 1)) / ...
    ((E_metal / E_ceramic)^(-1 / (m_metal - 1)) + (E_ceramic / E_metal)^(-1 / (m_ceramic - 1)));

Vf_metal = 1 - Vf_ceramic;

% Apply the rule of mixtures to compute the effective material properties
E_effective = Vf_ceramic * E_ceramic + Vf_metal * E_metal;
m_effective = (log(E_effective / E_ceramic) / log(E_metal / E_ceramic)) + 1;

You'll need to load your finite element structure data at the appropriate location in the code.

Please adapt the code to load your specific finite element structure data as needed.

Please refer to the documentation of rand() function for more details:

https://in.mathworks.com/help/matlab/ref/rand.html

Hope it resolve your query!