Analytical Micromechanical Model

Abstract

Analytical Micromechanical Model: This program implements the analytical micromechanical model proposed by J. Useche and M. Pagnola in the work Vibration Analysis of Functionally Graded Epoxy/Graphene Composite Plates Using the Boundary Element Method and New Micromechanical Model, for the calculation of the elastic modulus of a composite material manufactured from the dispersion of graphene nanoplates in a homogeneous matrix. The program calculates the elastic modulus for a range of weight percentage %wg of aggregate in the matrix. From the %wg, the equivalent dimensions of the aggregate are calculated, depending on its k ratio (lg/hg). Developed by: Jairo F. Useche, M.Sc., Ph.D. and Pagnola M.R. Eng. Ph.D. ,2022

Note: In the case of porous materials, it is necessary to run the original program by modifying:

a. The Young's modulus is considered for the matrix (Em). In our composites, the value of Em associated with the epoxy matrix was 0.675 GPa [1].

b.The graphene elasticity modulus “Eg” is replaced by the isothermal compression modulus of air under normal pressure and temperature conditions (Ea = 0.1013 MPa [2]). c.The program enters the characteristic pore size values as “tg” and “lrve” values. This establishes that the shape ratio Lg/hg = 1 represents the pore shape. The pore was described as a sphere, which is compatible with what was observed by microscopy (If not, change the relationship to the one that corresponds). d.In the graph corresponding to the original software, the abscissa expresses the values of “Graphene Weight - Wg”; however, when applying points "b" and "c" by the proposed method (making our approximation), the abscissa should be read as “% porosity.”

[1]Berhanuddin N.I.C., Zaman I., Rozlan S.A.M., Karim M.A.A., Manshoor B., Khalid A., Chan S.W. and Meng Q. (2017). Enhancement of mechanical properties of epoxy/graphene nanocomposite, Journal of Physics: Conference Series, 914(1), 012036, DOI: 10.1088/1742-6596/914/1/012036 [2]Cohen M.L. (1985). Calculation of bulk moduli of diamond and zinc-blende solids, Phys. Rev. B, 32 (12), 7988 – 7991, DOI: 10.1103/PhysRevB.32.7988