Abstract
A rectangle filled with closely packed spheres of random size and properties is considered as a micromechanical model of a two-phase particulate composite. A numerical simulation is used to determine the effective mechanical properties of the assembly and their scatter as a function of the number of spheres. It is shown that, in a system with relatively small number of particles (up to 300), the scatter of Young's modulus decreases with the system size. However, the rate of the scatter decrease becomes smaller with growing size of the system, so that the convergence to zero most likely takes place at infinity.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J. Pan and W. J. D. Shaw, “Materials characterization of polyamide/polyethylene mechanically alloyed polymers,” Microstruct Sci., 20, 351-365.
J. Aboudi, Mechanics of Composite Materials: a Unified Micromechanical Approach, Elsevier (1991).
Z. Hashin, “Analysis of composite materials — a survey,” J. Appl. Mech., 50, 481-505 (1983).
D. Gavrilov and O. Vinogradov, “Recursive inverse matrix algorithm in granular mechanics applications,” Computat. Mech., No. 20, 407-411 (1997).
O. G. Vinogradov, “Algorithm of stiffness matrix inversion based on substructuring concept,” Comput. Struct., 22, No. 3, 253-259 (1986).
S. Wolfram, The Mathematica Book, Cambridge University Press (1999).
R. D. Mindlin and H. Deresiewicz, “Elastic spheres in contact under varying oblique forces,” J. Appl. Mech., 20, No. 1, 327-344 (1953).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Vinogradov, O. On a Representative Volume in the Micromechanics of Particulate Composites. Mechanics of Composite Materials 37, 245–250 (2001). https://doi.org/10.1023/A:1010646702365
Issue Date:
DOI: https://doi.org/10.1023/A:1010646702365