Table of Contents Author Guidelines Submit a Manuscript
Modelling and Simulation in Engineering
Volume 2016, Article ID 9010576, 10 pages
Research Article

Numerical Estimation of Effective Mechanical Properties for Reinforced Plexiglas in the Two-Dimensional Case

1Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, GSP-1, 1 Leninskiye Gory, Main Building, Moscow 119991, Russia
2Fidesys LLC, Office 402, 1 Building 77, MSU Science Park, Leninskie Gory, Moscow 119234, Russia
3Tver State University, 33 Zhelyabov Street, Tver 170100, Russia

Received 1 May 2016; Accepted 25 July 2016

Academic Editor: Dimitrios E. Manolakos

Copyright © 2016 Vladimir Levin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The paper describes an algorithm for numerical estimation of effective mechanical properties in two-dimensional case, considering finite strains. The algorithm is based on consecutive application of different boundary conditions to representative surface elements (RSEs) in terms of displacements, solution of elastic boundary value problem for each case, and averaging the stress field obtained. Effective properties are estimated as a quadratic dependence of the second Piola-Kirchhoff stress tensor upon the Green strain tensor. The results of numerical estimation of effective mechanical properties of plexiglas, reinforced with steel wire, are presented at finite strains. Numerical calculations were performed with the help of CAE Fidesys using the finite element method. The dependence of the effective properties of reinforced plexiglas upon the concentration of wires and the shape of wire cross section is investigated. In particular, it was found that the aspect ratio of reinforcing wire cross section has the most significant impact on effective moduli characterizing the material properties in the direction of larger side of the cross section. The obtained results allow one to estimate the influence of nonlinear effects upon the mechanical properties of the composite.