Eventos Anais de eventos
MECSOL 2019
7th International Symposium on Solid Mechanics
Influence of Boundary Layer on the Effective Modulus of 3-1 Longitudinally Porous Elastic Solid
Submission Author:
Uziel Paulo da Silva , SP
Co-Authors:
Adair Aguiar, Edmar Borges Theóphilo Prado, Uziel Paulo da Silva
Presenter: Uziel Paulo da Silva
doi://10.26678/ABCM.MECSOL2019.MSL19-0058
Abstract
The evaluation of the effective properties of nonhomogeneous solids using analytical methods is, in general, based on the assumption that these solids have infinite dimensions. Here, we investigate the influence of the number of holes and boundary layer of a solid with finite dimensions on the determination of these properties. We use the Asymptotic Homogenization Method (AHM) to determine the effective shear modulus $c_{44}^{ef}$ of an elastic solid with infinite dimensions containing a uniform and periodic distribution of circular cylindrical holes. We also use the Finite Element Method (FEM) to determine this modulus in the case of a solid with finite dimensions containing the same uniform distribution of cylindrical holes away from its boundary. Near the boundary, we consider a layer of material, which is usually left in the fabrication process of samples. Both solids have the same elastic properties and are subjected to similar anti-plane shear loadings. For the finite medium, when the number of holes increases and the boundary layer thickness is fixed, or, when the boundary layer thickness decreases and the number of holes is fixed we note the convergence of numerical solutions to the analytical solution via AHM. For example, graphs of $c_{44}^{ef}$ versus void volume fraction show very good agreement between analytical results obtained via AHM and numerical results obtained via FEM. This investigation represents an ongoing effort of the research group to obtain the effective moduli of elastic solids using analytical, computational, and experimental methods.
Keywords
Linear Elasticity, Asymptotic homogenization method, Finite Element Method, effective modulus, Boundary Layer
