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Research Papers

# Quadrilateral Subcell Based Finite Volume Micromechanics Theory for Multiscale Analysis of Elastic Periodic Materials

[+] Author and Article Information
Xiguang Gao

College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, 29 Yudao Street, Nanjing, 210016, P.R.Cgaoxiguang@gmail.com

Yingdong Song, Zhigang Sun

College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, 29 Yudao Street, Nanjing, 210016, P.R.C

J. Appl. Mech 76(1), 011013 (Nov 06, 2008) (7 pages) doi:10.1115/1.2966176 History: Received December 05, 2007; Revised May 21, 2008; Published November 06, 2008

## Abstract

In this paper, we extend the finite volume direct average micromechanics to enable the use of quadrilateral subcells. To do this work, the quadrilateral subcells are used to discretize the repeating unit cells first. Then the average displacement and traction defined on the boundary of the subcell are evaluated by direct integral method. This contrasts with the original formulation in which all of the subcells are rectangular. Following the discretization, the cell problem is defined by combining the directly volume-average of the subcell stress equilibrium equations with the displacement and traction continuity in a surface-average sense across the adjacent subcell faces. In order to assemble the above equations and conditions into a global equation system, the global and local number systems, which index the boundary of subcell in different manners, are employed by the extended method. Finally, the global equation system is solved and the solutions give the formulations of the microstress field and the global elastic moduli of material. The introduction of quadrilateral subcells increases the efficiency of modeling the material’s microstructure and eliminates the stress concentrations at the curvilinear bimaterial corners. Herein, the advantage of the extension is presented by comparing the global moduli and local stress fields predicted by the present method with the corresponding results obtained from the original version.

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## Figures

Figure 1

Subcell of FVDAM is strictly limited to a rectangle

Figure 2

(a) A continuously reinforced multiphase composite with a periodic microstructure in the x2‐x3 plane constructed with repeating unit cells. (b) RVE is discretized by a quadrangular subcell, which is employed by QFVDAM.

Figure 3

(a) Illustration of boundaries and corner points of subcell and the (b) definition of the direction vector and the normal vector of the subcell’s boundary

Figure 4

Number system of QFVDAM: (a) relation between the global number system and the subcell number system, (b) definition of the global number system, and (c) definition of the subcell number system

Figure 5

The corners of the repeating unit cell are constrained

Figure 6

Unit cell discretization for FVDAM and QFVDAM

Figure 7

Time for calculation

Figure 8

Local effective stress predicted by QFVDAM and FVDAM, comparison of the QFVDAM prediction with the corresponding result predicted by FVDAM

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