International Journal of Aerospace and Lightweight Structures

doi: 10.3850/S2010428612000256

A Micromechanics-Based Finite Element for Dynamic Modeling of Heterogeneous Materials

Z. H. Zhu^a and Mahnaz M. Gandomani Department of Earth and Space Science and Engineering, York University, 4700 Keele Street, Toronto, Ontario M3J 1P3, Canada. ^agzhu@yorku.ca

ABSTRACT

This paper develops a micromechanics-based finite element to treat the dynamics of heterogeneous materials containing circular inhomogeneities. The eight-noded element is constructed from a square cell containing a single circular inhomogeneity at its center. The stiffness and mass matrices of the element are derived explicitly using the complex potentials of Muskhelishvili and the Laurent series expansion method. The element calculates the stress and displacement of inhomogeneous materials inside the element analytically based on the nodal values. The performance of the proposed element is demonstrated by its ability to treat the heterogeneous solids containing inhomogeneity under general dynamic loading conditions. Assessment of the accuracy and efficiency of the devised element is obtained by comparing its performance against existing analytical and traditional finite element attempts.

Keywords: Finite element, Micromechanics, Inhomogeneities, Muskhelishvili complex potentials, Laurent series, Dynamics.

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