Asymptotic Homogenization and Numerical Implementation to Predict the Effective Mechanical Properties for Electromagnetic Composite Conductor

Abstract

Conventional mechanics-based homogenization model and the finite element approaches have inherent limitations and errors when applying to calculate the effective properties of composites. These errors are either caused from the upper and lower bounds due to the difference of the prescribed boundary conditions, or from the effect of the size and the boundary condition of the representative element. Asymptotic theory-based homogenization does not have the inherent bounds and boundary errors but requires a complicated numerical implementation in order to apply the theory. This paper reports a development of an asymptotic theory-based homogenization approach with its numerical implementation and considers its application to predicting the effective mechanical properties of electric conductor consisting of conductor core and multi-layered composite insulations. The numerical implementation is developed based on using the finite element technique for the meshing generation and for the application of boundary conditions, with the developed computational algorithm for numerical calculation of effective homogenization properties. The developed computational program bridges the commercial CAD and finite element software, thus allows the design studies and parametric analyses of composite conductors with complex geometry and material composition.

Keywords

homogenization theory electromagnetic composite conductor composite unit cell effective properties characterization

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