Abstract

LEON-MECIAS, A et al. Improved bounds for the effective energy of nonlinear 3D conducting composites. Rev. mex. fis. [online]. 2007, vol.53, n.3, pp.164-170. ISSN 0035-001X.

Recent variational inequalities of Talbot are used to improve the lower and upper bounds for the effective energy of nonlinear 3-D two-phase conducting composites. The effective conductivity of the linear isotropic two-phase periodic conducting composite used as comparison material in the inequalities is computed through an asymptotic homogenization model by finite element analysis of the local problem on the three-dimensional cubic unit cell with one spherical inclusion. A brief mathematical description of the numerical method is included. Numerical calculations of the effective conducting linear property are compared with Bruno's bounds. It shows that the numerical solution for the limit cases of superconducting and empty inclusions improves the bounds when the inclusion volume fraction is greater than about 0.4. It is natural to expect an improvement in the whole volume fraction of Talbot's bounds for nonlinear conducting composites when the numerical calculation is used instead of bounds for the linear comparison problem, as is the case here.

Keywords : Variational bounds; effective properties; conducting composites; asymptotic homogenization method; finite element method.

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