Homogenization of temperature-dependent thermal conductivity in composite materials

Of the various homogenization approaches, the asymptotic expansion homogeni zation (AEH) approach for homogenizing nonlinear composite material propert ies continues to grow in prominence due to its ability to handle complex mi crostructural shapes while relating continuum fields of different scales. T he objective is to study the AEH approach for nonlinear thermal heat conduc tion with temperature-dependent conductivity. First, two approaches are pro posed to investigate the sensitivity of the homogenized conductivity to hig her-order terms of the asymptotic series. Under conditions of symmetry such as in unidirectional composites, the two approaches give the same homogeni zed properties, Then validations are shown fur unidirectional composites fo r changing volume fraction and temperature. The validations are performed u sing measurements and analytical formulas available in the literature. The findings show good agreement between the present numerical predictions and independent results. Finally, a simple nonlinear steady-state heat conducti on problem is demonstrated to illustrate the multi-scale procedure, The num erically predicted results are verified using a Runge-Kutta solution.