Numerization of a memory effect for an homogenized composite material with a large contrast in the phase thermal conductivities. (November 2015) - Dureisseix, David; Royer, Pascale; Faverjon, Béatrice
Highlights: A numerical solution method is proposed to derive homogenized material parameters. Focus is on the memory effect function, a non standard emerging transient property. Suited finite element algorithms are proposed for an automatic determination. Approximate closed form solutions are proposed and validated on two numerical examples. Abstract: In this article, we propose a systematic numerical solution method for deriving the homogenized material parameters in the case where a large contrast in the phase thermal properties leads to a macroscopic memory effect. Focus is therefore set on the determination of this memory effect for a periodic microstructure. As for other and more classical homogenized parameters, the possibility of analyzing with the finite element method a single periodic cell is used, and a transient simulation allows to provide the incremental evolution of the memory effect function. Additionally, some approximations are proposed for a low cost estimate of this function, and validated on two examples.