Zm. Grabowski et al., TRANSIENT TEMPERATURE DISTRIBUTION IN A COMPOSITE WITH PERIODIC MICROSTRUCTURE, Composites engineering, 4(11), 1994, pp. 1055-1072
An approach based on the assumption of periodicity of the composite st
ructure is utilized to develop a method for the calculation of transie
nt temperature profiles in layered, fibrous or particulate composites.
The periodic microstructure gives rise to a temperature perturbation,
which is represented by an implicit integral equation in the Fourier
transform space. Fiber-matrix and fiber-fiber interactions at high vol
ume fractions are accounted for by Laue interference integrals calcula
ted in closed form. The effective material properties are found to be
time dependent. For one-dimensional problems the transient effective t
hermal composite properties are shown to undergo a transition from the
rule-of-mixtures value (Voigt average) at time zero to the steady-sta
te value (rule-of-harmonic-means or Reuss average) at time infinity.