Neural computations of effective response of random composites

The e€ective response of disordered heterogeneous materials, in general, is not amenable to exact analysis because the phase geometry may not be completely speci®ed. Besides the bounds for the e€ective moduli, most reported results are essentially approximate, may contradict each other or even violate the bounds. With increasing number of phases, and therefore increasing uncertainty inherent in the very statement of the problem, the investigation of e€ective response becomes less amenable to analytical treatment, in particular, by methods of boundary-value problems of mathematical physics. The present paper reports a methodology for investigating the e€ective response of disordered composites with the help of neural networks as well as particular results obtained for e€ectively isotropic and macroscopically homogeneous two-phase materials. It is shown that, after incorporating the bounds and proper training, simple neural networks may describe a wide variety of the e€ective response for two-phase composites, though in general more complicated networks appear necessary.