Composite Damage Models for Diffusivity of Distressed Materials

Abstract

A distressed material can be considered as a two-phase composite material with the distressed areas (volumes) as one phase and the original material as the other phase. A parallel diffusion model was developed in which the damaged phase and the original phase are arranged parallel to the direction of diffusion. The parallel model is associated with the isogradient principle in that the concentration gradients in the damaged phase and in the original phase are the same. A serial diffusion model was developed in which the two phases are arranged perpendicular to the direction of diffusion. The serial model is associated with the isoflux principle in that the fluxes in the two phases are the same. The two-phase composite models were further extended into general multiphase composite models to evaluate the effect of multilevel damage on the effective diffusivity of distressed materials. A principle of minimum complementary “chemical-flux energy” and a principle of minimum “potential chemical energy” were established similar to the commonly used principles of minimum complementary energy and minimum potential energy. Based on the two new minimum energy principles, it was shown that the parallel model is the lower bound and the serial model is the upper bound for effective diffusivity of distressed materials. Diffusivity of distressed concrete was used as an example. The experimental data agreed quite well with predictions of the theoretical models.