Non-local structural derivative Maxwell model for characterizing ultra-slow rheology in concrete

Abstract

Ultra-slow rheological phenomena have widely been observed in engineering materials. The logarithmic law is normally used to describe the slow rheology, but it does not work well for the long-term ultra-slow rheology. In this paper, we devise a new Maxwell-type viscoelastic model to capture the ultra-slow rheology by using the non-local structural derivative, where the inverse Mittag-Leffler (ML) structural function is adopted. The viscoelastic responses of the ultra-slow Maxwell model are analytically derived, including creep and relaxation. The logarithmic creep law can be regarded as a special case of the ultra-slow Maxwell model. In addition, the proposed model is tested by several experimental data of concrete. Compared with the existed models, the present ultra-slow Maxwell model shows the reasonable accuracy. The derived results indicate that the non-local structural derivative involving the inverse ML function is feasible to capture the ultra-slow rheology of concrete.