Non-local Maxwell model for ultraslow relaxation of concrete under different normal stress levels

Abstract

Stress relaxation is widely present in concrete structures and has a significant impact on the long-term mechanical properties of materials and structural safety. The previous stress relaxation models for concrete follow exponential or power-law law, which cannot accurately describe the ultraslow relaxation phenomenon with a logarithmic law. Thus, this paper proposes a non-local Maxwell model, i.e. Hadamard fractional derivative Maxwell (HFM) model with a normalized logarithmic kernel, and derives the constitution and relaxation modulus. A set of relaxation experimental data of cement concrete under different normal stresses is used to test the HFM model. Compared with the power-law fractional Maxwell model, the HFM model shows reasonable accuracy and can effectively capture the ultraslow relaxation in concrete. The fitting results indicate that the larger derivative order in the HFM model represents faster relaxation. Interestingly, the results also show that the normal stress in the concrete specimen is positively correlated with the derivative order in the HFM model.