Description of Wheat Straw Relaxation Behavior Based on a Fractional-Order Constitutive Model

Stress relaxation behavior is an important mechanical property of wheat (Triticum aestivum L.) straw densified biofuel. In this study, 21 cultivars of wheat straw were collected and their lignocellulose components (cellulose, hemicellulose, and lignin) were analyzed. The cellulose, hemicellulose, and lignin contents in these wheat straws ranged from 39.46 to 47.56%, from 30.39 to 35.98%, and from 5.54 to 12.12%, respectively. Stress relaxation tests of wheat straw were performed on an Instron testing machine. It was found that the wheat straw stress relaxation data had a two-stage characteristic, in which >80% of the total relaxed stress was rapidly released in the initial 10 s, and the stress relaxation was subsequently dominated by a slow stage until an equilibrium stress was reached. Four constitutive models including the Peleg model, the generalized Maxwell model, the Zener model, and the fractional Zener model were proposed to describe this stress relaxation behavior. The results showed that the fractional Zener model gave the best predictions of the wheat straw stress relaxation behavior, followed by the generalized Maxwell model, the Peleg model, and the Zener model. The relationship between stress relaxation behavior and wheat straw lignocellulose components was also further investigated. The fractional derivative coefficient decreased and increased with the increase of cellulose and hemicellulose + lignin contents, respectively. We suggest that the elasticity and viscosity of the wheat straw stress relaxation behavior is closely related with its lignocellulose components.