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SUMMARYFractional calculus has been successfully applied to characterize the rheological property of viscoelastic materials; however, geomaterials were seldom involved in fractional order constitutive models (FOCM), and the topic of first loading and then unloading is rarely discussed through fractional calculus. In this paper, mechanical properties are considered as a ‘spectrum’, both ends of which are elasticity and viscosity, and the fractional order can be utilized to describe such properties quantitatively. In addition to conditions such as creep, stress‐relaxation, and constant‐strain‐rate loading, stress‐strain relationship under the condition of first loading and then unloading was also derived using FOCM. FOCM is then adopted to simulate triaxial tests of geomaterials under corresponding conditions. A comparison of test and numerical results demonstrates that FOCM can reasonably describe the mechanical characteristics of geomaterials.Copyright © 2012 John Wiley & Sons, Ltd.

On the basis of using the variable fractional order to characterize the time-dependent mechanical property, a variable order fractional viscoelastic model is presented to represent the time-dependent evolution of mechanical property including strain softening behaviors. The developed model is applied to analyze the constant strain rate tension and compression tests in ductile metals and soils. It is shown that the model can reasonably characterize the hardening and softening stages of constant strain rate tests and describe the evolution of mechanical property. The time-dependent mechanical property evolution can be split into three parts: in the first stage, the mechanical property is almost invariable, the second phase is a mutation stage, and in the third stage it changes slowly and linearly with strain. The simulated results reveal that the evolution from strain hardening to strain softening is a continuous linear change of mechanical property. Furthermore, it is known that the order obtained through fitting some test data can be greater than 1, which corresponds to strain softening response, while for a long time the order was always assumed to be between 0 and 1.

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