The fractional constitutive models for nonlocal material based on scattering wave equations

Abstract

This paper proposes some fractional nonlocal viscoelastic models which are under the framework of both Eringen’s nonlocal theory and gradient elasticity theory. Introducing different combinations of new mechanical elements derived from the spatial nonlocal theory, a set of time-space-fractional constitutive models for nonlocal material, such as the Kelvin–Voigt model and the Maxwell model, and their corresponding wave equations are presented. In addition, by applying the wave equations to describe the scattering attenuation from a general energy loss standpoint, the undetermined parameters of the presented constitutive models are obtained. As a discussion of the results, the scattering attenuation curve of the presented model is investigated and is found to be in good agreement with the Blair scattering model. Moreover, the nonlocal fractional Kelvin–Voigt model is applied to describe the creep of sand-bearing soft soil and then compared to existing models as well as experimental data.