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.

本文在Eringen的非局部理论和梯度弹性理论的框架下提出了一些分数非局部粘弹性模型。介绍了从空间非局部理论推导出的新机械元素的不同组合，提出了一组非局部材料的时空分形本构模型，例如开尔文-沃格特模型和麦克斯韦模型，以及它们相应的波动方程。此外，通过应用波动方程从一般能量损失的角度描述散射衰减，可以获得所提出的本构模型的不确定参数。作为结果的讨论，对提出的模型的散射衰减曲线进行了研究，发现与Blair散射模型非常吻合。此外，