Rheological models based on fractional order derivatives have been applied to characterize the linear viscoelasticity of asphalt cements for a long time. Such models provide continuous spectra which are fundamentally related to the molecular characteristics and facilitate analytical investigations as compared to discrete representations. With the increasing complexity in asphalt composition to satisfy various purposes, however, the inadequacy of existing fractional models has been noted. This paper proposed a generalized fractional Maxwell-dashpot (GFMD) model as a general framework for describing the modulus behaviors of asphalt cements. The generalized fractional Voigt (GFV) model was considered the counterpart for the compliances. The material functions given by each model are primarily the superposition of its constituent fractional Maxwell-dashpot or fractional Voigt (FV) elements. Geometric features of these elements were investigated such that a proper initial guess of model parameters can be obtained graphically with relative ease. For computational efficiency, the continuous spectra were discretized to provide the Prony representations of the material functions. To demonstrate the model capability, the dynamic mechanical data of a neat asphalt showing the typical behavior and a heavily polymer-modified asphalt exhibiting strong cross-linking were utilized. For the typical behavior, the GFMD and GFV models containing two fractional elements yielded excellent descriptions. A third fractional unit was necessitated in both models to account for the cross-linking mechanism for the modified asphalt. A relaxation/retardation mode density of two points equidistantly per decade produced material functions with negligible waviness and almost the same accuracy as compared to the use of the continuous spectra.

中文翻译：

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沥青水泥线性粘弹性表征的一般分数模型

长期以来，基于分数阶导数的流变模型已被应用于表征沥青水泥的线性粘弹性。与离散表示相比，此类模型提供了与分子特征基本相关的连续光谱，并有助于分析研究。然而，随着沥青成分的日益复杂以满足各种目的，已经注意到现有分数模型的不足。本文提出了一个广义分数麦克斯韦缓冲器 (GFMD) 模型作为描述沥青水泥模量行为的一般框架。广义分数 Voigt (GFV) 模型被认为是符合性的对应模型。每个模型给出的材料函数主要是其组成分数麦克斯韦缓冲器或分数 Voigt (FV) 元素的叠加。研究了这些元素的几何特征，以便可以相对容易地以图形方式获得模型参数的正确初始猜测。为了计算效率，连续光谱被离散化以提供材料函数的 Prony 表示。为了证明模型能力，使用了显示典型行为的纯沥青和显示强交联的高度聚合物改性沥青的动态力学数据。对于典型行为，包含两个分数元素的 GFMD 和 GFV 模型产生了极好的描述。在两个模型中都需要第三个分数单位来解释改性沥青的交联机制。与使用连续光谱相比，每十年等距两点的弛豫/延迟模式密度产生的材料函数具有可忽略的波纹度和几乎相同的精度。