沥青混合料动态黏弹性的分数阶微分本构模型

为准确描述沥青混合料的动态黏弹性力学行为,在分数阶微分Zener模型(FDZ模型)的基础上,提出了一种改进的分数阶微分Zener模型(mFDZ模型),给出了频域内动态模量、存储模量、损耗模量和损耗正切等动态黏弹性能表达式,它们满足Kronig-kramers关系。mFDZ模型参数通过两步确定,一是结合不同温度和加载频率下沥青混合料的复模量试验结果,通过Wicket图给出了mFDZ模型中与温度无关的模型参数,二是利用时间-温度等效原理与WLF方程确定了与温度相关的模型参数,同时得到了沥青混合料动态黏弹性能主曲线。将mFDZ模型与FDZ模型和Sigmoid函数经验模型进行比较,结果表明:传统Sigmoid函数经验模型和FDZ模型只能描述具有对称性的动态黏弹特性,而mFDZ模型能够准确描述沥青混合料的动态黏弹性能的非对称特性,且模型与试验结果吻合良好,克服了传统Sigmoid函数经验模型和FDZ模型的不足,为沥青混合料动态黏弹性力学行为的本构描述提供了新的思路与参考。

Fractional Differential Constitutive Model for Dynamic Viscoelasticity of Asphalt Mixture

In order to accurately describe the dynamic viscoelasticity of asphalt mixtures, a modified fractional differential Zener model (mFDZ model) was proposed based on the fractional differential Zener model (FDZ model). The dynamic viscoelastic functions for dynamic modulus, storage modulus, loss modulus, and loss factor were derived in the frequency domain, which satisfy the Kramers-kronig relation. The parameters of the mFZD model were determined in two steps. Based on the test results of the complex modulus of the asphalt mixture at different temperatures and loading frequencies, the temperature-independent parameters of the mFDZ model were determined by the Wicket diagram. The temperature-dependent model parameters were given by the time-temperature superposition principle and Williams-landel-ferry equation, and accordingly the master curves for the dynamic viscoelastic properties of asphalt mixture were obtained. Moreover, the mFDZ model was evaluated by comparison with the FDZ model and empirical sigmoidal function. It is shown that the empirical sigmoidal function and FDZ model can only describe the symmetric dynamic viscoelastic functions. On the other hand, the mFDZ model can accurately capture the asymmetric characteristics of the dynamic viscoelastic properties of asphalt mixture, and shows good agreement with experimental results. Therefore, the mFDZ model overcomes the shortcomings of the empirical sigmoidal function and FDZ model, and provides new insight into the constitutive modeling of the dynamic viscoelasticity of asphalt mixtures.