Data fitting and interconversion remain to be a difficult task in linear viscoelasticity. On the basis of transfer function, a generalized fractional model is proposed to fit linear viscoelastic data. The new model is modified from the fractional Maxwell model, and it is abbreviated as the MFM model in this paper. Common fractional viscoelastic models, including the fractional Kelvin and fractional Maxwell models, can be considered as special cases of the MFM model. Apart from inheriting the properties of the fractional Maxwell model, the MFM model is capable of adjusting the transient region between the power-law and plateau regions. Case studies are provided to apply the MFM model in data fitting of various kinds of viscoelastic data, and the results generally demonstrate improved fitting quality with fewer fitting modes compared with the generalized Maxwell model. In addition, the MFM model is used as a venue to convert time-domain data (including creep compliance data, creep data with ringing, and realistic relaxation data) to dynamic moduli data. Compared with classical numerical methods for data interconversion, this method appears to be more direct and convenient.

在线性粘弹性方面，数据拟合和互转换仍然是一项艰巨的任务。在传递函数的基础上，提出了适合线性粘弹性数据的广义分数模型。该新模型是对分数麦克斯韦模型进行了改进，在本文中简称为MFM模型。常见的分数粘弹性模型（包括分数开尔文模型和分数麦克斯韦模型）可以视为MFM模型的特例。MFM模型除了继承分数麦克斯韦模型的特性外，还能够调整幂律和平稳区域之间的瞬态区域。提供了案例研究，以将MFM模型应用于各种粘弹性数据的数据拟合，与一般的Maxwell模型相比，结果总体上证明了改进的拟合质量，且拟合模式更少。此外，MFM模型还用作将时域数据（包括蠕变柔量数据，带有振铃的蠕变数据和实际松弛数据）转换为动态模量数据的场所。与用于数据互转换的经典数值方法相比，该方法似乎更加直接和方便。