A new method for formulating linear viscoelastic models

Abstract

Classical spring-dashpot models encounter difficulties in modeling the responses of realistic viscoelastic materials. Multiple modes are typically needed to describe realistic data, resulting in overfitting issues. Compared with classical models, fractional viscoelastic models have been shown to depict the linear viscoelasticity of materials containing multilevel structures with fewer parameters. However, the series-parallel structure for fractional models restricts one to build more general constitutive models that are not bounded by such presumed structure. In this paper, we attempt to adopt a transfer function method for formulating linear viscoelastic models, especially for fractional viscoelastic models. Fractional models can be established by constructing a transfer function connecting two selected limiting viscoelastic models. With this transfer function method, we can establish generalized fractional models that have not been previously available. Furthermore, the viscoelastic responses of the resulting models can be obtained analytically or numerically using transfer function theories. For demonstration, the overall methodology is used in model fitting to experimental data of polymeric materials, leading to fitting models with fewer parameters.