On the General Form of the Constitutive Equations of Classical Viscoelastic Models in the Laplace Domain

Classical viscoelastic models constructed using linear springs and dashpots not only lay an important foundation of the theory of viscoelasticity, but also are the most common models adopted to describe the mechanical behaviors of viscoelastic materials in scientific research and engineering. Due to the complicated nature of time-dependent mechanical behaviors of viscoelastic materials and their sensitive dependence on the initial conditions, it is essential to rigorously consider the effects of the initial conditions when using those models in order to achieve accurate analysis results. The purpose of this article is to present the general form of the constitutive equations of classical viscoelastic models in the Laplace domain that is rigorously incorporated with the effects of the initial conditions. The constitutive equations of some fundamental classical viscoelastic models in the Laplace domain are presented as examples. Compared to the general form of the constitutive equations of classical viscoelastic models in the Laplace domain without considering the initial conditions reported in literature, two examples of analysis demonstrate that the newly introduced form incorporated with the effects of the initial conditions can provide accurate analysis results. The newly introduced general form of the constitutive equations of classical viscoelastic models in the Laplace domain not only helps to improve the understanding of concepts in the theory of viscoelasticity, but also provides a tool for accurately describing the mechanical behaviors of viscoelastic materials.