ABSTRACT
The response of several materials including some soils is time-dependent with the deformation range being dependent upon the rate at which the loads are applied. Modeling of such time-dependent behavior is available in the framework of viscoelasticity and viscoplasticity. Viscoelasticity consists of two components: viscosity and elasticity. Viscosity is a measure of resistance to flow, which is a fluid property while elasticity is a characteristic of solids. Viscoplasticity based models can incorporate the inelastic strains also which, in a sense, is the rate-dependent version of plasticity where material exhibits permanent deformations but over time.
In this chapter, the focus is to understand the basic elements of these theories. First, a number of rheological models consisting of simple springs and dashpots are presented. Some composite forms of these fundamental models are then presented to formulate stress-strain relationships for a rate-dependent material. Three essential approaches to deal with the time factor associated with the numerical methods of analysis namely; Direct time integration, Fourier transform, and Laplace transform and their mathematical formulations (with MATLAB codes) are introduced within the context of layered viscoelastic systems. Lastly, the basics of viscoplasticity is introduced in a 1-D problem where rutting behavior of concrete pavement is investigated.
