RHEOLOGICAL MODELS

The attached notes are written for a course on plasticity.  When I update the notes, I will post a link on my twitter account:  https://twitter.com/zhigangsuo.  

Rheology is the science of deformation.  This science poses a question for every material:  Given a history of stress, how do we predict the history of strain, or the other way around?

Rheology answers this question using mathematical models. In constructing a rheological model, we let material evolve through a sequence of homogeneous, but multiaxial, states of stress and strain.  We represent a history of stress by a tensor as a function of time, and represent a history of strain by another tensor as a function of time.

For a given material, we fit a rheological model to the experimental data of some histories of stress and strain, and then use the model to predict other histories of stress and strain.

Deformation is often large, and rheological models are usually nonlinear.  In this course we have studied several most successful rheological models:  linear viscosity, nonlinear viscosity, viscoplasticity, and perfect plasticity.  Here we summarize these models, and then construct several others:  strain hardening, elastoplasticity, and viscoelasticity.  In a separate course, we study large-deformation elasticity, electroelasticity, and poroelasticity (Suo 2013).

We will focus on models in their simplest forms.  For deeper and more extensive discussions, see review articles and textbooks (e.g., Tanner 2000; Nemat-Nasser 2004; Xiao, Bruhns, Meyers 2006; Gurtin, Fried, Anand 2010; Irgens 2014).