ETH Polymer Physics seminar


2016-04-06
10:15 at HCI J498

Thermodynamic Modeling of Glasses: Identification of the Cauchy Stress, and the Effects of Physical Aging and Mechanical Rejuvenation

Markus Hütter

Eindhoven University of Technology, Mechanical Engineering, Polymer Technology, The Netherlands

Polymer glasses typically age and change their mechanical behaviour when kept for a certain waiting time at a temperature below their glass transition temperature before mechanical testing. Particularly, the yield stress increases with the waiting (=aging) time. On the other hand, the application of a high mechanical load tends to ‘rejuvenate’ the aged sample. In this paper, I am concerned with modelling the influence of physical aging on the viscoplasticity (yield- and postyield-behavior) of glassy materials. To that end, the concept of two distinct subsystems, kinetic and configurational, is combined with elasto-viscoplasticity. In the literature, the configurational subsystem is described by a so-called configurational (a.k.a. fictive or effective) temperature, whereas in this presentation I use the corresponding entropy density instead. Using nonequilibrium thermodynamics, it is shown that the stress tensor is in general not simply related to the derivative of the thermodynamic potential with respect to deformation, but that there can be non-potential contributions (akin to hypoelasticity) that vanish as the system tends to thermal equilibrium. This has ramifications for the driving forces for viscoplastic deformation and mechanical rejuvenation. Part of this thermodynamic modelling, namely the identification of the stress tensor, is related to the Poisson operator that must satisfy the Jacobi identity. Checking this identity is usually tedious, certainly in the current case. I present some lessons learned that help to drastically simplify the corresponding calculations. The main step is to use a Lagrangian formulation of the model for which the Jacobi identity can be checked readily, and subsequently reducing the Lagrangian Poisson bracket to the Eulerian setting.


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