IWNET12
IWNET12
Rheology, plasticity and thermal expansion in a nonequilibrium ther-
modynamical framework
Tamás Fülöp1, Péter Ván1 and Attila Csatár1
1 Montavid Thermodynamic Research Group, Hungary
Abstract
A recent approach [1] has introduced kinematic quantities for elasticity, plasticity, and thermal expansion
of solids by working on spacetime directly - rather than in a reference frame -, and utilizing the notions of
the relaxed metric and the current metric of the material manifold. Namely, elastic deformedness measures
the dierence between the current metric and the relaxed metric, thermal expansion means a temperature
dependent - typically volumetric - change of the relaxed metric, and the plastic rearrangement of the solid is
described by another type of - typically volume preserving - change of the relaxed metric.
The talk reports on how these kinematic ingredients help us building a non-equilibrium thermodynamical theory
for elasticity, rheology, plasticity and thermal stresses. Starting from the elastic behaviour and heat capacity, we
construct the naturally emerging entropy function. Next, we nd that the dynamical consequences of thermal
expansion can easily be incorporated in the entropy function. In the third step, plasticity is added, and we
show how the entropy production can be kept positive denite via natural constitutive prescriptions on what
governs plastic changes. These prescriptions are of pseudolinear Onsagerian nature. At last, rheology is added
in the form of a tensorial dynamical degree of freedom, a non-equilibrium extra term in the entropy function.
As an application, an experiment of a uniaxially loaded and plastically deformed sample is presented, and the
measured results are analysed via our model.
References
[1] T. Fülöp and P. Ván, Kinematics of nite elastic and plastic deformations, Mathematical Methods in the
Applied Sciences, 2012, to appear. [E-print: arXiv:1007.2892].
E-mail: tamas.fulop@gmail.com