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Gradient field theory of material instabilities

Valanis K.

Archives of Mechanics

2000

Vol. 52, nr 4-5

817-838

Previously, we developed a gradient thermodynamic theory of internal fields (migratory motions). The theory predicts the observed periodic deformation structures, in material domains under uniform tractions. More recently we showed, in a uniform stress field, that the theory has the proper mathematical framework for the prediction of Portevin-Le Chatelier (PLC for short) instabilities. Here we review our previous work and address the more difficult problem of a non-uniform stress field. Specifically, we predict the points of instability of a solid cylinder under torsion, with the experiments of Dillon as backdrop. Again, we find close agreement between theory and experiment.