Viscoelastic fluid relation for the deformation of ice

Abstract

A frame-indifferent differential operator relation between stress, stress-rate, strain-rate, and strain-acceleration is constructed to describe the qualitative features of both constant stress and constant strain-rate responses in uni-axial stress experiments. The structure of the tensor relation cannot be determined by uni-axial data, and a variety of models reducing to the required uni-axial form are presented. The differential relation allows exact description of a family of strain-rate curves at different constant uni-axial stresses, and of some features of the stress curves at different constant strain-rates. This shows that constant stress and constant strain-rate responses reflect some common properties, and also that they reflect independent properties of the relation. That is, both types of response are necessary to define the model. A reduced model which adopts a restricted form of dependence on stress and strain-rate invariants is also analysed. Idealised families of constant-stress responses are constructed and various forms of limited matching to the reduced model are presented to show the extent to which the simplified relation can describe the complete response.