Applications of a Nonlinear Constitutive Equation for Creeping Snow
AbstractIn the seventies the author carried out numerous laboratory tests, simultaneously performedunder six different states of stress and deformation (totally 121 identical three samplestested). The aim was to obtain a three dimensional nonlinear constitutive equation, i.e.,one which higher applies to stresses.The theoretical background was a constitutive equation consistent with the principle of maximum entropy production. The irreversible part - whichwas exclusively considered - depends only on the dissipafion function, represented by anexponential series. The final result consists of nine coefficients of three invariants of thestress tensor. Unfortunately, the resulting equation was never used to resolve practicalproblems in snow mechanics. This paper is aimed to demonstrate the use fulness of theequation by means of simple examples. For a uniform horizontal snow cover, it was firstlyshown that snow behaves strongly non-symmetrically under compression and tension. Andsecondly, it was seen that the settlement (compression) deformation rates are up to 50 percent higher than those with linear behaviour. In an other example, the development of ashear crack on the occasion of snow slab release has demonstrated that fracture starts earlierupslope and propagates faster than downslope. On the other hand, linearity between shearstresses and shear deformation can be justified.
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