On the definitions of failure and critical states in hypoplasticity |
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Authors: | V A Osinov |
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Institution: | (1) Institute of Geotechnical Engineering, University of Natural Resources and Applied Life Sciences, Feistmantelstr. 4, 1180 Vienna, Austria |
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Abstract: | A granular body is said to be at failure or in a critical state if the stress state does not change while the body is continuously
deformed. Within the framework of hypoplasticity, such states, generally called stationary states,are conventionally defined
by the condition that an objective (the Jaumann) stress rate vanishes. However, not all stationary states attained under monotonic
deformation lie within the scope of this definition. Simple shear is an example. In fact, stationary states are characterized
by zero material time derivative of the stress tensor rather than zero Jaumann rate. In the present paper, we give a generalized
definition of stationarity by the condition of zero material time derivative of the stress tensor. The new definition extends
the set of possible stationary states and includes those which are not covered by the previous definition. Stationary states
are analysed quantitatively using calibrated hypoplastic equations. It is shown numerically that, if the norm of the spin
tensor is of the same order as, or smaller than, the norm of the stretching tensor, the old definition approximates all possible
sationary states with sufficient accuracy.
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Keywords: | Failure Critical state Granular material Hypoplasticity |
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