Constitutive models for granular materials including quasi-static frictional behaviour: Toward a thermodynamic theory of plasticity |
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Authors: | B Svendsen K Hutter L Laloui |
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Institution: | (1) Federal Institute for Materials Research and Testing, D-12200 Berlin, Germany , DE;(2) Institute of Mechanics, Darmstadt University of Technology, D-64289 Darmstadt, Germany , DE;(3) Laboratory of Soil Mechanics, Swiss Federal Institute of Technology, CH-1015 Lausanne, Switzerland , CH |
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Abstract: | This work deals with the thermodynamic formulation of constitutive models for materials whose quasi-static behaviour is governed
by internal friction, e.g., dry granular materials. The process of internal friction is represented here phenomenologically
with the help of a second-order, symmetric-tensor-valued internal variable. A general class of models for the evolution of
this variable is considered, including as special cases a hypoelastic-like form for this relation as well as the hypoplastic
form of Kolymbas (1991). The thermodynamic formulation is carried out in the context of the Müller-Liu entropy principle.
Among other things, it is shown that for the hypoelastic-type models, a true equilibrium inelastic Cauchy stress exists. On
the other hand, such a stress does not exist for the hypoplastic model due to its rate-independence and incremental non-linearity.
With the help of a slight generalization of the notion of thermodynamic equilibrium, i.e., to thermodynamic “quasi-equilibrium,”
however, such a Cauchy stress can be formulated for the hypoplastic model. As it turns out, this quasi-equilibrium for the
Cauchy stress represents a thermodynamic generalization of the so-called quasi-static stress postulated for example by Goddard
(1986) in the context of his viscoplastic model for a frictional-dissipative, and in particular for granular, materials.
Received January 22, 1999 |
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