210 research outputs found

    Important aspects in the formulation of solid-fluid debris-flow models. Part I. Thermodynamic implications

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    This article points at some critical issues which are connected with the theoretical formulation of the thermodynamics of solid-fluid mixtures of frictional materials. It is our view that a complete thermodynamic exploitation of the second law of thermodynamics is necessary to obtain the proper parameterizations of the constitutive quantities in such theories. These issues are explained in detail in a recently published book by Schneider and Hutter (Solid-Fluid Mixtures of Frictional Materials in Geophysical and Geotechnical Context, 2009), which we wish to advertize with these notes. The model is a saturated mixture of an arbitrary number of solid and fluid constituents which may be compressible or density preserving, which exhibit visco-frictional (visco-hypoplastic) behavior, but are all subject to the same temperature. Mass exchange between the constituents may account for particle size separation and phase changes due to fragmentation and abrasion. Destabilization of a saturated soil mass from the pre- and the post-critical phases of a catastrophic motion from initiation to deposition is modeled by symmetric tensorial variables which are related to the rate independent parts of the constituent stress tensor

    Important aspects in the formulation of solid-fluid debris-flow models. Part II. Constitutive modelling

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    This article is the continuation of Part I: ‘Thermodynamic Implications' of a article with the same title. Knowledge of the content/results of Part I, Hutter and Schneider (Continuum Mech. Thermodyn., 2009) or Schneider and Hutter (Solid-Fluid Mixtures of Frictional Materials in Geophysical and Geotechnical Context, 2009), is assumed. The intention is to see whether (i) well-known formulations of binary mixture models can be derived from the thermodynamic model, (ii) classical hypo-plasticity is deducible from the frictional evolution equation and (iii) the popular assumption of pressure equilibrium is justified. To this end, we ignore mass and volume fraction interaction rate densities, restrict considerations to isothermal processes, ignore higher order non-linearities in the constitutive relations and use the principle of phase separation. These assumptions transform the equilibrium stresses, heat flux and interaction forces to considerably simplified forms. Furthermore, the analysis shows that classical hypo-plasticity can be reconstructed with the introduction of a new objective time derivative for the stress-like variable. Non-equilibrium contributions to the stresses and interaction forces are also briefly discussed. It is, finally, shown that the assumption of pressure equilibrium precludes the application of frictional stresses in equilibrium. This unphysical assumption is, therefore, replaced by a thermodynamic closure condition that is more flexible and less restrictive. It allows for frictional stresses in thermodynamic equilibrium and, therefore, is sufficiently general for applications to mixture theorie

    A viscoelastic damage model for polycrystalline ice, inspired by Weibull-distributed fiber bundle models. Part II: Thermodynamics of a rank-4 damage model

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    We consider a viscoelastic-viscoplastic continuum damage model for polycrystalline ice. The focus lies on the thermodynamics particularities of such a constitutive model and restrictions on the constitutive theory which are implied by the entropy principle. We use Müller's formulation of the entropy principle, together with Liu's method of exploiting it with the aid of Lagrange multipliers

    Thermally driven interaction of the littoral and limnetic zones by autumnal cooling processes

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    In autumn, during the transition period, shores influence the interior dynamics of large temperate lakes by the formation of horizontal water-temperature gradients between the shallow and deep areas, whilst vertical temperature gradients are smoothed by convection due to surface cooling. A simple heat budget model, based on the heat balance of the water column without horizontal advection and turbulent mixing, allows deduction of the time-dependent difference between the mean temperature within the littoral area and the temperature in the upper mixed layer. The model corroborates that littoral areas cool faster than regions distant from shores, and provides a basis for an estimation of structure of flows from the beginning of cooling process till the formation of the thermal bar. It predicts the moment in the cooling process, when the corresponding density difference between the littoral and limnetic parts reaches a maximum. For a linear initial vertical temperature profile, the time-dependent "target depth" is explicitly calculated; this is the depth in the pelagic area with a temperature, characteristic of the littoral zone. This depth is estimated as 4/3 of the (concurrent) thickness of the upper mixed layer. It is shown that, for a linear initial vertical temperature profile, the horizontal temperature profile between the shore and the lake has a self-similar behavior, and the temperature difference between the littoral waters and the upper mixed off-shore layer, divided by the depth of the upper mixed layer, is an invariant of the studied process. The results are in conformity with field data

    A viscoelastic damage model for polycrystalline ice, inspired by Weibull-distributed fiber bundle models. Part I: Constitutive models

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    We consider a constitutive model for polycrystalline ice, which contains delayed-elastic and viscous deformations, and a damage variable. The damage variable is coupled to the delayed-elastic deformation by a fiber bundle ansatz. We construct an isotropic theory, which can be calibrated with experimental data. Furthermore, we generalize the theory to a damage model in terms of rank-four tensors. This general model allows the evolution of anisotropic damage
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