The objective of this review is to examine how the concept of plasticity is used in geophysical fluid dynamics. Rapid mass movements such as snow avalanches or debris flows involve slurries of solid particles (ice, boulder, clay, etc.) within an interstitial fluid (air, water). The bulk behavior of these materials has often been modeled as plastic materials, i.e., a plastic material yields and starts to flow once its stress state has significantly departed from equilibrium. Two plastic theories are of common use in fluid dynamics: Coulomb plasticity and viscoplasticity. These theories have little in common, since ideal Coulomb materials are two-phase materials for which pore pressure and friction play the key role in the bulk dynamics, whereas viscoplastic materials (e.g., Bingham fluids) typically behave as single-phase fluids on the macroscopic scale and exhibit a viscous behavior after yielding. Determining the rheological behavior of geophysical materials remains difficult because they encompass coarse, irregular particles over a very wide range of size. Consequently, the true nature of plastic behavior for geophysical flows is still vigorously debated. In this review, we first set out the continuum-mechanics principles used for describing plastic behavior. The notion of yield surface rather than yield stress is emphasized in order to better understand how tensorial constitutive equations can be derived from experimental data. The notion of single-phase or two-phase behaviors on the macroscopic scale is then examined using a microstructural analysis on idealized suspensions of spheres within a Newtonian fluid; for these suspensions, the single-phase approximation is valid only at very high or low Stokes numbers. Within this framework, the bulk stress tensor can also be constructed, which makes it possible to give a physical interpretation to yield stress. Most of the time, depending on the bulk properties (especially, particle size) and flow features, bulk behavior is either Coulomb-like or viscoplastic in simple-shear experiments. The consequences of the rheological properties on the flow features are also examined. Some remarkable properties of the governing equations describing thin layers flowing down inclined surfaces are discussed. Finally, the question of parameter fitting is tackled: since rheological properties cannot be measured directly in most cases, they must be evaluated from field data. As an example, we show that the Coulomb model successfully captures the main traits of avalanche motion, but statistical analysis demonstrates that the probability distribution of the friction coefficient is not universal.

/pdf/plasticity-and-geophysical-flows-a-review-4bos64lahx.pdf

Plasticity and geophysical flows: A review

In this Chapter we explain the origins of Nonsmooth Mechanics and of the Inequality Problems. To do this we use the two notions of convex and of nonconvex superpotentials. We consider boundary conditions and material laws resulting from convex or nonconvex, nonsmooth energy functions using the concept of sub differential or of generalized gradient. For additional information on these subjects the reader is referred to the monographs and books of Duvaut and Lions [Duv72], Panagiotopoulos [Pan85], Hlavacek et al. [H188], Moreau, Pana-giotopoulos, Strang [Mor88a,b], Antes, Panagiotopoulos [Ant92], as well as to [Mor68,86,88c] and [Ger74].

Nonsmooth Mechanics I

Transport mechanics in systems of orientable particles. IV. convective transport

Das Cosserat Kontinuum

Publisher Summary This chapter emphasizes the fact that, mathematically, elasticity theory has much in common with modern theories of thin elastic shells, plates, or rods; static theories of liquid crystals; and various other local theories associated with the most common types of variational principles. This chapter discusses that the interest in elasticity theory lies in improving the theory underlying the somewhat mystical process whereby definite forms of constitutive equations are selected. The domain of constitutive equations may include subdomains that are, in principle, inaccessible to the experimentist. The operationalist holds a contrary view. The chapter highlights that the elasticity theory can predict the effects that are not commonly thought of as being associated with the adjective “elastic.” In such cases, elasticity theory enters into free competition with other theories capable of describing the effect at hand.

Special Topics in Elastostatics

Six Lectures on Modern Natural Philosophy

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Six Lectures on Modern Natural Philosophy