Constitutive+Models

= Constitutive modelling of slip and plasticity =

The following topics were brought up by Peter Sollich and Anael Lemaitre on Tuesday August 23 for discussion. A recording of that discussion can be found at [] What should it be able to predict? (a) Bulk flows (mainly shear): - linear response; broad relaxation timescale spectrum - flow curves: yield stress, sigma-sigma_yield ~ (shear rate)^p [but is this just a fit or more fundamental?] - stress overshoots (shear startup), transients for/change of shear rate - history dependence (repeated deformation: work hardening), aging - normal stresses (or differences), dilatancy (b) Localization/shear banding: - when stable, what type (e.g. shear rate=0 except for narrow region [=slip], or two [or more?] bands with nonzero shear rates, or one band with shear rate=0) - when dynamically accessible (nature of instability) - stick-slip transition/intermittency/link to localization and fracture - aging? [could occur in unsheared or weakly sheared zones] (c) Variation with important "external" control parameters, in addition to shear rate or stress: - volume fraction - temperature - normal stress/pressure for earthquakes? Physical basis of models - are non-spatial models adequate at least for bulk flows, i.e. are rearrangements/catastrophes sufficiently uniform and interactions sufficiently long-ranged [to get mean-field behaviour] or short-ranged [to avoid strong spatial correlations]? - nature of dissipative events; localized for small perturbations but extended (cooperative) in steady shear? - nature of state variables [area of contact/granular temperature/density] - how _many_ state variables do we need (1 or 2 [rate-state, STZ], or a whole function [SGR])? - can we get away with similar models for different materials? e.g.: (colloids/emulsions; basic constituents are compressible, system including solvent is incompressible) [most], granulars) colloids, pore fluid in earthquakes...) How can experiments constrain/discriminate between models? - various types of shear banding/localization? - occurrence of stick-slip? - can experiments constrain the choice of state variable? Existing modelling approaches [review on demand] - single state variable: rate-state, Bonn et al's viscosity bifurcation; Ajdari/Lequeux et al's fluidity models (non-spatial, normally single relaxation timescale or ill-defined linear response) - continuum: damage rheology, phase field (good at localization, less good at broad linear response?) - mesoscopic/coarse-grained models: but can be extended; good for deformation history, and with effective temperature maybe also be aging, but single relaxation timescale) clear/unique; has aging effects and broad relaxation time spectrum but this is put in by hand via rho(E))) al; not convected [yet] and so far explored mainly for localization and stress propagation) [amplitude-dependent] linear response; predicts single possible exponent p=1/5 for flow curve) Other open questions: - regeneration of dissipative zones in systems where kT=0? - for localization: what lengthscales do we need (size of STZ/SGR-element?); how do we put these into continuum theories? - in non-spatial models, what assumptions on homogeneity (stress? strain? strain rate?)
 * hard materials (granulars; dilatancy is important?) vs soft ones
 * thermal (atomic/molecular glasses) vs athermal ones (colloids, emulsions
 * type of local dissipation (friction in granulars, solvent flows in
 * STZ and variations, e.g. granular (mainly without spatial information,
 * SGR (non-spatial; can be extended, but coupling between regions not
 * Picard's stress propagation (similar to earthquake models by Obukhov et
 * Hebraud & Lequeux's "mode coupling" theory (non-spatial; unusual