Abstract
We consider a model of an elastic manifold driven on a disordered energy landscape, with generalized long range elasticity. Varying the form of the elastic kernel by progressively allowing for the existence of zero modes, the model interpolates smoothly between mean-field depinning and finite dimensional yielding. We find that the critical exponents of the model change smoothly in this process. Also, we show that in all cases the Herschel-Buckley exponent of the flow curve depends on the analytical form of the microscopic pinning potential. Within the present elastoplastic description, all this suggests that yielding in finite dimensions is a mean-field transition.
Highlights
We consider a model of an elastic manifold driven on a disordered energy landscape, with generalized long range elasticity
The problem of depinning of an elastic manifold moving on a disordered landscape has been rationalized by analogy with the theory of critical phenomena [1, 2] and studied for over 30 years already
In this sense, depinning has shaped the theoretical endeavors in the understanding of the yielding transition of amorphous solids under deformation, that received full attention of the statistical physics community only recently
Summary
We consider a model of an elastic manifold driven on a disordered energy landscape, with generalized long range elasticity. This anisotropy is a curse for the FRG approach and the responsible for special avalanche correlations in the form of slip lines (or planes), that greatly determine the differences among the plastic yielding transition and its elastic depinning counterpart.
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