We study a continuum model of dislocation transport in order to investigatethe formation of heterogeneous dislocation patterns. We propose a physicalmechanism which relates the formation of heterogeneous patterns to the dynamicsof a driven system which tries to minimize an internal energy functional whilesubject to dynamic constraints and state dependent friction. This leads us to anovel interpretation which resolves the old 'energetic vs. dynamic' controversyregarding the physical origin of dislocation patterns. We demonstrate therobustness of the developed patterning scenario by considering the simplestpossible case (plane strain, single slip) yet implementing the dynamics of thedislocation density evolution in two very different manners, namely (i) ahydrodynamic formulation which considers transport equations that arecontinuous in space and time while assuming a linear stress dependency ofdislocation motion, and (ii) a stochastic cellular automaton implementationwhich assumes spatially and temporally discrete transport of discrete 'packets'of dislocation density which move according to an extremal dynamics. Despitethe huge differences between both kinds of models, we find that the emergentpatterns are mutually consistent and in agreement with the prediction of alinear stability analysis of the continuum model. We also show how differenttypes of initial conditions lead to different intermediate evolution scenarioswhich, however, do not affect the properties of the fully developed patterns.
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