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Statistical-Mechanics Approach to Collective Dislocation Dynamics

By Markus Hütter (Eindhoven University of Technology, Mech. Engng.)
Co-authors: Marleen Kooiman (Eindhoven University of Technology, Mech. Engng.)
Marc G. D. Geers (Eindhoven University of Technology, Mech. Engng.)


This contribution concerns the modeling of crystal plasticity in terms of the elementary dynamics of dislocations. Particularly, the focus is on studying the collective effects of large numbers of dislocations, and on the corresponding emerging phenomena. To achieve this goal, nonequilibrium thermodynamics and statistical mechanics [1-3] are used. Departing from the elementary dynamics of a collection of many dislocations, we derive the dynamics for coarse-grained dislocation densities. This dynamics is driven by a free-energy derivative, which in turn is then convoluted with a memory kernel, the latter playing the role of an effective macroscopic mobility. Particularly, explicit expressions are derived for both the free energy [4-6] and the memory kernel [7, 8], respectively. Two aspects of this procedure are particularly beneficial. First, since the adopted coarse-graining approach is systematic, it has a minimal number of assumptions. And second, it is not only shown that there is an emergent contribution in the coarse-grained dynamics, but also that this emergent contribution is actually the dominant one. This implies that, although the force-velocity relation at the elementary discrete-dislocation level is linear, a strongly non-linear relation between stress and strain rate naturally emerges at the coarse-grained level. Acknowledgement: This work is part of the NWO Complexity programme, project CorFlux (nr. 10012310), which is financed by the Netherlands Organisation for Scientific Research (NWO). References: [1] M. Grmela, H.C. Öttinger. Phys. Rev. E, 56:6620-6632, 1997. [2] H.C. Öttinger, M. Grmela. Phys. Rev. E, 56:6633-6655, 1997. [3] H.C. Öttinger. Beyond Equilibrium Thermodynamics. Wiley, 2005. [4] M. Kooiman, M. Hütter, and M.G.D. Geers. J. Stat. Mech. Theory E., P04028, 2014. [5] M. Kooiman, M. Hütter, and M.G.D. Geers. J. Mech. Phys. Solids, 78, 186-209, 2015. [6] M. Kooiman, M. Hütter, and M.G.D. Geers. J. Mech. Phys. Solids, 88, 267-273, 2016. [7] M. Kooiman, M. Hütter, and M.G.D. Geers. J. Stat. Mech. Theory E., P06005, 2015. [8] M. Kooiman, M. Hütter, and M.G.D. Geers. J. Mech. Phys. Solids, 90, 77-90, 2016.

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