Elasto-plastic evolution of single crystals driven by dislocation flow

This work introduces a model for large-strain, geometrically nonlinear elasto-plastic dynamics in single crystals. The key feature of our model is that the plastic dynamics are entirely driven by the movement of dislocations, that is, 1-dimensional topological defects in the crystal lattice. It is well known that glide motion of dislocations is the dominant microscopic mechanism for plastic deformation in many crystalline materials, most notably in metals. We propose a novel geometric language, built on the concepts of space-time slip trajectories and the crystal scaffold to describe the movement of (discrete) dislocations and to couple this movement to plastic flow. The energetics and dissipation relationships in our model are derived from first principles drawing on the theories of crystal modeling, elasticity, and thermodynamics. The resulting force balances involve a new configurational stress tensor describing the forces acting against slip. In order to place our model into context, we further show that it recovers several laws that were known in special cases before, most notably the equation for the Peach-Koehler force (linearized configurational force) and the fact that the combination of all dislocations yields the curl of the plastic distortion field. Finally, we also include a brief discussion on how a number of other effects, such as hardening, softening, dislocation climb, and coarse-graining, could be incorporated into our model.

Automated summary

This work introduces a model for large-strain, geometrically nonlinear elasto-plastic dynamics in single crystals, where the plastic dynamics are entirely driven by the movement of dislocations. The authors propose a novel geometric language to describe the movement of dislocations and couple it to plastic flow. The energetics and dissipation relationships in the model are derived from first principles. The authors further show that the model recovers several known laws and discuss how other effects could be incorporated.