| Abstract: |
| Dislocations are line defects in crystalline materials whose dissipative motion drives plastic deformation. Their evolution involves complex topological changes and the formation of singular geometries.
In this talk, we propose a variational framework for rate-dependent dislocation dynamics with superlinear dissipation. Dislocations are modeled as integral currents, which naturally capture the underlying geometric singularities. The evolution is formulated as a generalized gradient flow of currents.
A central difficulty is that the dissipation is not lower semicontinuous in the natural weak${}^*$ topology, due to the rate dependence. To overcome this, we introduce an additional Young-measure structure for the velocity field, which captures the spatial micro-oscillations arising in the limit.
The evolution is constructed via the Weighted-Energy-Dissipation (WED) variational approach, leading to solutions satisfying an energy--dissipation inequality. |
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