On the Motion of Curved Dislocations in Three Dimensions: Simplified Linearized Elasticity

@article{Fonseca2021OnTM,
  title={On the Motion of Curved Dislocations in Three Dimensions: Simplified Linearized Elasticity},
  author={I. Fonseca and Janusz Ginster and Stephan Wojtowytsch},
  journal={SIAM J. Math. Anal.},
  year={2021},
  volume={53},
  pages={2373-2426}
}
It is shown that in core-radius cutoff regularized simplified elasticity (where the elastic energy depends quadratically on the full displacement gradient rather than its symmetrized version), the force on a dislocation curve by the negative gradient of the elastic energy asymptotically approaches the mean curvature of the curve as the cutoff radius converges to zero. Rigorous error bounds in Holder spaces are provided. As an application, convergence of dislocations moving by the gradient flow… Expand
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Renormalized Energy and Forces on Dislocations
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1
2
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4
5
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