COMPLAS 2025

A Nonlinear Variational Model of Cracks and Dislocations

  • Engrand, Godefroy (Université Paris-Saclay, ONERA, CNRS, LEM)
  • Ruffini, Antoine (Université Paris-Saclay, ONERA, CNRS, LEM)
  • Le Bouar, Yann (Université Paris-Saclay, ONERA, CNRS, LEM)
  • Finel, Alphonse (Université Paris-Saclay, ONERA, CNRS, LEM)

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In crystalline materials, fracture is often coupled with plastic activity. A comprehensive mesoscale modeling of fracture should therefore incorporate crack propagation and its interplay with dislocation multiplication and glide. Both cracks and dislocations are associated with discontinuities in the displacement field [1][2]. Therefore, it should be possible to construct a model based only on the displacement field. This requires the identification of a nonlinear elastic energy functional that is invariant with respect to the point group of the lattice, but also with respect to any shear deformation that leaves the lattice invariant. In this talk, we show how to construct this infinitely degenerate potential energy and discuss the numerical implementation of the model. Finally, we present simulation results that reproduce spontaneously, through the dynamics of the displacement field alone, the complex interplay between evolving fractures and dislocations, including dislocation nucleation at the crack tip and crack nucleation due to strain localisation generated by dislocation glide. REFERENCES [1] BAGGIO, R., ARBIB, EDOARDO, BISCARI, P., ET AL. LANDAU-TYPE THEORY OF PLANAR CRYSTAL PLASTICITY. PHYSICAL REVIEW LETTERS, 2019, VOL. 123, NO 20, P. 205501. [2] MARCONI, V. I. et JAGLA, E. A. Diffuse interface approach to brittle fracture. Physical Review E—Statistical, Nonlinear, and Soft Matter Physics, 2005, vol. 71, no 3, p. 036110.