Sharp-interface limits for brittle fracture via the inverse-deformation formulation
<|reference_start|>Sharp-interface limits for brittle fracture via the inverse-deformation formulation: We derive sharp-interface models for one-dimensional brittle fracture via the inverse-deformation approach. Methods of Gamma-convergence are employed to obtain the singular limits of previously proposed models. The latter feature a local, non-convex stored energy of inverse strain, augmented by small interfacial energy, formulated in terms of the inverse-strain gradient. They predict spontaneous fracture with exact crack-opening discontinuities, without the use of damage (phase) fields or pre-existing cracks; crack faces are endowed with a thin layer of surface energy. The models obtained herewith inherit the same properties, except that surface energy is now concentrated at the crack faces. Accordingly, we construct energy-minimizing configurations. For a composite bar with a breakable layer, our results predict a pattern of equally spaced cracks whose number is given as an increasing function of applied load.<|reference_end|>
@article{healey2024sharp-interface,
    title={Sharp-interface limits for brittle fracture via the inverse-deformation
  formulation},
    author={Timothy J. Healey, Roberto Paroni, Phoebus Rosakis},
    journal={arXiv preprint arXiv:2403.00838},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.00838},
    primaryClass={math.AP cs.NA math.NA}
}