A Dimension-Reduction Model for Brittle Fractures on Thin Shells with Mesh Adaptivity

@article{Almi2020ADM,
  title={A Dimension-Reduction Model for Brittle Fractures on Thin Shells with Mesh Adaptivity},
  author={Stefano Almi and Sandro Belz and Stefano Micheletti and Simona Perotto},
  journal={ArXiv},
  year={2020},
  volume={abs/2004.08871}
}
In this paper, we derive a new 2D brittle fracture model for thin shells via dimension reduction, where the admissible displacements are only normal to the shell surface. The main steps include to endow the shell with a small thickness, to express the three-dimensional energy in terms of the variational model of brittle fracture in linear elasticity, and to study the [Formula: see text]-limit of the functional as the thickness tends to zero. The numerical discretization is tackled by first… 

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