COMPLAS 2023

Keynote

Virtual Elements for Phase Field Modeling of Fracture in Plates

  • Aldakheel, Fadi (Leibniz Universität Hannover)
  • Hudobivnik, Blaž (Leibniz Universität Hannover)
  • Korelc, Jože (University of Ljubljana)
  • Wriggers, Peter (Leibniz Universität Hannover)

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This work outlines a computational phase-field approach to model brittle fracture in plates using the recently developed virtual element method (VEM). VEM allows using elements with an arbitrary number of nodes and non-convex shapes. The definition of the ansatz at the boundary in VEM permits revisiting the construction of the Kirchhoff-Love (KL) elements of arbitrary shape. The C 1 -continuity condition is much easier to handle in the VEM framework than in the traditional Finite Elements methodology [1]. In the presented contribution, we introduce a variational principle for the phase-field fracture evolution problem in plates. The phase-field approach regularizes sharp crack surfaces within a pure continuum setting [2]. This is based on the introduction of history fields that contain maximum reference energy obtained in the deformation history. This local variable drives the evolution of the fracture phase field and it allows the construction of an extremely robust operator split scheme that successively updates in a typical time step the history field, the crack phase field, and finally the displacement field. On the numerical side, the VEM is employed to resolve the complex crack topologies problems. Due to VEM’s flexible choice of element shapes and nodes number, elements can be changed easily during the simulation process. The performance of VEM-based KL plates for the phase-field formulation of fracture will be demonstrated by means of representative numerical examples. REFERENCES: [1] Wriggers, P., Hudobivnik, B., Allix O., On two simple virtual Kirchhoff-Love plate elements for isotropic and anisotropic materials. Comput. Mech., 69 (2), 615-637, 2022. [2] Aldakheel, F., Hudobivnik, B., Hussein, A., Wriggers, P., Phase-field modeling of brittle fracture using an efficient virtual element scheme. Comput. Methods Appl. Mech. Engrg., 341:443–466, 2013.