Cohesive crack propagation analysis by the hybrid equilibrium element formulation and element side rotation

  • Parrinello, Francesco (University of Palermo)
  • Borino, Guido (University of Palermo)

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The present paper proposes an original formulation for the analysis of propagation of a cohesive crack in elastic solids by the approach of hybrid equilibrium element coupled with a minimal finite element re-meshing, requiring only the rotation of the element sides, according to the orientation of maximum principal stress direction. The hybrid equilibrium element (HEE) is an accurate stress-based formulation developed in the variational framework of minimum complementary energy principle and it provides an effective numerical tool for modelling the inter-element fracture propagation, as proposed in Ref. [5, 6] for static problems. The inter-element cohesive behaviour is modelled by the extrinsic interface proposed in Ref. [6]. The interface can be assumed to be implicitly embedded at every element side and it affects the overall response only when the interface opening condition is attained. The interface is modelled as a function of the same degrees of freedom of the HEE (generalized stress components) and the pre- and post-failure behaviour of the interface can be modelled without any additional degree of freedom. The direction of maximum principal stress at the crack tip is assumed as the direction of crack propagation. The crack is meshed as an extrinsic interface embedded at the closest element side, which is rotated around the tip in order to be geometrically co-aligned to the crack. The numerical problem of finding the element side orientation is strongly non-linear and the search of the crack propagation direction requires an iterative procedure. The element side rotation is updated with the evolution of the stress field at the crack tip, as long as one point of the embedded extrinsic interface is still undamaged. Moreover, in order to prevent erroneous crack prediction, a maximum rotation angle between two contiguous element sides along the crack path is assumed. The HEE with the extrinsic interface embedded at the element sides is developed and implemented in an open-source finite element code, employing quadratic, cubic and quartic stress fields. Numerical simulations of some fracture propagation problems are presented and the related results discussed.