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The Variational Approach to Fracture: A Theoretical Model and Some Numerical Results

In: Variational Analysis and Aerospace Engineering

Author

Listed:
  • Gianpietro Del Piero

    (Università di Ferrara
    International Research Center M&MoCS)

Abstract

The evolution of the response of an elastic-plastic bar from the initial unstressed state to rupture is studied with a one-dimensional model based on incremental energy minimization. The model can reproduce both brittle and ductile fracture, as well as an intermediate fracture mode, called ductile–brittle, in which, due to an extreme localization of the plastic deformation, the bar suddenly breaks after a more or less protracted plastic regime. Numerical simulations obtained from the model’s implementation are compared with the results of tensile tests on bars made of steel and of non-reinforced concrete. With an accurate choice of the analytical shapes of the plastic strain energy, not only the overall behavior, but also many details of the experimental response can be captured.

Suggested Citation

  • Gianpietro Del Piero, 2016. "The Variational Approach to Fracture: A Theoretical Model and Some Numerical Results," Springer Optimization and Its Applications, in: Aldo Frediani & Bijan Mohammadi & Olivier Pironneau & Vittorio Cipolla (ed.), Variational Analysis and Aerospace Engineering, pages 169-189, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-45680-5_7
    DOI: 10.1007/978-3-319-45680-5_7
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