Cracks on paintings are a common effect of deterioration that may compromise the maintenance of artworks. These fractures often propagate almost instantaneously and are usually organized in patterns. The most classical and well-established approach to study brittle fracture propagation is the sharp-crack one, based on Griffith’s criterion. Nevertheless, considering the geometrical complexity of the patterns, for computational issues, it is more convenient to employ a phase-field approach. In the phase-field context, rate-independent evolutions are often obtained by discrete time schemes, which provide at each time step an equilibrium configuration of the system. In practice, equilibria are calculated by descent methods for the potential energy equipped with an appropriate irreversibility constraint on the phase-field parameter. These discrete evolutions in time are considered as approximations of their continuous limit in time, to be computed when the time step vanishes. In [21] we studied in detail this continuous time limit, providing a general result: it satisfies a phase-field version of Griffith criterion. In this paper, we present the outcomes of some numerical simulations that confirm our theoretical results. Specifically, we considered two model problems, one for steady and one for unsteady-state crack propagations showing the consistency of the phase-field model with Griffith criterion.

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Griffith Criterion for Steady and Unsteady-State Crack Propagation

  • Eleonora Maggiorelli

摘要

Cracks on paintings are a common effect of deterioration that may compromise the maintenance of artworks. These fractures often propagate almost instantaneously and are usually organized in patterns. The most classical and well-established approach to study brittle fracture propagation is the sharp-crack one, based on Griffith’s criterion. Nevertheless, considering the geometrical complexity of the patterns, for computational issues, it is more convenient to employ a phase-field approach. In the phase-field context, rate-independent evolutions are often obtained by discrete time schemes, which provide at each time step an equilibrium configuration of the system. In practice, equilibria are calculated by descent methods for the potential energy equipped with an appropriate irreversibility constraint on the phase-field parameter. These discrete evolutions in time are considered as approximations of their continuous limit in time, to be computed when the time step vanishes. In [21] we studied in detail this continuous time limit, providing a general result: it satisfies a phase-field version of Griffith criterion. In this paper, we present the outcomes of some numerical simulations that confirm our theoretical results. Specifically, we considered two model problems, one for steady and one for unsteady-state crack propagations showing the consistency of the phase-field model with Griffith criterion.