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Publication 17-CNA-013
Vaibhav Agrawal Kaushik Dayal Abstract: Phase-field models for crack propagation enable the simulation of complex crack patterns without
complex and expensive tracking and remeshing as cracks grow. In the setting without inertia, the
crack evolution is obtained from a variational energetic starting point, and leads to an equation for
the order parameter coupled to elastostatics. Careful mathematical analysis has shown that this is
consistent with the Griffith model for fracture. Recent efforts to include inertia in this formulation
have replaced elastostatics by elastodynamics. In this brief note, we examine the elastodynamic augmentation,
and find that it effectively causes the Griffith surface energy to depend on the velocity of
the crack. That is, considering two identical specimens that are each fractured by a single crack that
grows at different velocities in the two specimens, it is expected that the final equilibrium configurations
are nominally identical; however, the phase-field fracture models augmented with elastodynamics
achieve final configurations – in particular, the Griffiths surface energy contributions – that
depend on the crack velocity. The physical reason is that the finite relaxation time for the stresses
in the elastodynamic setting enables the cracked region to widen, beyond the value observed in the
quasistatic setting. Once the crack widens, the "no-healing" condition prevents it from relaxing even
after the specimen reaches equilibrium. In phase-field models, crack width in the reference configuration
is unrelated to the physical opening of the crack but is instead a measure of Griffiths surface
energy. This observation suggests that elastodynamic phase-field fracture models should not be used
in settings where the crack velocity is large.Get the paper in its entirety as 17-CNA-013.pdf |