Crack propagation in brittle materials with anisotropic surface energy is important in applications involving
single crystals, extruded polymers, or geological and organic materials. Furthermore, when this anisotropy
is strong, the phenomenology of crack propagation becomes very rich, with forbidden crack propagation
directions or complex sawtooth crack patterns. This problem interrogates fundamental issues in fracture
mechanics, including the principles behind the selection of crack direction. Here, we propose a variational
phase-field model for strongly anisotropic fracture, which resorts to the extended Cahn-Hilliard framework
proposed in the context of crystal growth. Previous phase-field models for anisotropic fracture were
formulated in a framework only allowing for weak anisotropy. We implement numerically our higherorder
phase-field model with smooth local maximum entropy approximants in a direct Galerkin method.
The numerical results exhibit all the features of strongly anisotropic fracture, and reproduce strikingly well
recent experimental observations.
http://onlinelibrary.wiley.com/doi/10.1002/nme.4726/abstract
On the phase-field approach
Dear Bin,
Thanks for sharing your interesting work!
I have a question or comment nevertheless. You consider ‘kappa' as a regularizing length
parameter that can vary and even go to zero providing convergence to the zero
width crack. May be I am missing the point but I assume that by varying ‘kappa'
you get different physical problems with different crack propagations. I do not
expect any convergence with the decreasing magnitude of ‘kappa'. To the best of my
understanding (not necessarily correct) the phase-field approach is not
different from the gradient type regularization in which the length parameter
cannot be arbitrarily varied because it does have a physical meaning.
Yours,
Kosta
Dear Konstantin,Thank
Dear Konstantin,
Thank you for your comments.
I agree with you, phase-field method shares much in common with a gradient damage approach to brittle fracture, and the regularization parameter is not arbitrarily and should be choosen according to real experimental data.
In the paper of "Amor, H., Marigo, J.-J., Maurini, C., 2009. Regularized formulation of the variational brittle fracture with unilateral contact: Numerical experiments. Journal of the Mechanics and Physics of Solids 57 (8), 1209 – 1229", they discussed the chocies of the value of regularization parameter that depending on it considered as a pure numerical parameter of the regularized model to brittle fracture or internal length of a non-local gradient damage model.
Our paper mainly focus on the anisotropic surface energy/fracture toughness, our model reproduce the experments observation of the paper "Takei A, Roman B, Bico J, Hamm E, Melo F. Forbidden directions for the fracture of thin anisotropic sheets: An analogy with the wulff plot. Physical Review Letters 2013; 110:144 301".
Thanks
Bin