Γ-convergence for high order phase field fracture: continuum and isogeometric formulations
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We consider second order phase field functionals, in the continuum setting, and their discretization with isogeometric tensor product B-splines. We prove that these functionals, continuum and discrete, Γ-converge to a brittle fracture energy, defined in the space GSBD^2. In particular, in the isogeometric setting, since the projection operator is not Lagrangian (i.e., interpolatory) a special construction is neeeded in order to guarantee that recovery sequences take values in [0,1]; convergence holds, as expected, if h = o (ε), being h the size of the physical mesh and ε the internal length in the phase field energy.
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