Second-order phase-field formulations for anisotropic brittle fracture
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2022-02-01
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Journal Article
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Abstract
We address brittle fracture in anisotropic materials featuring two-fold and four-fold symmetric fracture toughness. For these two classes, we develop two variational phase-field models based on the family of regularizations proposed by Focardi (2001), for which Γ-convergence results hold. Since both models are of second order, as opposed to the previously available fourth-order models for four-fold symmetric fracture toughness, they do not require basis functions of C1-continuity nor mixed variational principles for finite element discretization. For the four-fold symmetric formulation we show that the standard quadratic degradation function is unsuitable and devise a procedure to derive a suitable one. The performance of the new models is assessed via several numerical examples that simulate anisotropic fracture under anti-plane shear loading. For both formulations at fixed displacements (i.e. within an alternate minimization procedure), we also provide some existence and uniqueness results for the phase-field solution.
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Volume
389
Pages / Article No.
114403
Publisher
Elsevier
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Subject
Anisotropic fracture; Two-fold symmetry; Four-fold symmetry; Phase-field modeling; Zig-zag cracking
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09697 - De Lorenzis, Laura / De Lorenzis, Laura