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A polyconvex phase‐field approach to fracture with application to finite‐deformation contact problems
Author(s) -
Franke Marlon,
Dittmann Maik,
Hesch Christian,
Betsch Peter
Publication year - 2017
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201710118
Subject(s) - finite strain theory , phase field models , fracture (geology) , stability (learning theory) , elasticity (physics) , convergence (economics) , field (mathematics) , isogeometric analysis , mathematics , computer science , mathematical optimization , phase (matter) , materials science , finite element method , structural engineering , engineering , physics , quantum mechanics , machine learning , economic growth , pure mathematics , economics , composite material
Variationally consistent phase‐field methods allow for an efficient investigation of complex three‐dimensional fracture problems (see [1, 2]). However, formulations for large deformation problems often exhibit a lack of numerical stability for different loading scenarios. In the underlying contribution a novel formulation for finite strain polyconvex elasticity is adapted to phase‐field fracture problems. In particular we introduce a new anisotropic split based on the principal invariants of the right Cauchy‐Green strain tensor for a proper treatment of fracture within the polyconvex framework (see [4]). This polyconvex phase‐field fracture formulation can be implemented in a straightforward manner and improves the numerical stability. Furthermore, a fourth order crack density functional is considered to improve accuracy and convergence. To account for the C1 requirement the system is embedded in a sophisticated isogeometric framework with the ability of local refinement. Eventually, a variationally consistent Mortar contact algorithm is applied (see [3]) to handle contact boundaries. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)