A polyconvex phase‐field approach to fracture with application to finite‐deformation contact problems. Issue 1 (15th March 2018)

• Record Type: Journal Article
• Authors: Franke, Marlon; Dittmann, Maik; Hesch, Christian; Betsch, Peter
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 17:Issue 1(2017)
• Page Start: 297
• Page End: 298
• Publication Date: 2018-03-15
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201710118
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: 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)