A time-adaptive finite element phase-field model suitable for rate-independent fracture mechanics

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dc.contributor.authorRörentrop, Felix
dc.contributor.authorBoddin, Samira
dc.contributor.authorKnees, Dorothee
dc.contributor.authorMosler, Jörn
dc.date.accessioned2025-12-02T10:10:09Z
dc.date.available2025-12-02T10:10:09Z
dc.date.issued2024-08-01
dc.description.abstractThe modeling of cracks is an important topic — both in engineering as well as in mathematics. Since crack propagation is characterized by a free boundary value problem (the geometry of the crack is not known beforehand, but part of the solution), approximations of the underlying sharp-interface problem based on phase-field models are often considered. Focusing on a rate-independent setting, these models are defined by a unidirectional gradient-flow of an energy functional. Since this energy functional is non-convex, the evolution of the variables such as the displacement field and the phase-field variable might be discontinuous in time leading to so-called brutal crack growth. For this reason, solution concepts have to be carefully chosen in order to predict discontinuities that are physically reasonable. One such concept is that of Balanced Viscosity solutions (BV solutions). This concept predicts physically sound energy trajectories that do not jump across energy barriers. The paper deals with a time-adaptive finite element phase-field model for rate-independent fracture which converges to BV solutions. The model is motivated by constraining the pseudo-velocity of the crack tip. The resulting constrained minimization problem is solved by the augmented Lagrangian method. Numerical examples highlight the predictive capabilities of the model and furthermore show the efficiency and the robustness of the final algorithm.en
dc.identifier.urihttp://hdl.handle.net/2003/44405
dc.language.isoen
dc.relation.ispartofseriesComputer methods in applied mechanics and engineering; 431
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectPhase-field theoryen
dc.subjectRate-independent systemsen
dc.subjectBrittle fractureen
dc.subjectDamage mechanicsen
dc.subjectTime-adaptivityen
dc.subjectBalanced viscosity solutionsen
dc.subjectAlternate minimizationen
dc.subject.ddc620
dc.subject.ddc670
dc.subject.rswkSprödbruch
dc.subject.rswkPhasenfeldmodell
dc.subject.rswkSchadensmechanik
dc.subject.rswkViskositätslösung
dc.titleA time-adaptive finite element phase-field model suitable for rate-independent fracture mechanicsen
dc.typeText
dc.type.publicationtypeArticle
dcterms.accessRightsopen access
eldorado.dnb.deposittrue
eldorado.doi.registerfalse
eldorado.secondarypublicationtrue
eldorado.secondarypublication.primarycitationFelix Rörentrop, Samira Boddin, Dorothee Knees, Jörn Mosler, A time-adaptive finite element phase-field model suitable for rate-independent fracture mechanics, Computer Methods in Applied Mechanics and Engineering, Volume 431, 2024, 117240, https://doi.org/10.1016/j.cma.2024.117240
eldorado.secondarypublication.primaryidentifierhttps://doi.org/10.1016/j.cma.2024.117240

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