5
views
0
recommends
+1 Recommend
0 collections
    0
    shares
      • Record: found
      • Abstract: found
      • Article: found
      Is Open Access

      Interior-point methods for the phase-field approach to brittle and ductile fracture

      Preprint
      , , ,

      Read this article at

      Bookmark
          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          Abstract

          The governing equations of the variational approach to brittle and ductile fracture emerge from the minimization of a non-convex energy functional subject to irreversibility constraints. This results in a multifield problem governed by a mechanical balance equation and evolution equations for the internal variables. While the balance equation is subject to kinematic admissibility of the displacement field, the evolution equations for the internal variables are subject to irreversibility conditions, and take the form of variational inequalities, which are typically solved in a relaxed or penalized way that can lead to deviations of the actual solution. This paper presents an interior-point method that allows to rigorously solve the system of variational inequalities. With this method, a sequence of perturbed constraints is considered, which, in the limit, recovers the original constrained problem. As such, no penalty parameters or modifications of the governing equations are involved. The interior-point method is applied in both a staggered and a monolithic scheme for both brittle and ductile fracture models. In order to stabilize the monolithic scheme, a perturbation is applied to the Hessian matrix of the energy functional. The presented algorithms are applied to three benchmark problems and compared to conventional methods, where irreversibility of the crack phase-field is imposed using a history field or an augmented Lagrangian.

          Related collections

          Author and article information

          Journal
          19 November 2020
          Article
          2011.10125
          7604975b-cb48-4134-87f6-c818d4271d3e

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

          History
          Custom metadata
          35 pages, 16 figures
          math.NA cs.NA

          Numerical & Computational mathematics
          Numerical & Computational mathematics

          Comments

          Comment on this article