An enhanced algorithmic scheme for relaxed incremental variational damage formulations at finite strains. Issue 1 (14th December 2021)

• Record Type: Journal Article
• Authors: Köhler, Maximilian; Neumeier, Timo; Peterseim, Daniel; Peter, Malte A.; Balzani, Daniel
• Editors: Kaliske, M.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 21:Issue 1(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2021-12-14
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.202100135
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: Relaxed damage formulations enable to overcome the mesh dependency induced by a loss of ellipticity. However, such approaches require the construction of a convex hull of the associated energy potential. Within this contribution, an improved one‐dimensional, relaxed damage formulation of [1] with a successive, computationally optimal convexification scheme, see [2], is presented. Instead of solving a non‐convex optimization problem at the material point level, we iterate over a discrete grid and build consecutively linear Taylor expansions to construct the convex hull. Due to the reduced computational effort, integration of the one‐dimensional mechanical model over orientation distributions to obtain the three‐dimensional response as proposed in [3] becomes more feasible.