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Mathematics > Optimization and Control

arXiv:2210.05502 (math)
[Submitted on 11 Oct 2022 (v1), last revised 9 Nov 2022 (this version, v2)]

Title:A new shape optimization approach for fracture propagation

Authors:Tim Suchan (1), Kathrin Welker (2), Winnifried Wollner (3) ((1) Helmut-Schmidt-Universität/Universität der Bundeswehr Hamburg, Germany, (2) Technische Universität Bergakademie Freiberg, Germany, (3) Universität Hamburg, Germany)
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Abstract:Within this work, we present a novel approach to fracture simulations based on shape optimization techniques. Contrary to widely-used phase-field approaches in literature the proposed method does not require a specified 'length-scale' parameter defining the diffused interface region of the phase-field. We provide the formulation and discuss the used solution approach. We conclude with some numerical comparisons with well-established single-edge notch tension and shear tests.
Comments: 10 pages, 6 figures, Accepted for publication in: Proceedings in Applied Mathematics and Mechanics 2022
Subjects: Optimization and Control (math.OC)
Cite as: arXiv:2210.05502 [math.OC]
  (or arXiv:2210.05502v2 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2210.05502

Submission history

From: Tim Suchan [view email]
[v1] Tue, 11 Oct 2022 14:57:25 UTC (6,262 KB)
[v2] Wed, 9 Nov 2022 16:46:34 UTC (6,264 KB)
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