Adaptive convexification of microsphere-based incremental damage for stress and strain softening at finite strains

  • The brief history of relaxation in continuum mechanics ranges from early application of non-convex plasticity and phase transition formulations to small and large strain continuum damage mechanics. However, relaxed continuum damage mechanics formulations are still limited in the following sense that their material response lack to model strain softening and the convexification of the non-convex incremental stress potential is computationally costly. This paper presents a reduced model for relaxed continuum damage mechanics at finite strains which includes strain softening by a fiber-specific damage in the microsphere approach. Computational efficiency is achieved by novel adaptive algorithms for the fast convexification of the one-dimensional fiber material model. The algorithms are benchmarked against state-of-the-art methods, and the choice of quadrature schemes for the microsphere approach is discussed. This contribution is finalized by a mesh independence test.

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Author:Maximilian Köhler, Timo NeumeierGND, Jan Melchior, Malte A. PeterORCiDGND, Daniel PeterseimORCiDGND, Daniel Balzani
Frontdoor URL
Parent Title (English):Acta Mechanica
Publisher:Springer Science and Business Media LLC
Year of first Publication:2022
Publishing Institution:Universität Augsburg
Release Date:2022/09/26
Tag:Mechanical Engineering; Computational Mechanics
First Page:4347
Last Page:4364
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Fakultätsübergreifende Institute und Einrichtungen
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehr- und Forschungseinheit Angewandte Analysis
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Numerische Mathematik
Fakultätsübergreifende Institute und Einrichtungen / Zentrum für Advanced Analytics and Predictive Sciences (CAAPS)
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):CC-BY 4.0: Creative Commons: Namensnennung (mit Print on Demand)