Dual-horizon peridynamics-based variational damage modeling for complex dynamic fractures

authored by: Huilong Ren, Xiaoying Zhuang, Yehui Bie, Timon Rabczuk, Hehua Zhu
Abstract: Fracture simulation by cutting bonds in non-ordinary state-based peridynamics may suffer from numerical instability. To solve this problem, we develop a dual-horizon peridynamics equipped with variational damage for the dynamic brittle fracture modeling in elastic solid. Without using damage variables explicitly, the damage field is a natural outcome or a post-processing of the strain energy field. Since the bond-cutting process is removed, the numerical stability of fracture propagation is greatly enhanced. Unlike peridynamics, which tracks the damage state of each bond throughout the simulation, the variational damage model employs a scalar damage variable to represent the state of each material point. This model expresses damage as a function of the “positive” strain energy density, utilizing the spectral decomposition of the strain tensor. Such a decomposition scheme effectively prevents crack surface interpenetration when the crack closes, ensuring physically consistent fracture behavior. A flowchart outlining the numerical implementation of this approach is presented. We demonstrate the capabilities of the current method by simulating a notched plate subjected to tensile/shear boundary conditions, the Kalthoff & Winkler experiment and fragmentation simulation in two and three dimensions.
Organisation(s): Institute of Photonics
External Organisation(s): Tongji University
Peking University
Bauhaus-Universität Weimar
Type: Article
Journal: Theoretical and Applied Fracture Mechanics
Volume: 138
No. of pages: 15
ISSN: 0167-8442
Publication date: 08.2025
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: General Materials Science, Condensed Matter Physics, Mechanical Engineering, Applied Mathematics
Electronic version(s): https://doi.org/10.1016/j.tafmec.2025.104974 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{526f02d140524c51916d90d4938a6add,
title = "Dual-horizon peridynamics-based variational damage modeling for complex dynamic fractures",
abstract = "Fracture simulation by cutting bonds in non-ordinary state-based peridynamics may suffer from numerical instability. To solve this problem, we develop a dual-horizon peridynamics equipped with variational damage for the dynamic brittle fracture modeling in elastic solid. Without using damage variables explicitly, the damage field is a natural outcome or a post-processing of the strain energy field. Since the bond-cutting process is removed, the numerical stability of fracture propagation is greatly enhanced. Unlike peridynamics, which tracks the damage state of each bond throughout the simulation, the variational damage model employs a scalar damage variable to represent the state of each material point. This model expresses damage as a function of the “positive” strain energy density, utilizing the spectral decomposition of the strain tensor. Such a decomposition scheme effectively prevents crack surface interpenetration when the crack closes, ensuring physically consistent fracture behavior. A flowchart outlining the numerical implementation of this approach is presented. We demonstrate the capabilities of the current method by simulating a notched plate subjected to tensile/shear boundary conditions, the Kalthoff & Winkler experiment and fragmentation simulation in two and three dimensions.",
keywords = "Brittle fracture, Damage, Explicit time integration, Nonlocality, Peridynamics",
author = "Huilong Ren and Xiaoying Zhuang and Yehui Bie and Timon Rabczuk and Hehua Zhu",
note = "Publisher Copyright: {\textcopyright} 2025 Elsevier Ltd",
year = "2025",
month = aug,
doi = "10.1016/j.tafmec.2025.104974",
language = "English",
volume = "138",
journal = "Theoretical and Applied Fracture Mechanics",
issn = "0167-8442",
publisher = "Elsevier BV",
}

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