Variational damage model

A novel consistent approach to fracture

authored by

Huilong Ren, Xiaoying Zhuang, Hehua Zhu, Timon Rabczuk

Abstract

The computational modeling of fractures in solids using damage mechanics faces challenge when dealing with complex crack topologies. One effective approach to address this challenge is by reformulating damage mechanics within a variational framework. In this paper, we present a novel variational damage model that incorporates a threshold value to prevent damage initiation at low energy levels. The proposed model defines fracture energy density (ϕ˜) and damage field (s) based on the energy density (ϕ), crack energy release rate (G_c

), and crack length scale (ℓ). Specifically, if ϕ≤[Formula presented], then ϕ˜=ϕ and s=0; otherwise, ϕ˜=−[Formula presented]. Furthermore, we extend the model with a threshold value to a higher-order version. Utilizing this functional, we derive the governing equation for fractures that evolve automatically with ease. The formulation can be seamlessly integrated into conventional finite element methods for elastic solids with minimal modifications. The proposed formulation offers sharper crack interfaces compared to phase field methods using the same mesh density. We demonstrate the capabilities of our approach through representative numerical examples in both 2D and 3D, including static fracture problems, cohesive fractures, and dynamic fractures. The open-source code is available on GitHub via the link github.com/hl-ren/vdm.

Organisation(s)

Institute of Photonics

External Organisation(s)

State Key Laboratory for Disaster Reduction of Civil Engineering
Bauhaus-Universität Weimar

Type

Article

Journal

Computers and Structures

Volume

305

ISSN

0045-7949

Publication date

01.12.2024

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Civil and Structural Engineering, Modelling and Simulation, General Materials Science, Mechanical Engineering, Computer Science Applications

Electronic version(s)

https://doi.org/10.1016/j.compstruc.2024.107518 (Access: Open)

Details in the research portal "Research@Leibniz University"

BibTeX

@article{e90a6bdaefdc42829b68dfd56cca1d22,
title = "Variational damage model: A novel consistent approach to fracture",
abstract = "The computational modeling of fractures in solids using damage mechanics faces challenge when dealing with complex crack topologies. One effective approach to address this challenge is by reformulating damage mechanics within a variational framework. In this paper, we present a novel variational damage model that incorporates a threshold value to prevent damage initiation at low energy levels. The proposed model defines fracture energy density (ϕ˜) and damage field (s) based on the energy density (ϕ), crack energy release rate (Gc), and crack length scale (ℓ). Specifically, if ϕ≤[Formula presented], then ϕ˜=ϕ and s=0; otherwise, ϕ˜=−[Formula presented]. Furthermore, we extend the model with a threshold value to a higher-order version. Utilizing this functional, we derive the governing equation for fractures that evolve automatically with ease. The formulation can be seamlessly integrated into conventional finite element methods for elastic solids with minimal modifications. The proposed formulation offers sharper crack interfaces compared to phase field methods using the same mesh density. We demonstrate the capabilities of our approach through representative numerical examples in both 2D and 3D, including static fracture problems, cohesive fractures, and dynamic fractures. The open-source code is available on GitHub via the link https://github.com/hl-ren/vdm.",
keywords = "Cohesive fracture, Crack propagation, Damage mechanics, Dynamic fracture, Fracture, Multiple failure modes, Threshold value",
author = "Huilong Ren and Xiaoying Zhuang and Hehua Zhu and Timon Rabczuk",
note = "Publisher Copyright: {\textcopyright} 2024 The Author(s)",
year = "2024",
month = dec,
day = "1",
doi = "10.1016/j.compstruc.2024.107518",
language = "English",
volume = "305",
journal = "Computers and Structures",
issn = "0045-7949",
publisher = "Elsevier Ltd.",
}

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