Details
| Original language | English |
|---|---|
| Article number | 107518 |
| Journal | Computers and Structures |
| Volume | 305 |
| Early online date | 18 Sept 2024 |
| Publication status | Published - 1 Dec 2024 |
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
ASJC Scopus subject areas
- Engineering(all)
- Civil and Structural Engineering
- Mathematics(all)
- Modelling and Simulation
- Materials Science(all)
- Engineering(all)
- Mechanical Engineering
- Computer Science(all)
- Computer Science Applications
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In: Computers and Structures, Vol. 305, 107518, 01.12.2024.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Variational damage model
T2 - A novel consistent approach to fracture
AU - Ren, Huilong
AU - Zhuang, Xiaoying
AU - Zhu, Hehua
AU - Rabczuk, Timon
N1 - Publisher Copyright: © 2024 The Author(s)
PY - 2024/12/1
Y1 - 2024/12/1
N2 - 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.
AB - 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.
KW - Cohesive fracture
KW - Crack propagation
KW - Damage mechanics
KW - Dynamic fracture
KW - Fracture
KW - Multiple failure modes
KW - Threshold value
UR - http://www.scopus.com/inward/record.url?scp=85203871656&partnerID=8YFLogxK
U2 - 10.1016/j.compstruc.2024.107518
DO - 10.1016/j.compstruc.2024.107518
M3 - Article
AN - SCOPUS:85203871656
VL - 305
JO - Computers and Structures
JF - Computers and Structures
SN - 0045-7949
M1 - 107518
ER -