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 -