An explicit phase field method for brittle dynamic fracture

H. L. Ren; X. Y. Zhuang; C. Anitescu; T. Rabczuk

doi:10.1016/j.compstruc.2019.03.005

An explicit phase field method for brittle dynamic fracture

H. L. Ren
, X. Y. Zhuang
, C. Anitescu
, T. Rabczuk^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

276 Citations (Scopus)

Abstract

In this paper, we propose an explicit phase field model for dynamic brittle fracture. The mechanical field is integrated with a Verlet-velocity scheme, while the phase field is incremented with sub-steps at each step. The sub-stepping is adaptive based on the phase field residual and fast convergence is obtained in a few sub-steps. The numerical difficulty in convergence and the calculation of anisotropic stiffness tensor in the implicit phase field model are avoided in the explicit scheme. The explicit phase field model uses the phase field modulus, rather than the conventional phase field viscosity. The proposed scheme can achieve the same result by the implicit dynamic scheme phase field model. Several numerical examples are presented to validate the explicit method.

Original language	English
Pages (from-to)	45-56
Number of pages	12
Journal	Computers and Structures
Volume	217
DOIs	https://doi.org/10.1016/j.compstruc.2019.03.005
Publication status	Published - 2019 Jun

Bibliographical note

Funding Information:
The authors acknowledge the supports from the COMBAT Program (Computational Modeling and Design of Lithium-ion Batteries, Grant No. 615132), the National Basic Research Program of China (973 Program: 2011CB013800) and NSFC (51474157), the Ministry of Science and Technology of China (Grant Nos. SLDRCE14-B-28, SLDRCE14-B-31).

Funding Information:
The authors acknowledge the supports from the COMBAT Program ( Computational Modeling and Design of Lithium-ion Batteries , Grant No. 615132 ), the National Basic Research Program of China (973 Program: 2011CB013800 ) and NSFC (51474157), the Ministry of Science and Technology of China (Grant Nos. SLDRCE14-B-28 , SLDRCE14-B-31 ).

Publisher Copyright:
© 2019 Elsevier Ltd

Keywords

Explicit dynamics
Sub-step
Tetrahedron element

ASJC Scopus subject areas

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

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10.1016/j.compstruc.2019.03.005

Cite this

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title = "An explicit phase field method for brittle dynamic fracture",

abstract = "In this paper, we propose an explicit phase field model for dynamic brittle fracture. The mechanical field is integrated with a Verlet-velocity scheme, while the phase field is incremented with sub-steps at each step. The sub-stepping is adaptive based on the phase field residual and fast convergence is obtained in a few sub-steps. The numerical difficulty in convergence and the calculation of anisotropic stiffness tensor in the implicit phase field model are avoided in the explicit scheme. The explicit phase field model uses the phase field modulus, rather than the conventional phase field viscosity. The proposed scheme can achieve the same result by the implicit dynamic scheme phase field model. Several numerical examples are presented to validate the explicit method.",

keywords = "Explicit dynamics, Sub-step, Tetrahedron element",

author = "Ren, \{H. L.\} and Zhuang, \{X. Y.\} and C. Anitescu and T. Rabczuk",

note = "Funding Information: The authors acknowledge the supports from the COMBAT Program (Computational Modeling and Design of Lithium-ion Batteries, Grant No. 615132), the National Basic Research Program of China (973 Program: 2011CB013800) and NSFC (51474157), the Ministry of Science and Technology of China (Grant Nos. SLDRCE14-B-28, SLDRCE14-B-31). Funding Information: The authors acknowledge the supports from the COMBAT Program ( Computational Modeling and Design of Lithium-ion Batteries , Grant No. 615132 ), the National Basic Research Program of China (973 Program: 2011CB013800 ) and NSFC (51474157), the Ministry of Science and Technology of China (Grant Nos. SLDRCE14-B-28 , SLDRCE14-B-31 ). Publisher Copyright: {\textcopyright} 2019 Elsevier Ltd",

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T1 - An explicit phase field method for brittle dynamic fracture

AU - Ren, H. L.

AU - Zhuang, X. Y.

AU - Anitescu, C.

AU - Rabczuk, T.

N1 - Funding Information: The authors acknowledge the supports from the COMBAT Program (Computational Modeling and Design of Lithium-ion Batteries, Grant No. 615132), the National Basic Research Program of China (973 Program: 2011CB013800) and NSFC (51474157), the Ministry of Science and Technology of China (Grant Nos. SLDRCE14-B-28, SLDRCE14-B-31). Funding Information: The authors acknowledge the supports from the COMBAT Program ( Computational Modeling and Design of Lithium-ion Batteries , Grant No. 615132 ), the National Basic Research Program of China (973 Program: 2011CB013800 ) and NSFC (51474157), the Ministry of Science and Technology of China (Grant Nos. SLDRCE14-B-28 , SLDRCE14-B-31 ). Publisher Copyright: © 2019 Elsevier Ltd

PY - 2019/6

Y1 - 2019/6

N2 - In this paper, we propose an explicit phase field model for dynamic brittle fracture. The mechanical field is integrated with a Verlet-velocity scheme, while the phase field is incremented with sub-steps at each step. The sub-stepping is adaptive based on the phase field residual and fast convergence is obtained in a few sub-steps. The numerical difficulty in convergence and the calculation of anisotropic stiffness tensor in the implicit phase field model are avoided in the explicit scheme. The explicit phase field model uses the phase field modulus, rather than the conventional phase field viscosity. The proposed scheme can achieve the same result by the implicit dynamic scheme phase field model. Several numerical examples are presented to validate the explicit method.

AB - In this paper, we propose an explicit phase field model for dynamic brittle fracture. The mechanical field is integrated with a Verlet-velocity scheme, while the phase field is incremented with sub-steps at each step. The sub-stepping is adaptive based on the phase field residual and fast convergence is obtained in a few sub-steps. The numerical difficulty in convergence and the calculation of anisotropic stiffness tensor in the implicit phase field model are avoided in the explicit scheme. The explicit phase field model uses the phase field modulus, rather than the conventional phase field viscosity. The proposed scheme can achieve the same result by the implicit dynamic scheme phase field model. Several numerical examples are presented to validate the explicit method.

KW - Explicit dynamics

KW - Sub-step

KW - Tetrahedron element

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DO - 10.1016/j.compstruc.2019.03.005

M3 - Article

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SN - 0045-7949

VL - 217

SP - 45

EP - 56

JO - Computers and Structures

JF - Computers and Structures

ER -

An explicit phase field method for brittle dynamic fracture

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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