Cracking elements method with a dissipation-based arc-length approach

The dissipated strain energy, representing a monotonically increasing state variable in nonlinear fracture mechanics, can be used to develop an arc-length constraint equation for tracking the energy dissipation path instead of the elastic unloading path of the response of a structure. This was the m...

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Published in:	Finite elements in analysis and design Vol. 195; p. 103573
Main Authors:	Zhang, Yiming, Huang, Junguang, Yuan, Yong, Mang, Herbert A.
Format:	Journal Article
Language:	English
Published:	Amsterdam Elsevier B.V 01.11.2021 Elsevier BV
Subjects:	Arc-length method Cracking elements method Energy dissipation Fracture mechanics Path following Peak load Quasi-brittle fracture Robustness (mathematics) Stiffness Strain Quasi-brittle fracture Cracking elements method Arc-length method Energy dissipation Path following
ISSN:	0168-874X, 1872-6925
Online Access:	Get full text
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Abstract	The dissipated strain energy, representing a monotonically increasing state variable in nonlinear fracture mechanics, can be used to develop an arc-length constraint equation for tracking the energy dissipation path instead of the elastic unloading path of the response of a structure. This was the motivation for the development of a dissipation-based arc-length method, followed by its implementation in the framework of the recently proposed Global Cracking Elements Method (GCEM). The dissipated energy is extracted with the help of the crack openings and tractions, i.e. by means of the displacement jumps and the cohesive forces between the two surfaces of a crack. The stiffness factor of the arc-length constraint equation is obtained in the solution process by means of the Sherman-Morrison formula. Several numerical tests are performed. The results demonstrate the robustness of the proposed method. It captures both global and local peak loads and all snap-back parts of the force-displacement responses of loaded structures with multiple cracks. •The dissipated energy is directly determined by the crack openings and tractions as opposed to indirect determination by forces and displacements.•Path following and crack propagating are treated simultaneously without a special strategy.•The Sherman-Morrison formula is used for implementation of the solution process and the coding efforts are reduced.•The stiffness factor of the arc-length constraint is obtained during, rather than before, the solution process.
AbstractList	The dissipated strain energy, representing a monotonically increasing state variable in nonlinear fracture mechanics, can be used to develop an arc-length constraint equation for tracking the energy dissipation path instead of the elastic unloading path of the response of a structure. This was the motivation for the development of a dissipation-based arc-length method, followed by its implementation in the framework of the recently proposed Global Cracking Elements Method (GCEM). The dissipated energy is extracted with the help of the crack openings and tractions, i.e. by means of the displacement jumps and the cohesive forces between the two surfaces of a crack. The stiffness factor of the arc-length constraint equation is obtained in the solution process by means of the Sherman-Morrison formula. Several numerical tests are performed. The results demonstrate the robustness of the proposed method. It captures both global and local peak loads and all snap-back parts of the force-displacement responses of loaded structures with multiple cracks. •The dissipated energy is directly determined by the crack openings and tractions as opposed to indirect determination by forces and displacements.•Path following and crack propagating are treated simultaneously without a special strategy.•The Sherman-Morrison formula is used for implementation of the solution process and the coding efforts are reduced.•The stiffness factor of the arc-length constraint is obtained during, rather than before, the solution process. The dissipated strain energy, representing a monotonically increasing state variable in nonlinear fracture mechanics, can be used to develop an arc-length constraint equation for tracking the energy dissipation path instead of the elastic unloading path of the response of a structure. This was the motivation for the development of a dissipation-based arc-length method, followed by its implementation in the framework of the recently proposed Global Cracking Elements Method (GCEM). The dissipated energy is extracted with the help of the crack openings and tractions, i.e. by means of the displacement jumps and the cohesive forces between the two surfaces of a crack. The stiffness factor of the arc-length constraint equation is obtained in the solution process by means of the Sherman-Morrison formula. Several numerical tests are performed. The results demonstrate the robustness of the proposed method. It captures both global and local peak loads and all snap-back parts of the force-displacement responses of loaded structures with multiple cracks.
ArticleNumber	103573
Author	Zhang, Yiming Huang, Junguang Yuan, Yong Mang, Herbert A.
Author_xml	– sequence: 1 givenname: Yiming orcidid: 0000-0002-3693-8039 surname: Zhang fullname: Zhang, Yiming email: yiming.zhang@hebut.edu.cn organization: School of Civil and Transportation Engineering, Hebei University of Technology, Xiping Road 5340, 300401, Tianjin, PR China – sequence: 2 givenname: Junguang surname: Huang fullname: Huang, Junguang organization: School of Civil and Transportation Engineering, Hebei University of Technology, Xiping Road 5340, 300401, Tianjin, PR China – sequence: 3 givenname: Yong surname: Yuan fullname: Yuan, Yong organization: Department of Geotechnical Engineering, Tongji University, Siping Road 1239, 200092, Shanghai, PR China – sequence: 4 givenname: Herbert A. surname: Mang fullname: Mang, Herbert A. email: herbert.mang@tuwien.ac.at organization: Institute for Mechanics of Materials and Structures (IMWS), Vienna University of Technology, Karlsplatz 13/202, 1040, Vienna, Austria
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Keywords	Quasi-brittle fracture Cracking elements method Arc-length method Energy dissipation Path following
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Snippet	The dissipated strain energy, representing a monotonically increasing state variable in nonlinear fracture mechanics, can be used to develop an arc-length...
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SubjectTerms	Arc-length method Cracking elements method Energy dissipation Fracture mechanics Path following Peak load Quasi-brittle fracture Robustness (mathematics) Stiffness Strain
Title	Cracking elements method with a dissipation-based arc-length approach
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