Abstract
In this paper, we develop a dual-horizon peridynamics (DH-PD) formulation that naturally includes varying horizon sizes and completely solves the 'ghost force' issue. Therefore, the concept of dual horizon is introduced to consider the unbalanced interactions between the particles with different horizon sizes. The present formulation fulfills both the balances of linear momentum and angular momentum exactly. Neither the 'partial stress tensor' nor the 'slice' technique is needed to ameliorate the ghost force issue. We will show that the traditional peridynamics can be derived as a special case of the present DH-PD. All three peridynamic formulations, namely, bond-based, ordinary state-based, and non-ordinary state-based peridynamics, can be implemented within the DH-PD framework. Our DH-PD formulation allows for h-adaptivity and can be implemented in any existing peridynamics code with minimal changes. A simple adaptive refinement procedure is proposed, reducing the computational cost. Both two-dimensional and three-dimensional examples including the Kalthoff-Winkler experiment and plate with branching cracks are tested to demonstrate the capability of the method.
| Original language | English |
|---|---|
| Journal | International Journal for Numerical Methods in Engineering |
| DOIs | |
| Publication status | Accepted/In press - 2016 |
| Externally published | Yes |
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Keywords
- Adaptive refinement
- Dual horizon
- Ghost force
- Horizon variable
- Peridynamics
- Spurious wave reflection
ASJC Scopus subject areas
- Engineering(all)
- Applied Mathematics
- Numerical Analysis
Cite this
Dual-horizon peridynamics. / Ren, Huilong; Zhuang, Xiaoying; Cai, Yongchang; Rabczuk, Timon.
In: International Journal for Numerical Methods in Engineering, 2016.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Dual-horizon peridynamics
AU - Ren, Huilong
AU - Zhuang, Xiaoying
AU - Cai, Yongchang
AU - Rabczuk, Timon
PY - 2016
Y1 - 2016
N2 - In this paper, we develop a dual-horizon peridynamics (DH-PD) formulation that naturally includes varying horizon sizes and completely solves the 'ghost force' issue. Therefore, the concept of dual horizon is introduced to consider the unbalanced interactions between the particles with different horizon sizes. The present formulation fulfills both the balances of linear momentum and angular momentum exactly. Neither the 'partial stress tensor' nor the 'slice' technique is needed to ameliorate the ghost force issue. We will show that the traditional peridynamics can be derived as a special case of the present DH-PD. All three peridynamic formulations, namely, bond-based, ordinary state-based, and non-ordinary state-based peridynamics, can be implemented within the DH-PD framework. Our DH-PD formulation allows for h-adaptivity and can be implemented in any existing peridynamics code with minimal changes. A simple adaptive refinement procedure is proposed, reducing the computational cost. Both two-dimensional and three-dimensional examples including the Kalthoff-Winkler experiment and plate with branching cracks are tested to demonstrate the capability of the method.
AB - In this paper, we develop a dual-horizon peridynamics (DH-PD) formulation that naturally includes varying horizon sizes and completely solves the 'ghost force' issue. Therefore, the concept of dual horizon is introduced to consider the unbalanced interactions between the particles with different horizon sizes. The present formulation fulfills both the balances of linear momentum and angular momentum exactly. Neither the 'partial stress tensor' nor the 'slice' technique is needed to ameliorate the ghost force issue. We will show that the traditional peridynamics can be derived as a special case of the present DH-PD. All three peridynamic formulations, namely, bond-based, ordinary state-based, and non-ordinary state-based peridynamics, can be implemented within the DH-PD framework. Our DH-PD formulation allows for h-adaptivity and can be implemented in any existing peridynamics code with minimal changes. A simple adaptive refinement procedure is proposed, reducing the computational cost. Both two-dimensional and three-dimensional examples including the Kalthoff-Winkler experiment and plate with branching cracks are tested to demonstrate the capability of the method.
KW - Adaptive refinement
KW - Dual horizon
KW - Ghost force
KW - Horizon variable
KW - Peridynamics
KW - Spurious wave reflection
UR - http://www.scopus.com/inward/record.url?scp=84979780569&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84979780569&partnerID=8YFLogxK
U2 - 10.1002/nme.5257
DO - 10.1002/nme.5257
M3 - Article
AN - SCOPUS:84979780569
JO - International Journal for Numerical Methods in Engineering
JF - International Journal for Numerical Methods in Engineering
SN - 0029-5981
ER -