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The implicit stabilized dual-horizon peridynamics-based strain gradient damage model

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Autoren

  • Yehui Bie
  • Yueguang Wei
  • Timon Rabczuk
  • Huilong Ren

Organisationseinheiten

Externe Organisationen

  • Peking University
  • Bauhaus-Universität Weimar
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    • Citation Indexes: 2
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Details

OriginalspracheEnglisch
Seiten (von - bis)630-658
Seitenumfang29
FachzeitschriftApplied mathematical modelling
Jahrgang128
Frühes Online-Datum28 Jan. 2024
PublikationsstatusVeröffentlicht - Apr. 2024

Abstract

In this paper, we propose the implicit stabilized dual-horizon peridynamics-based strain gradient damage model (GDH-PD) to describe the cross-scale fracture behavior of materials. To this end, firstly, the strain energy density function of GDH-PD is reformulated by considering the energy compensation to eliminate zero-energy modes of the traditional higher-order peridynamics. And then, the constitutive force state of GDH-PD is derived and explicitly expressed with the help of the proposed special dimension reduction of the nonlocal higher-order tensors. To solve the steady-state crack propagation problems, the implicit GDH-PD is developed by deriving the lower- and higher-order micro-modulus double state, such that the linearization of the equilibrium equation of GDH-PD is established. At last, the bond length-dependent energy-based failure criterion is used to characterize the cross-scale fracture in the form of bond breakage. The effectiveness of GDH-PD to characterize microstructure size effects and macrostructure strain gradient effects are investigated by numerical simulations. The numerical results are in good agreement with the analytical solutions or the available experimental results. We believe that the proposed GDH-PD may pave the way to an increased application of peridynamics to be used in the cross-scale fracture predictions for the advanced material.

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The implicit stabilized dual-horizon peridynamics-based strain gradient damage model. / Bie, Yehui; Wei, Yueguang; Rabczuk, Timon et al.
in: Applied mathematical modelling, Jahrgang 128, 04.2024, S. 630-658.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Bie Y, Wei Y, Rabczuk T, Ren H. The implicit stabilized dual-horizon peridynamics-based strain gradient damage model. Applied mathematical modelling. 2024 Apr;128:630-658. Epub 2024 Jan 28. doi: 10.1016/j.apm.2024.01.040
Bie, Yehui ; Wei, Yueguang ; Rabczuk, Timon et al. / The implicit stabilized dual-horizon peridynamics-based strain gradient damage model. in: Applied mathematical modelling. 2024 ; Jahrgang 128. S. 630-658.
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T1 - The implicit stabilized dual-horizon peridynamics-based strain gradient damage model

AU - Bie, Yehui

AU - Wei, Yueguang

AU - Rabczuk, Timon

AU - Ren, Huilong

N1 - Funding Information: This work is supported by the National Natural Science Foundation of China (Grant Nos. 11890681 , 12032001 and 11521202 ).

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Y1 - 2024/4

N2 - In this paper, we propose the implicit stabilized dual-horizon peridynamics-based strain gradient damage model (GDH-PD) to describe the cross-scale fracture behavior of materials. To this end, firstly, the strain energy density function of GDH-PD is reformulated by considering the energy compensation to eliminate zero-energy modes of the traditional higher-order peridynamics. And then, the constitutive force state of GDH-PD is derived and explicitly expressed with the help of the proposed special dimension reduction of the nonlocal higher-order tensors. To solve the steady-state crack propagation problems, the implicit GDH-PD is developed by deriving the lower- and higher-order micro-modulus double state, such that the linearization of the equilibrium equation of GDH-PD is established. At last, the bond length-dependent energy-based failure criterion is used to characterize the cross-scale fracture in the form of bond breakage. The effectiveness of GDH-PD to characterize microstructure size effects and macrostructure strain gradient effects are investigated by numerical simulations. The numerical results are in good agreement with the analytical solutions or the available experimental results. We believe that the proposed GDH-PD may pave the way to an increased application of peridynamics to be used in the cross-scale fracture predictions for the advanced material.

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