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Separation work analysis of cohesive law and consistently coupled cohesive law

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Abstract

An appropriate coupled cohesive law for predicting the mixed mode failure is established by combining normal separation and tangential separation of surfaces in the cohesive zone model (CZM) and the cohesive element method. The Xu-Needleman exponential cohesive law with the fully shear failure mechanism is one of the most popular models. Based on the proposed consistently coupled rule/principle, the Xu-Needleman law with the fully shear failure mechanism is proved to be a non-consistently coupled cohesive law by analyzing the surface separation work. It is shown that the Xu-Needleman law is only valid in the mixed mode fracture when the normal separation work equals the tangential separation work. Based on the consistently coupled principle and the modification of the Xu-Needleman law, a consistently coupled cohesive (CCC) law is given. It is shown that the proposed CCC law has already overcome the non-consistency defect of the Xu-Needleman law with great promise in mixed mode analyses.

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Abbreviations

ϕ n, ϕ t :

separation work

q :

coupling parameter of work

r :

coupling parameter of opening

D n,D t :

damage level factors

H n,H t :

integrity residual factors

W n ,W t :

separation work

δ n , δ t :

characteristic opening

Δn,Δt :

opening displacements

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Authors and Affiliations

  1. Department of Civil Engineering, Tsinghua University, Beijing, 100084, P. R. China

    Ming-hua He  (何铭华) & Ke-gui Xin  (辛克贵)

  2. Key Laboratory of Civil Engineering Safety and Durability of China Ministry of Education, Beijing, 100084, P. R. China

    Ming-hua He  (何铭华) & Ke-gui Xin  (辛克贵)

  3. Department of Civil and Environmental Engineering, University of California at Berkeley, Berkeley, California, 94720, USA

    Ming-hua He  (何铭华)

Authors
  1. Ming-hua He  (何铭华)
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  2. Ke-gui Xin  (辛克贵)
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Corresponding author

Correspondence to Ke-gui Xin  (辛克贵).

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 50878117 and 51038006), the China Scholarship Council Project (No. M. H. HE-2009621076), and the Tsinghua University Initiative Scientific Research Program (No. 20101081766)

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He, Mh., Xin, Kg. Separation work analysis of cohesive law and consistently coupled cohesive law. Appl. Math. Mech.-Engl. Ed. 32, 1437–1446 (2011). https://doi.org/10.1007/s10483-011-1513-x

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  • DOI: https://doi.org/10.1007/s10483-011-1513-x

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2010 Mathematics Subject Classification

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