Applied Mathematics and Mechanics

, Volume 32, Issue 11, pp 1437–1446 | Cite as

Separation work analysis of cohesive law and consistently coupled cohesive law

  • Ming-hua He (何铭华)
  • Ke-gui Xin (辛克贵)Email author


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.

Key words

cohesive element cohesive zone model (CZM) cohesive law separation work analysis consistently coupled rule/principle consistently coupled cohesive (CCC) law non-consistently coupled cohesive law 


ϕn, ϕt

separation work


coupling parameter of work


coupling parameter of opening


damage level factors


integrity residual factors


separation work

δn, δt

characteristic opening


opening displacements

Chinese Library Classification

TU31 O346 

2010 Mathematics Subject Classification

65D99 74A45 


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Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Ming-hua He (何铭华)
    • 1
    • 2
    • 3
  • Ke-gui Xin (辛克贵)
    • 1
    • 2
    Email author
  1. 1.Department of Civil EngineeringTsinghua UniversityBeijingP. R. China
  2. 2.Key Laboratory of Civil Engineering Safety and Durability of China Ministry of EducationBeijingP. R. China
  3. 3.Department of Civil and Environmental EngineeringUniversity of California at BerkeleyBerkeleyUSA

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