Applied Mathematics and Mechanics

, Volume 32, Issue 11, pp 1437–1446

# Separation work analysis of cohesive law and consistently coupled cohesive law

Article

DOI: 10.1007/s10483-011-1513-x

He, Mh. & Xin, Kg. Appl. Math. Mech.-Engl. Ed. (2011) 32: 1437. doi:10.1007/s10483-011-1513-x

## 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.

### Key words

cohesive elementcohesive zone model (CZM)cohesive lawseparation work analysisconsistently coupled rule/principleconsistently coupled cohesive (CCC) lawnon-consistently coupled cohesive law

### Nomenclature

ϕn, ϕt

separation work

q

coupling parameter of work

r

coupling parameter of opening

Dn,Dt

damage level factors

Hn,Ht

integrity residual factors

Wn,Wt

separation work

δn, δt

characteristic opening

Δnt

opening displacements

TU31O346

65D9974A45