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# Determination of crack opening displacement and critical load parameter within a cohesive zone model

## Abstract

A semi-analytical approach for investigation of the stress and strain state of a cracked body is presented. A cohesive zone model is used to take into account the failure zones which are formed in front of the crack tip. It is proposed to satisfy the crack smooth closure condition approximately. It allows to get rid of solving nonlinear equations for the cohesive lengths. An effective algorithm is developed to find solutions for the uniform traction–separation law. The algorithm is based on the iterative procedure of determination of contact stresses between crack faces, so the possible contact interaction between crack faces can easily be taken into account. In the case of mixed mode cracks, multiple cohesive zone models are considered.

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## Author information

Correspondence to Mikhailo F. Selivanov.

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Communicated by Andreas Öchsner.

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Selivanov, M.F., Chornoivan, Y.O. & Kononchuk, O.P. Determination of crack opening displacement and critical load parameter within a cohesive zone model. Continuum Mech. Thermodyn. 31, 569–586 (2019). https://doi.org/10.1007/s00161-018-0712-0

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### Keywords

• Cohesive zone model
• Crack smooth closure condition
• Multiple cohesive zone
• Collinear cracks
• Mixed mode crack