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An analytical singular element for the study of cohesive zone model based crack propagation

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Abstract

In the present study, a singular element is proposed to deal with crack propagation problem in which the nonlinear behavior in front of the crack tip is considered. And cohesive zone model (CZM) is used to simulate the nonlinear behavior. At first, a new singular element is constructed and further extended to deal with CZM based cracks. Cohesive tractions act on the cohesive crack surfaces can be approximately expressed in the form of polynomial. Then special solution corresponding to each expanding term is specified analytically so it has strictly satisfied the requirements of both differential equations of interior domain and the corresponding cohesive traction component acting on cohesive crack surface. Then the special solution can be transformed into nodal forces. Based on the situation of that the crack propagation is governed by cohesive laws an efficient iteration procedure is proposed. Finally, the cohesive crack propagation under arbitrary external loading can be simulated. In the present method the hypotheses of CZM are completely satisfied such that stress singularity vanishes and virtual crack length can be measured. And the validity of the present method is illustrated by numerical examples.

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Acknowledgments

The work described in this paper was supported by the National Natural Science Foundation of China (No. 11372065).

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Authors and Affiliations

  1. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, 116024, China

    Weian Yao, Peng Zhang & Xiaofei Hu

  2. Beijing Institute of Spacecraft Environment Engineering, Beijing, 100094, People’s Republic of China

    Haiyang Gao

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  1. Weian Yao
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  2. Peng Zhang
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  3. Haiyang Gao
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  4. Xiaofei Hu
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Correspondence to Weian Yao.

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Yao, W., Zhang, P., Gao, H. et al. An analytical singular element for the study of cohesive zone model based crack propagation. Int J Fract 197, 189–199 (2016). https://doi.org/10.1007/s10704-016-0075-0

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