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Acta Mechanica

, Volume 230, Issue 10, pp 3667–3692 | Cite as

A coupling extended multiscale finite element and peridynamic method for modeling of crack propagation in solids

  • Hongwu ZhangEmail author
  • Hui Li
  • Hongfei Ye
  • Yonggang ZhengEmail author
  • Yixiong Zhang
Original Paper
  • 146 Downloads

Abstract

A coupling extended multiscale finite element and peridynamic method is developed for the quasi-static mechanical analysis of large-scale structures with crack propagation. Firstly, a novel incremental peridynamic (PD) formulation based on the ordinary state-based PD model is derived utilizing the Taylor expansion technique. To combine the high computational efficiency of the EMsFEM and advantages of dealing with discontinuous problems of the PD, a coupling strategy based on the numerical base function is proposed, in which the displacement constraint relationships between the coarse element nodes of the EMsFEM and the material points of the PD among the coupling domain are constructed by the numerical base functions and are represented by a coupling strain energy function using the Lagrange multiplier method. Then, a bilinear softening material model is adopted to describe the damage and failure of the bond, and the incremental-iterative algorithms are applied to obtain the steady-state solutions. Finally, several representative numerical examples are presented, and the results demonstrate the accuracy and efficiency of the proposed coupling method for the quasi-static mechanical analysis of large-scale structures with crack propagation. Comparing with the single EMsFEM and PD method, the present coupling method can reduce much computational cost and well deal with crack problems, simultaneously.

Notes

Acknowledgements

The supports from the National Natural Science Foundation of China (Nos. 11672062, 11772082 and 11672063), the LiaoNing Revitalization Talents Program (XLYC1807193), the 111 Project (No. B08014) and Fundamental Research Funds for the Central Universities are gratefully acknowledged.

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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.International Research Center for Computational Mechanics, State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Faculty of Vehicle Engineering and MechanicsDalian University of TechnologyDalianPeople’s Republic of China
  2. 2.Science and Technology on Reactor System Design Technology LaboratoryNuclear Power Institute of ChinaChengduPeople’s Republic of China

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