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Adaptive consistent element-free Galerkin method for phase-field model of brittle fracture

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Abstract

Efficient implementation of the element-free Galerkin (EFG) method for a phase-field model of linear elastic fracture mechanics is presented, in which the convenience of the meshfree method to construct high order approximation functions and to implement h-adaptivity is fully exploited. A second-order moving-least squares approximation for both displacement and phase field is employed. Domain integration of the weak forms is evaluated by the quadratically consistent 3-point integration scheme. The refinement criterion using maximum residual strain energy history is proposed and the insertion of nodes is based on the background mesh. Numerical results show that the developed method is more efficient than the standard finite element method (3-node triangle element) due to the proposed h-adaptivity. In comparison with the standard EFG method, the proposed consistent EFG method significantly improves the computational efficiency and accuracy. The advantage of the quadratic approximation is also demonstrated. In addition, the feasibility of extending the proposed method to 3D is validated by the modeling of a twisting crack.

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Acknowledgements

The authors are pleased to acknowledge the support of this work by Science Challenge Project through contract/Grant Numbers TZ2018002 and JCKY2016212A502, the National Natural Science Foundation of China through contract/Grant Number 11672062, the Fundamental Research Funds for the Central Universities through contract/Grant Numbers DUT17LK18 and DUT18LK04, the open funds of the State Key Laboratory of Water Resources and Hydropower Engineering Science (Wuhan University) through contract/Grant Number 2015SGG03, the open funds of the State Key Laboratory of Geohazard Prevention and Geoenvironment Protection (Chengdu University of Technology) through contract/Grant Number SKLGP2016K007.

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  1. State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, 2 Linggong Road, Dalian, 116024, Liaoning, People’s Republic of China

    Yulong Shao, Qinglin Duan & Shasha Qiu

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  1. Yulong Shao
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  2. Qinglin Duan
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Correspondence to Qinglin Duan.

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Shao, Y., Duan, Q. & Qiu, S. Adaptive consistent element-free Galerkin method for phase-field model of brittle fracture. Comput Mech 64, 741–767 (2019). https://doi.org/10.1007/s00466-019-01679-2

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