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SJTU Team Presented Peridynamic Model for Axisymmetric Problems

July 12, 2018      Author: Publicity Department of the School of Naval Architecture, Ocean & Civil Engineering (NAOCE)

Lately, top-notch journal in computational mechanics the Computer Methods in Applied Mechanics and Engineering published the research result of Professor Qiao Pizhong's team, NAOCE, SJTU, with the title of An Axisymmetric Ordinary State-based Peridynamic Model for Linear Elastic Solids. The research, for the first time, builds peridynamic (PD) model for axisymmetric problems, expanding the application scope of Peridynamics. During the paper review, the reviewer thought highly of the innovativeness and importance of their research: "This paper is now an excellent introduction and analysis of a new numerical technique. The conclusions are thorough and sound, and consistent with the field of Peridynamics. Doctor Zhang Yong is the first author and Professor Qiao Pizhong is the corresponding author of the paper.

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The research is funded by Natural Science Foundation of China (NSFC) (51478265,51679136).

Abstract: In this study, a new axisymmetric ordinary state-based peridynamic (PD) model for axisymmetric problems of linear elastic solids is presented. A fracture criterion based on the PD bond energy density is proposed. Adaptive dynamic relaxation (ADR) method is adopted to obtain equilibrium solutions, and a viable fictitious density of the model is derived and proven to be valid for implementation in the ADR method. Performance and validity of the proposed axisymmetric PD model are demonstrated by three kinds of numerical problems, i.e., compression test, pull-out deformation, and indentation fracture. In the compression test with focus on constant-strain deformation, the displacement predicted by the present model is compared with classical analytical solutions, and the results show good agreements. Both m- convergence and δ-convergence behaviors under four influence functions are investigated and discussed based on a thorough error analysis in different compression cases.  The recovery of the Poisson's ratios in the model are tested in detail as well. The capability of capturing general non-uniform axisymmetric deformation by the proposed model is verified in the pull-out analysis. The equilibrium displacement fields predicted by the present model agree very well with those by the finite element method. The peridynamic evaluation of strains and stresses also show good match with the finite element ones. The proposed fracture criterion is validated by the third example of indentation cracking which is compared with the available experimental data. The model developed can effectively be used to analyze axisymmetric problems of linear elastic solids in the framework of the ordinary state-based peridynamics.

 

Translated by Chen Wanrong   Reviewed by Wang Bingyu