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Mathematical Problems in Engineering
Volume 2017, Article ID 1750876, 7 pages
Research Article

An Effective Way to Control Numerical Instability of a Nonordinary State-Based Peridynamic Elastic Model

Department of Engineering Mechanics, Hohai University, Nanjing 211100, China

Correspondence should be addressed to Qing Zhang; nc.ude.uhh@gniqgnahzxl

Received 28 November 2016; Accepted 29 January 2017; Published 20 February 2017

Academic Editor: Paolo Maria Mariano

Copyright © 2017 Xin Gu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The constitutive modeling and numerical implementation of a nonordinary state-based peridynamic (NOSB-PD) model corresponding to the classical elastic model are presented. Besides, the numerical instability problem of the NOSB-PD model is analyzed, and a penalty method involving the hourglass force is proposed to control the instabilities. Further, two benchmark problems, the static elastic deformation of a simple supported beam and the elastic wave propagation in a two-dimensional rod, are discussed with the present method. It proves that the penalty instability control method is effective in suppressing the displacement oscillations and improving the accuracy of calculated stress fields with a proper hourglass force coefficient, and the NOSB-PD approach with instability control can analyze the problems of structure deformation and elastic wave propagation well.