An effective way to control numerical instability of a nonordinary state-based peridynamic elastic model.

*(English)*Zbl 1426.74165Summary: 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.

##### MSC:

74H55 | Stability of dynamical problems in solid mechanics |

74S30 | Other numerical methods in solid mechanics (MSC2010) |

##### Software:

LAMMPS
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\textit{X. Gu} et al., Math. Probl. Eng. 2017, Article ID 1750876, 7 p. (2017; Zbl 1426.74165)

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##### References:

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