Title: Wave Dispersion in Peridynamics

Authors: Bingquan Wang, Selda Oterkus and Erkan Oterkus

Address: University of Strathclyde, 100 Montrose Street Glasgow G4 0LZ United Kingdom

Abstract: Peridynamics \[1-7\] is a new non-local continuum mechanics formulation. Therefore, there are several differences between classical continuum mechanics and peridynamics since classical continuum mechanics is a local theory. Classical continuum mechanics uses partial differential equations for its governing equation. Although these equations have been used for the solution of numerous problems of structural mechanics for the last two hundred years, they confront difficulties if discontinuities exist in the structures such as cracks. For these special conditions, special treatments are necessary since derivatives are not defined along discontinuity surfaces. Peridynamics does not suffer from discontinuity related problems since its governing equations are in the form of integro-differential equations and do not contain spatial derivatives. In addition, peridynamics has a length scale parameter called “horizon” which doesn’t exist in classical continuum mechanics. Another important characteristic of peridynamics is its capability to represent wave dispersion which is observed in real materials especially at shorter wave lengths. In other words, wave frequency and wave number has a non-linear relationship in peridynamics as opposed to linear relationship in classical continuum mechanics. Hence, in this study, we present wave dispersion characteristics of peridynamics and compare against classical continuum mechanics.

REFERENCES

\[1\] Silling, S.A., 2000. Reformulation of elasticity theory for discontinuities and long-range forces. *Journal of the Mechanics and Physics of Solids*, *48*(1), pp.175-209.

\[2\] S. A. Silling and E. Askari, E. A meshfree method based on the peridynamic model of solid mechanics. *Computers & Structures*, Vol. 83(17-18), pp.1526-1535, 2005.

\[3\] Silling, S.A., Epton, M., Weckner, O., Xu, J. and Askari, E., 2007. Peridynamic states and constitutive modeling. *Journal of Elasticity*, *88*(2), pp.151-184.

\[4\] E. Madenci and E. Oterkus, *Peridynamic theory and its applications*, New York: Springer, 2014.

\[5\] Warren, T.L., Silling, S.A., Askari, A., Weckner, O., Epton, M.A. and Xu, J., 2009. A non-ordinary state-based peridynamic method to model solid material deformation and fracture. *International Journal of Solids and Structures*, *46*(5), pp.1186-1195.

\[6\] De Meo, D., Zhu, N. and Oterkus, E., 2016. Peridynamic modeling of granular fracture in polycrystalline materials. *Journal of Engineering Materials and Technology*, *138*(4).

\[7\] Wang, H., Oterkus, E. and Oterkus, S., 2018. Predicting fracture evolution during lithiation process using peridynamics. *Engineering Fracture Mechanics*, *192*, pp.176-191.

 

 


Wave Dispersion in Peridynamics

Division / Sponsors: 
Aerospace, Bioengineering, Applied Mechanics, Design Engineering Division, Advanced Energy Systems, Manufacturing Engineering Division, Noise Control and Acoustics, Nondestructive Evaluation, Diagnosis, and Prognosis (NDPD), Nuclear Engineering Division, Process Industries Division, Fluids Engineering, Heat Transfer, Materials, Microelectromechanical Systems, Safety Engineering and Risk Analysis, Computers & Information in Engineering


Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2020/volume/84478

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