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An equivalent von Mises stress and corresponding equivalent plastic strain for elastic–plastic ordinary peridynamics

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Abstract

Simple formulas for calculating equivalent von Mises stress and von Mises effective plastic strain in an elastic–plastic ordinary peridynamic analysis are proposed. The equivalent von Mises stress is calculated by equating the deviatoric part of strain energy obtained from classical continuum mechanics and peridynamics. The effective plastic strain is proposed so that it reduced to uniaxial plastic strain in uniaxial tension test. Two example problems of the plate with a hole and a central crack under tension are considered to verify the validity of the proposed formulas. The plots of von Mises stress, equivalent plastic strain, plastic zone area and horizontal and vertical displacements are extracted and compared with the results obtain from the finite element analysis. The results show the good accuracy of the peridynamics in predicting the above mentioned parameters as well as the validity of the suggested formulas in predicting von Mises stress and equivalent plastic strain.

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Funding

This work was supported by the Sharif University of Technology [Grant Number QA961027].

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Authors and Affiliations

  1. Department of Aerospace Engineering, Sharif University of Technology, Azadi Street, P.O. Box 11155-8639, Tehran, Iran

    Mojtaba Asgari & Mohammad Ali Kouchakzadeh

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  1. Mojtaba Asgari
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  2. Mohammad Ali Kouchakzadeh
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Correspondence to Mohammad Ali Kouchakzadeh.

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Asgari, M., Kouchakzadeh, M.A. An equivalent von Mises stress and corresponding equivalent plastic strain for elastic–plastic ordinary peridynamics. Meccanica 54, 1001–1014 (2019). https://doi.org/10.1007/s11012-019-00975-8

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