The collective behavior of shear strain localizations in dipolar materials

•The collective behavior of shear bands in nonpolar and dipolar materials is studied.•Numerical algorithm for performing mathematical modeling is proposed.•Numerical simulation of the shear bands formation in dipolar materials is performed.•Statistical distributions of the characteristic process par...

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Bibliographic Details
Published inApplied mathematics and computation Vol. 338; pp. 164 - 174
Main Authors Kudryashov, N.A., Muratov, R.V., Ryabov, P.N.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.12.2018
Subjects
Differential equations
Numerical simulation
Self-organization
Shear band
Strain localization
Numerical simulation
Strain localization
Shear band
Differential equations
Self-organization
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Summary:•The collective behavior of shear bands in nonpolar and dipolar materials is studied.•Numerical algorithm for performing mathematical modeling is proposed.•Numerical simulation of the shear bands formation in dipolar materials is performed.•Statistical distributions of the characteristic process parameters were obtained. We study the collective behavior of shear bands in HY-100 steel and OFHC copper taking into account the dipolar effects. Starting from mathematical model, we present new numerical methodology that allows one to simulate the processes of shear strain localization in nonpolar and dipolar materials. The verification procedure was performed to prove the efficiency and accuracy of the proposed method. Using the proposed algorithm we investigate the statistical characteristics of the shear strain localization processes in dipolar materials and compare results with nonpolar case. In particular, we obtain the statistical distributions of the width of localization zones and distance between them.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2018.06.005