Summary
Strain localization of nonlinear micropolar elastic material in plane strain deformation is discussed. Attention is focused on the case when the micro-rotation is linearly related to the macro-rotation and when the material is centro-symmetric. The strain localization is regarded as a perturbation on the otherwise homogeneous deformation field. General formulations for the initiation of the localization are given. Numerical results for a special material are presented. Since the effects of microstructures of materials are considered, the analysis gives not only the critical stretches for localized banding, but also the thickness of the band.
Übersicht
Untersucht wird die Lokalisierung der Verformungen von nichtlinearen, mikropolar elastischen Werkstoffen im ebenen Formänderungszustand. Hauptaugenmerk liegt dabei auf der linearen Abhängigkeit der Mikrodrehung von der Makrodrehung im Falle eines zentralsym-metrischen Werkstoffes. Die Lokalisierung wird als eine Störung des ansonsten homogenen Verformungsfeldes betrachtet. Algemeine Bedingungen für die Initiierung der Lokalisierung werden formuliert und für einen ausgewählten Werkstoff numerisch ausgewertet. Dank der Betrachtung der Mikrostruktureinflüsse liefert die dargestellte Analyse nicht nur die Werte der kritischen Streckungen für lokalisierte Bänder, sondern auch deren Dicke.
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This work was prepared when the Author was visiting University of Kaiserslautern in Germany. The author appreciates very much the fellowship awarded him by the A. v. Humboldt Foundation and the hospitality of Prof. Dr.-Ing. U. Wittek. Later part of the work was also supported by National Natural Science Foundation of China through grant 19002014.
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Su, X.M. Strain localization in plane strain micropolar elasticity. Arch. Appl. Mech. 64, 258–266 (1994). https://doi.org/10.1007/BF00789124
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DOI: https://doi.org/10.1007/BF00789124