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On uniqueness criteria and minimum principles for crystalline solids at finite strain

Eindeutigkeitskriterien und Minimalprinzipien für kristalline Festkörper endlicher Verzerrungen

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Summary

New uniqueness criteria and minimum principles for quasi-static, rate-type boundary value problems in crystalline solids are derived. The analysis is based upon a general constitutive theory of finite elastic-plastic deformation encompassing the distinct mechanisms of lattice straining and crystallographic slip. Locally sufficient uniqueness criteria and a related minimum principle permitting the independent variation of velocity and plastic shear rates are established for the case when the two dominant principal stresses are everywhere tensile.

Zusammenfassung

Es werden neue Eindeutigkeitskriterien und Minimalprinzipien für quasistatische inkrementelle Randwertprobleme in kristallinen Festkörpern hergeleitet. Die Analyse beruht auf einer allgemeinen konstitutiven Theorie endlicher, elastisch-plastischer Verformungen, welche die getrennten Vorgänge von Gitterdehnung und Kristallgleitung einschließen. Örtlich hinreichende Eindeutigkeitskriterien und ein damit zusammenhängendes Minimalprinzip ermöglichen die unabhängige Variation von Verformungsgeschwindigkeit und plastischer Gleitgeschwindigkeit und werden aufgestellt für den Fall, daß die beiden dominierenden Hauptspannungen überall positiv sind.

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Authors and Affiliations

  1. Department of Civil Engineering, North Carolina State University, 27607, Raleigh, NC, USA

    K. S. Havner

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  1. K. S. Havner
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Havner, K.S. On uniqueness criteria and minimum principles for crystalline solids at finite strain. Acta Mechanica 28, 139–151 (1977). https://doi.org/10.1007/BF01208794

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  • DOI: https://doi.org/10.1007/BF01208794

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