Abstract
A review is presented of a set of elastic-viscoplastic constitutive equations that incorporate isotropic and directional hardening and additional hardening due to nonproportional loading. These equations employ the isotropic form of the flow law in the presence of directional hardening and a physical argument is given to justify this use. An alternative form of the flow law is also suggested that could account for deviations of the directions of stress and plastic strain rate. Generalization of the theory to large deformations has been carried out using Lagrangian quantities and thermodynamic restrictions. Examples of simple tension and simple shear show that the large strain theory produces physically plausible results.
Résumé
Un système d’équations élasto-viscoplastiques est présenté, caractérisant l’écrouissage isotrope et directionnel ainsi qu’un écrouissage supplémentaire dû à des charges non-proportionnelles. Ces équations utilisent la forme isotrope de la loi d’écoulement sous des conditions d’écrouissage directionnel; une argument physique justifiant cette procédure est présenté. Une forme alternative de la loi d’écoulement est aussi suggérée. Celle-ci pourrait tenir compte des déviations dans les directions de la contrainte et de la vitesse de déformation plastique. La théorie est généralisée afin d’inclure le cas des déformations finies en utilisant des quantités Langrangiennes et des restrictions thermodynamiques. Des exemples de tension simple et d’écoulement de cisaillement simple démontrent que la théorie de déformations finies fournit des résultats physiques plausibles.
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Bodner, S.R., Rubin, M.B. (1986). A Unified Elastic-Viscoplastic Theory with Large Deformations. In: Gittus, J., Zarka, J., Nemat-Nasser, S. (eds) Large Deformations of Solids: Physical Basis and Mathematical Modelling. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3407-8_9
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DOI: https://doi.org/10.1007/978-94-009-3407-8_9
Publisher Name: Springer, Dordrecht
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