Finite elastic-plastic deformations: Beyond the plastic spin

One important aspect of finite elastic-plastic deformation constitutive theories is addressed in this work, namely the appropriate embedding of tensor-valued internal variables into the plastic deformation continuum description, which has been called physico-geometrical coupling reflecting the r...

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Bibliographic Details
Main Author: Dafalias Yannis F.
Format: Article
Language:English
Published: Serbian Society of Mechanics & Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade 2011-01-01
Series:Theoretical and Applied Mechanics
Subjects:
Online Access:http://www.doiserbia.nb.rs/img/doi/1450-5584/2011/1450-55841104321D.pdf
Description
Summary:One important aspect of finite elastic-plastic deformation constitutive theories is addressed in this work, namely the appropriate embedding of tensor-valued internal variables into the plastic deformation continuum description, which has been called physico-geometrical coupling reflecting the relation between geometry of deformation and the physical nature of an internal variable. In the past it was assumed hat such embedding was co-rotational with a material substructure, rotating independently from the continuum, which required the introduction of the concepts of constitutive and plastic spins for each internal variable. This assumption is now extended to cases where the embedding is convected with the plastic deformation, and it is possible to obtain a common formulation for both rotational and convected embeddings. Explicit expressions are obtained for the plastic multiplier (or loading index) from the consistency condition and the free energy function, making use of certain analytical properties of isotropic scalar and tensor valued functions of scalar and tensor-valued variables, such isotropy arising from the need to satisfy objectivity.
ISSN:1450-5584