Finite elastic-plastic deformations: Beyond the plastic spin

Abstract

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.