An isoclinic elasto‐plasticity model at finite strains with the notion of plastic spin

In forming processes metal sheets undergo large deformations. The crystallographic texture changes and preferred directions in the macroscopic behaviour are introduced as a result. This yields an anisotropic behaviour in plastic deformations and, furthermore, these preferred directions may rotate with evolution of plasticity. A phenomenological model for the description of orthotropic elasto‐plastic solids with the notion of plastic spin is developed. The latter is the spin of the continuum relative to the material substructure. A multiplicative decomposition of the deformation gradient tensor into an elastic and a plastic part serves as the basis for the formulation and computational implementation. The resulting incompatible intermediate manifold is identified in the model as an isoclinic configuration. Moreover, the described rate‐independent constitutive model is capable of modelling isotropic elastic and orthotropic plastic material behaviour. The latter is dominated by pre‐existing preferred orientations in the material and is described by a Hill‐type yield criterion. These orientations are allowed to rotate by introduction of the plastic spin into the model. Finally, numerical simulations demonstrate the performance of the model. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)