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Abstract

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)