Incompatible deformations - plastic intermediate configuration

There are many approaches in continuum mechanics involving incompatible deformations, one well-known example being the polar decomposition of the deformation gradient tensor. Such deformations have in the past been regarded rather in the context of local configurations. In the present paper, we discuss incompatible deformations among others, also from the point of view of material lines. Related covariant derivatives and spatial differential operators are introduced and investigated. In particular, it is shown that components of curvature tensors, present in many gradient constitutive theories, may be expressed in terms of the difference between different connections for the same manifold. These issues are illustrated with reference to multiplicative decompositions of deformation gradient tensors into elastic and plastic parts. Two classes of model materials are addressed, non-polar and micropolar ones. (C) 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.