Micropolar plasticity-Part I: modeling based on curvature tensors related by mixed transformations

When formulating finite deformation micropolar plasticity, the structure of the theory strongly depends on the choice of the variables describing the deformation kinematics. This holds true even for classical plasticity. However, in contrast to classical plasticity, the set of kinematical variables in micropolar plasticity includes, besides strain tensors, so-called micropolar curvature tensors. There are only a few investigations addressing such aspects, so the aim of the paper is to highlight the effect of a specific micropolar curvature kinematics on the structure of a micropolar plasticity. We do this by developing a general finite deformation micropolar plasticity, which relies upon a class of micropolar curvature tensors related to each other by mixed transformations. That means, the pull-back and push-forward transformations characterizing the class involve both deformation gradient and micropolar rotation tensors. The curvature kinematics is discussed by using geometrical methods developed previously. The plasticity theory is based on the assumption that the yield function and the flow rules are functions of specific micropolar Mandel's stress tensors. The definition of the Mandel's stress tensor is suggested by the adopted curvature kinematics and reveals a characteristic feature of the resulting plasticity. Moreover, the presence of curvature variables in plastic arc length gives reason to introduce a characteristic internal material length, which in turn seems to urge the form of the formulation of the theory. A specific version of von Mises micropolar plasticity with kinematic and isotropic hardening, derived in the theoretical context of the present paper, is elaborated in Part II.