Universal deformations of micropolar isotropic elastic solids

For homogeneous nonlinear isotropic micropolar solids a class of universal deformations is obtained. The kinematics of micropolar media is determined by two independent fields, which are the position vector of material particles and the microrotation tensor which describes the rotational degrees of freedom. We present two types of universal deformation. The first type is uniform deformations. Here the deformation gradient tensor and the microrotation tensor are both constant. In addition the microrotation tensor coincides with the macrorotation tensor from the polar decomposition of the deformation gradient or differs from the latter by a half-turn about one of the principal axes of the stretch tensor. The second type of universal deformation consists of six families of non-uniform deformations. It is obtained for incompressible materials. Each family includes a few subfamilies which differ from each other by the form of the microrotation tensor.