We present a linear continuum theory incorporating asymmetric stress fields as well as symmetric strains and antisymmetric rotations. We discuss the related constitutive laws and balance equations. In this theory, the motion equation related to the balance of the antisymmetric part of stresses replaces that for the stress moments. Our theory proves that the rotation waves may exist even in a homogeneous elastic continuum.

Different kinds of extreme deformations are considered. The wave solutions, including the coaction of the rotation and twist fields, are presented and discussed. The dislocation density–stress relations are derived with the help of the symmetric and antisymmetric parts of stresses. The synchronization solution, rotation, and twist, shifted in phase by π/2, are presented for a material in an advanced deformation state with granulation and microcracking. Some examples of the spin and twist motion records are reported that confirm this synchronization hypothesis.

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