General equations of the theory of small deformations superposed on an arbitrary deformed state in isotropic non-linear Cosserat continuum are considered. Analytical solutions of static problems of the continuum under homogeneous initial deformation are presented. Characteristic determinants have been found for the problems of stability of a stripe. Consideration is given to the problem of surface instability. The issue of a possible local instability of Cosserat pseudocontinuum is also discussed.
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