| Abstract: | There is considered the structure of fields of symmetric tensors η generated by the incompatibility operator Ink acting according to the formula Inkη =  × η × . This operator which is closely related to internal stresses in bodies was considered by Kroner /1/ in application to the continuum theory of dislocations. Allied to the study of the structure of tensor fields is the problem of their restoration according to a given incompatibility and divergence as well as the decomposition into incompatible and compatible strain. For a sufficiently smooth Kröner tensor field that vanishes at infinity, by starting from the analogy with the properties of a vector field, it is shown that such a decomposition exists and is unique. In the supplement to /2/, this problem is solved in practice, where an effective algorithm is developed for the decomposition into appropriate invariant components by using projection operators. Analogous questions are examined below in application to finite domains as well as in connection with the decomposition of a tensor into deviatoric and spherical parts. |
