Structure of tensor fields of the second rank generated by an incompatibility operator (Q793529)

The author is concerned with the structure of symmetric tensors of the second rank, generated by Kröner's incompatibility operator (i.e., \(I_{nk}\eta =\nabla \times \eta \times \nabla)\) [\textit{E. Kröner}, Continuum theory of dislocations and eigenstresses (1958; Zbl 0084.400)]. It is shown that the tensor is uniquely decomposed into the deviator and spherical parts, and it is proved that every piecewise continuously differentiable tensor field can be decomposed into an incompatible deviator and a compatible part.