I have implemented a constitutive equation of elastic materials (Hooke's law) in my 3D weakly compressible SPH solver based on . The coding seems to be correct. To verify the implementation I started to check the solver through simple test cases. One of them is a rotating planar object in zero gravity (initial conditions contain the velocity field of rigidbody-like rotation).
The offdiagonal members of the Cauchy-stress tensor (concerning each particle) should remain zero, but they start to rise as the body deviates from its initial configuration. The larger the deviation the larger the shear-stress in the particles. This results in an oscillatory motion of the body instead of pure rotation. In  very large deflections occur, however in my solver these are obstructed by the spurious shears.
What is the reason of this behaviour? Due to the Jaumann-rate the stress-derivative should be objective. Is it true? Are there any non-trivial steps in the calculations of  that are not introduced?
 J.P. Gray, J.J. Monaghan, R.P. Swift. SPH elastic dynamics, 2001. URL:http://www.sciencedirect.com/science/article/pii/S0045782501002547