As per Maxwell reciprocal theorem, it is valid only for elastic materials and structures indergoing small displacements.That is k12 = k21, kij = kji hence stiffness matrix is symmetric.
Howbver, I just have been going through MY OWN written programs for geometric non linear problems and I observe that stiffness matrix (assembled stiffness matrix) is well symmetric.
How can stiffness matrix be symmmetric for non linear behaviour of structures?