In the theory of elasticity there is an important object, the displacement increment vector $u_i$. The derivative of such an object can be decomposed into symmetric and antisymmetric parts:
$$ \partial_i u_j = \underbrace{\frac{1}{2} (\partial_i u_j + \partial_j u_i)}_{u_{ij}} + \frac{1}{2} (\partial_i u_j - \partial_j u_i) $$
The antisymmetric part describes rotation:
It is obvious that whole body rotation doesn't change energy. But local rotations can lead to changes of energy. But usually energy of a deformed body is described by:
$$ E = \lambda^{ijkl} u_{ij} u_{kl} $$
Why do we not include contributions of the antisymmetric part? Local rotations will change energy of system.