 Distortion free energy density

For a unit nematic director, the bulk elastic density is $[K_1(\nabla \cdot \mathbf{n}{)}^2+K_2(\mathbf{n}\cdot \nabla \times \mathbf{n}{)}^2+K_3|\mathbf{n}\times \nabla \times \mathbf{n}{|}^2]/2$. The three positive moduli penalize nematic splay, nematic twist, and nematic bend. Boundary elastic terms, chirality, or varying nematic order require additional contributions.

Distortion free energy density is a concept from materials science and thermodynamics, particularly in the study of phase transitions and elasticity in materials. It typically relates to the energy required to deform a material without introducing additional defects or fluctuations in its internal structure. In the context of crystal structures and phase transitions, "distortion" refers to any deviation of the crystal lattice from its ideal, symmetrical arrangement.