When nematic liquid crystals are constrained to a curved surface, the geometry induces distortions in the molecular orientation. The mechanisms of the geometrical frustration involve the intrinsic as well as the extrinsic geometry of the underlying substrate. We show that the nematic elastic energy promotes the alignment of the flux lines of the nematic director towards geodesics and/or lines of curvature of the surface. As a consequence, the influence of the curvature can be tuned through the Frank elastic moduli. To illustrate this effect, we consider the simple case of nematics lying on a cylindrical shell. By combining the curvature effects with external magnetic fields, the molecular alignment can be reoriented or switched between two stable configurations. This enables the manipulation of nematic alignment for the design of new materials and technological devices.

We propose a continuum model to describe the molecular alignment in thin nematic shells. By contrast with previous accounts, the two-dimensional free energy, aimed at describing the physics of thin films of nematics deposited on curved substrates, is not postulated, but it is deduced from the conventional three-dimensional theories of nematic liquid crystals. Both the director and the order-tensor theories are taken into account. The so-obtained surface energies exhibit extra terms compared to earlier models. These terms reflect the coupling of the shell extrinsic curvature with the nematic order parameters. As expected, the shape of the shell plays a key role in the equilibrium configurations of nematics coating it.

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We found a mistake in the derivation of the torque tensor in [2]. It does not affect all the other results contained in that paper, such as the derivations of the equilibrium equations and the stress tensor.Equation ( 35) in [2] is wrong. To derive the torque tensor and the equation of balance of torques, one must appeal to the frame indifference of the energy density w = w(ν, L, n, ∇ s n, q, ∇ s q) and not to the invariance under rigid virtual displacements as stated in [2]. Therefore, by following similar arguments as in [1] the invariance of the energy density w under infinitesimal rigid rotations implies thatwhere Ω is an arbitrary skew-symmetric tensor. In view of equation ( 21) in [2] and the representation of the stress tensor reported there, (1) can be rewritten asBecause of the arbitrariness of the skew-symmetric tensor Ω, the tensor between the curly brackets in ( 2) is symmetric and thus its corresponding axial vector vanishes, namely(3) Next, on using the equilibrium equation ( 24) in [2] we obtain Corrigendum

We give conditions on the strain-energy function of nonlinear anisotropic hyperelastic materials that ensure compatibility with the classical linear theories of anisotropic elasticity. We uncover the limitations associated with the volumetric deviatoric separation of the strain energy used, for example, in many Finite Element (FE) codes in that it does not fully represent the behavior of anisotropic materials in the linear regime. This limitation has important consequences. We show that, in the small deformation regime, a FE code based on the volumetric-deviatoric separation assumption predicts that a sphere made of a compressible anisotropic material deforms into another sphere under hydrostatic pressure loading, instead of the expected ellipsoid. For finite deformations, the commonly adopted assumption that fibres cannot support compression is incorrectly implemented in current FE codes and leads to the unphysical result that under hydrostatic tension a sphere of compressible anisotropic material deforms into a larger sphere.