We propose in this paper a dielectric-graphene-dielectric tunable infrared waveguide based on multilayer metamaterials with ultrahigh refractive indices. The waveguide modes with different orders are systematically analyzed with numerical simulations based on both multilayer structures and effective medium approach. The waveguide shows hyperbolic dispersion properties from mid-infrared to far-infrared wavelength, which means the modes with ultrahigh mode indices could be supported in the waveguide. Furthermore, the optical properties of the waveguide modes could be tuned by the biased voltages on graphene layers. The waveguide may have various promising applications in the quantum cascade lasers and bio-sensing.

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The objective of the present study is to develop a solid element for large deformation analysis of hyperelastic shell structures. To attain high computational efficiency and annihilate shear and membrane lockings, a hybrid-strain stabilization approach is adopted. To overcome the thickness locking of the element, the enhanced assumed thickness strain modes are incorporated. Starting from the virtual work principle and a weak form that enforces the equality of the hybrid-strain and the strain arising from the displacement and the enhanced assumed strain, an eighteen-node element for large deformation analysis of hyperelastic shells is developed. The salient feature of the present element for higher computational efficiency is that the element uses only the second order quadrature for integration along the two in-plane natural coordinates and the stabilization vectors can be formed without using any integration loops. Efficacy of the element is illustrated by popular benchmark problems.