Patterned liquid crystal elastomer (LCE) has been shown to have significant promise in surface topography control. Large and diverse shapes and surface adaptive responses have been shown using LCE materials with patterned director profiles. Using various techniques, crystal orientation across the surface of the material as well as through the thickness can be achieved yielding the capability to design out-of-plane deformation. These topological features can be used as active flow effectors manipulating, among other things, drag on an object in cross-flow.

It is well known that surface topography can have a large effect on skin friction drag by effecting the boundary layer transition, separation, and interfering with the shedding of vortices. In regards to a cylinder in a cross-flow, spatially manipulating surface topography, and thus drag, in this way gives rise to forces exerted by the fluid on the body. An imbalance of forces due to non-uniform surface topography can then be used to control the cylinder.

Designing such a system requires optimization of the surface topography via optimization of the crystal orientation pattern over a wide range of environments. Key to this optimization, described in detail in the presented work, is an accurate material model validated against experimental data. By representing the strain energy of the material as a combination of contributions of the elastomer backbone and the liquid crystals separately, unique material properties can be properly modeled. This is achieved by combining a traditional isotropic 3 chain Arruda-Boyce hyperelastic equation modeling the elastomer backbone with an anisotropic extension modeling the patterned liquid crystals, resulting in an anisotropic hyperelastic material model. The model can then be used to predict the material response of various patterns and investigate the design space of possible surface topographies.

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