Computational optimization of director patterns in liquid crystal elastomers

We present a computational framework for optimizing the director distributions in viscoelastic liquid crystal elastomer (LCE) structures. The framework begins with a finite element implementation of a viscoelastic finite strain model to capture the time-dependent behavior of LCEs. This model is coupled with an optimization scheme that optimizes the spatially continuous director field for targeted mechanical performance. A time-dependent adjoint sensitivity analysis is employed to enable efficient gradient-based design updates. The framework is demonstrated through numerical examples that maximize mechanical work and maximize energy dissipation. Maximizing the mechanical work produces optimized director patterns that are aligned with principal stress directions, resulting in minimal reorientation and increased stiffness. Maximizing the energy dissipation produces director patterns that depend on whether viscous director rotation or network deformation is the dominant dissipation mechanism. These results highlight opportunities for optimizing LCE structures and underscore the importance of accurately modeling the viscoelastic response when designing LCE structures for reliable, long-term functionality.