Multilevel approach for simulating the reorientation of mesogens in nematic liquid crystal elastomers

Nematic liquid crystal elastomers (LCEs) are well-known for their actuation properties and are thus very suitable for the construction of artificial muscles. The distinguishing features of nematic LCEs are possible due to their molecular configuration and the orientation of the mesogens. The simulation of LCEs is very challenging, since a very large amount of elements is usually needed and also several variables might be necessary for mimicking their unusual behavior. Improving the numerical methods for dealing with the simulation of nematic LCEs is essential. For this purpose, we describe and implement a multilevel numerical procedure for modeling the reorientation of the mesogens. The algorithm is implemented in the dynamic numerical framework with distinct drilling degrees of freedom for the rotations of the mesogens and the bulk elastomer. In each time step, the drilling degrees of freedom are obtained from an elementwise system of equations. In this regard a new invariant free energy density is introduced for the sake of preventing the singularity of the tangent. Afterwards, the rotations at the local nodes are included in the global system of equations by static condensation. We compare results obtained by the multilevel approach with the ones from the monolithic procedure for the case of a virtual experiment, in which Dirichlet and Neumann boundary conditions on the orientation mapping are applied.