A new mixed finite element formulation for reorientation in liquid crystalline elastomers

Liquid crystalline elastomers (LCE) belong to the class of soft materials and are capable of large deformations induced by temperature changes and ultraviolet irradiation. These materials are under investigation as actuator materials in light-weight structures. In order to numerically simulate LCE materials by using a space-time finite element method, a continuum model is necessary which combines a thermo-viscoelastic material formulation with a dissipative reorientation process of mesogens. Mesogens are rigid and rod-shaped molecules linked with the polymer chains of the elastomer. The dissipative reorientation of the mesogens can be described by a combination of an independent field of orientation vectors with unit length and micropolar rotational degrees of freedom. The orientation vector field follow from a partial differential equation and possesses initial-boundary conditions. The unit length of the orientation vector field for any time is guaranteed by a local rotation with the micropolar rotational degrees of freedom. The dissipative reorientation process is introduced by a local time evolution equation with respect to the micropolar rotational degrees of freedom. This is analogous to thermo-viscoelasticity and can be variationally-based formulated. In this paper, we present this new variational-based reorientation finite element formulation in a dynamical framework. We arrive at an energy-momentum consistent mixed finite element formulation with a Galerkin-based space-time integration.

Automated summary

Liquid crystalline elastomers (LCE) are soft materials that can undergo large deformations due to temperature changes and ultraviolet irradiation. This study presents a continuum model and a variational-based reorientation finite element formulation for numerical simulations of LCE materials. The dissipative reorientation of mesogens is described using an orientation vector field and micropolar rotational degrees of freedom.