Modeling elastic instabilities in nematic elastomers

Liquid crystal elastomers are cross-linked polymer networks covalently bonded with liquid crystal mesogens. In the nematic phase, due to strong coupling between mechanical strain and orientational order, these materials display strain-induced instabilities associated with formation and evolution of orientational domains. Using a three-dimensional finite element elastodynamics simulation, we investigate one such instability, the onset of stripe formation in a monodomain film stretched along an axis perpendicular to the nematic director. In our simulation, we observe the formation of striped domains with alternating director rotation. This model allows us to explore the fundamental physics governing dynamic mechanical response of nematic elastomers and also provides a potentially useful computational tool for engineering device applications.

Figure 1

(Color online) Simulation: stretching a nematic elastomer film at an angle of $90°$ to the director. Initially a monodomain, the director field evolves to form a striped microstructure. Darkest regions have director parallel or perpendicular to the stretching direction; brightest regions have director oriented at $\pm 45°$ to the stretching direction.

Figure 2

(Color online) Engineering stress (circles) and director rotation (squares) vs applied strain, for the system shown in Fig. 1. Onset of director rotation and the stress-strain plateau both occur at the same strain.

Figure 3

(Color online) Engineering stress (circles) and director rotation (squares) vs applied strain, applied at an angle of $60°$ from the nematic director.

Figure 4

(Color online) Simulation: stretching a nematic elastomer film at an angle of $60°$ to the director. Initially a monodomain, the director field rotates smoothly without sharp gradients in orientation. Darkest regions have director parallel or perpendicular to the stretching direction; brightest regions have director oriented at $\pm 45°$ to the stretching direction.

Figure 5

(Color online) Dependence of the stress-strain response on strain rate.

Figure 6

(Color online) Simulation: A nematic elastomer disk is stretched radially. The director field smoothly transforms from a homogeneous vertically oriented monodomain to a nearly radial configuration.