Numerical study on crack tip fields in liquid crystal elastomers

Abstract

This study presents a numerical investigation into the crack tip fields in liquid crystal elastomers (LCEs) using finite element simulations. LCEs exhibit unique mechanical behaviors, such as soft elasticity and directionally adjustable anisotropy, due to the coupling between the deformation of polymer networks and the rotation of liquid crystal mesogens. The numerical simulations focus on a rectangular LCE plate with a small central crack, subjected to uniform stretching. Simulation results reveal the presence of a uniaxial stress state near the crack tip and a universal stress singularity obeying a power law with an exponent of −1. Along the circumferential direction around the crack tip, the stress distribution exhibits a prominent polarization, with the polarization direction precisely aligned with the initial mesogen orientation. For the mesogen reorientation at the crack tip, two types of mesogen rotation—rigid body rotation with the polymer network and relative rotation due to network stretching—are distinguished. The rigid body rotation is found to cause significant heterogeneity in mesogen orientation at the crack tip, but the relative rotation tends to make the mesogen orientation more uniform, generally aligning with the direction of applied stretch. The final mesogen orientation, determined by the initial orientation and rotation, is closely related to the magnitude of the stress field at the crack tip. These findings provide valuable insights into the fracture behavior of LCEs and can serve as a foundation for future experimental and theoretical studies.