Title: Inflation Instabilities in Nematic Elastomer Tubes

Code: AM2122B

Project Description:

Nematic liquid crystal elastomers are advanced multifunctional
materials that combine the exibility of polymeric networks with the ne-
matic structure of liquid crystals. Due to their complex molecular architec-
ture, they are capable of exceptional responses, such as large spontaneous
deformations and phase transitions, which are reversible and repeatable
under certain external stimuli (e.g., heat, light, solvents, electric or mag-
netic elds). Their accurate description requires multiphysics modelling
combining elasticity and liquid crystal theories.

In particular, internally pressurised hollow spheres and tubes are relevant
in many engineering and biomedical applications. This project focuses
on ination instabilities in a nematic circular cylindrical tube where the
liquid crystal mesogens may rotate during deformation. Assuming dier-
ent material models for ideal nematic elastomers, the aim is to show that,
depending on the particular model, the required internal pressure may in-
crease monotonically, or increase and then decrease, or increase, decrease,
and then increase again. A comparison with similar phenomena in purely
elastic tubes will also be performed.

Type: 20 credits

Supervisor: Dr Angela Mihai

Prerequisite modules: (2nd year) Real Analysis, Calculus of Several Variables, Linear Algebra; (3rd year) Partial Differential Equations, Methods of Applied Mathematics, Finite Elasticity

Maximum number of students: 1