Title: Cavitation in nematic elastomer spheres

Code: AM2122A

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, instabilities in liquid crystalline solids can be of potential
interest in a range of applications. This project focuses on the cavitation
instability where a void forms at the centre of a nematic sphere under
radial symmetric tensile load. Assuming an initially unit sphere described
by a simple neoclassical model for ideal nematic elastomers, the aim is
to determine the critical load for the onset of cavitation, and to verify
if the associated bifurcation from the trivial solution where the sphere
remains undeformed is supercritical, i.e., if the cavity radius increases
as the applied load increases. A comparison with similar phenomena in
purely elastic spheres will also be performed.

Project offered as a Double module.

Type: 20 credits

Supervisor: Dr Angela Mihai

Prerequisite 2nd year modules: Real Analysis, Calculus of Several Vari-
ables, Linear Algebra

Prerequisite 3rd year modules for concurrent study: Partial Differential
Equations, Methods of Applied Mathematics, Finite Elasticity

Maximum number of students: 1