MAGIC113: Introduction to Mathematical Modelling of Liquid Crystal Elastomers

Course details

A specialist MAGIC course


Autumn 2023
Monday, October 2nd to Friday, December 8th


Live lecture hours
Recorded lecture hours
Total advised study hours


12:05 - 12:55 (UK)

Course forum

Visit the MAGIC113 forum


Liquid crystal elastomers (LCEs) are advanced multifunctional materials that combine elasticity with orientational order. Specifically, mechanical strains give rise to changes in liquid crystalline order and, conversely, changes in the orientational order generate mechanical stresses and strains.

The quest for responsive materials with the ability to mimic living systems or to enable green energy production and conversion processes is one of the major challenges for modern materials design. Because of their large reversible deformations and complex material responses in the presence of natural stimuli like heat or light, and electric or magnetic fields, LCEs are suitable for a wide range of applications in science, manufacturing, and medical research. Moreover, biodegradable, recyclable and reprocessable LCEs have also been achieved.

This course offers an introduction to core concepts in the mathematical modelling of LCEs by linking nonlinear elasticity with liquid crystal theory in a unified and coherent manner. There are many similarities between LCEs and conventional rubber on the one hand, and between solid mechanics and the analysis of liquid crystals on the other hand, and all similarities or differences need to be examined carefully.


The study of LCEs is an interdisciplinary subject involving chemistry, physics, materials science, mathematics and computational simulations. For this course, a general background in applied mathematics is required, including algebra, calculus, geometry, differential equations and continuum mechanics.


  1. 1. Introduction
  2. 1.1. Over view of tensor theory
  3. 2. Isotropic nonlinear elasticity 
  4. 2.1. Hyperelastic models 
  5. 2.2. Stresses and strains
  6. 3. Liquid crystal theory
  7. 3.1. Order parameters
  8. 3.2. Isotropic to nematic phase transition
  9. 4. Nematic liquid crystal elastomers
  10. 4.1. Ideal nematic elastomers
  11. 4.2. Stresses and stress-free configurations
  12. 4.4. Shear striping instability
  13. 4.5. Variational formulation
  14. 5.  Photo-mechanical effects


  • Professor Angela Mihai

    Professor Angela Mihai

    Cardiff University


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The assessment for this course will be released on Monday 8th January 2024 at 00:00 and is due in before Friday 19th January 2024 at 11:00.

Assessment for all MAGIC courses is via take-home exam which will be made available at the release date (the start of the exam period).

You will need to upload a PDF file with your own attempted solutions by the due date (the end of the exam period).

If you have kept up-to-date with the course, the expectation is it should take at most 3 hours’ work to attain the pass mark, which is 50%.

Please note that you are not registered for assessment on this course.


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