University of Cambridge

ESR 7 – Putting Gauss Curvature to Work


The University of Cambridge is an ancient university located in the United Kingdom. The university has accommodated many great historical names, including Newton, Darwin and Maxwell, and, more recently 121 Nobel Laureates. Unusually the University is composed of 31 autonomous colleges, some ancient and some modern, which each host individual communities of students and faculty.

The ESR will be principally based in Cambridge University Engineering Department, a large integrated department located in the city center. Specifically, the ESR will join the Oatley laboratory, which houses numerous theoretical, computational and experimental researchers working at the intersection of mechanics, materials and biology. The ESR will also be closely associated with the theory of condensed matter group in the physics department (Cavendish Laboratory), a celebrated theory/computation group specializing in statistical mechanics, many body quantum mechanics, statistical mechanics and biophysics.


Cambridge is a small (125,000 people) and attractive university city in the East of England, a short (50min) train ride from London. The city center hosts many ancient university buildings, and is a vibrant center of tourism, shopping and gastronomy. The city is rapidly expanding center of high tech and bioscience businesses, and recently attracted the global headquarters of Astrazeneca.



Dr John Biggins (Cambridge Engineering Department)



Prof Mark Warner (Cambridge Physics Department)


Contact email address of the supervisor:

Research project

The soft, anisotropic materials of the project, liquid crystal elastomers (LCEs) and glasses, contract along their director on heating/illumination. LCEs are also exquisitely programable materials: a flat LCE sheet may be prepared with any desired spatial director pattern written into it. On actuation, this director encodes a pattern of contraction which will change the metric of the sheet and morph it into a curved surface. Such “metric mechanics” allows the sheet to actuate into a surface which bears Gaussian curvature (e.g. a spherical cap or a cone) and hence cannot be flattened without energetically prohibitive stretch. Patterned LCE sheets can thus form powerful monolithic machines, which perform useful tasks as they actuate. In this project, we will design LCE patterns to create strong lifters, grabbers, manipulators, microfluidic pumps/valves.

The student will combine differential geometry, computation and micro-mechanics to elucidate the fundamental mechanics and design of programmed LCE sheets. The aim is to actually design and optimize director patterns for sheets for the above elements, and other components of soft robotics. There will also be secondments with experienced experimental partners: at Preceyes (Netherlands; Beelen), in Tampere (Finland; Arri Primägi) and Eindhoven (Netherlands; Dick Broer, Danqing Liu), to fabricate and test the resultant LCE patterns.

Beyond simple LCE sheets, the student will also be encouraged to search for further applications and novel mechanics in the area of composite LC/non-LC solid assemblies leading to instabilities, snapping, encapsulation and novel, non-isometric origami. There is also the opportunity to collaborate with the emerging in-house experimental effort in Cambridge.

PhD programme – University: University of Cambridge, Department of Engineering


Candidate’s profile: 

Required Masters degree in physics, engineering, mathematics or related subject

English level: At least CEFR C (see specific requirements link for details)

Desired skills: knowledge of (continuum) mechanics/elasticity, geometry, and some experience of programming (e.g. python or Cpp)


Specific requirements for the enrolment in the PhD Programme: 

A separate application to Cambridge must be made before the university deadline on June 30th 2021. Full requirements for acceptance onto the programme are listed at

If the applicant does not have appropriate UK immigration status, they will need to obtain a “Global Talent visa” (route two at before starting work.