PhD Studentship: Generalised robust asymptotic numerical methods for non-linear buckling instabilit

United Kingdom
Jan 25, 2016
Jan 23, 2017
Organization Type
University and College
Full Time

PhD Studentship: Generalised robust asymptotic numerical methods for non-linear buckling instability problems in biological systems and bio-inspired morphing structures.

nCATS Research Group

Location:  Highfield Campus
Closing Date:   Sunday 22 January 2017
Reference:  682316BX

Project Reference: NGCM-0011


Buckling instabilities in biological systems play a critical role in biophysical processes such as morphogenesis, growth, ageing and mechanobiological adaptation and it is therefore essential to have access to robust numerical tools (particularly those based on the finite element method) which can be used to elucidate some (bio)physical aspects of these instabilities.

As humans age, their skin undergoes a series of natural biophysical alterations which occur in combination with the effects of external environmental factors. During this process, the formation and evolution of wrinkles alter the physical properties of the skin surface.  Unveiling the underlying mechanical principles that condition the morphologies and patterns of wrinkles are therefore essential in predicting how an aged skin interacts with its environment.

Similar instabilities also arise in electroactive soft morphing surfaces which is a very hot engineering topic at the moment with a wide range of applications in space, air, on land and underwater.

From the view point of physics, buckling instabilities are the result of a complex interplay between material and structural properties, boundary and loading conditions, the exact nature of which remains to be elucidated.

The project

Current available numerical tools are not robust enough to handle these highly non-linear phenomena in an automatic and systematic way for materials of arbitrary complexity/physics. It is proposed to develop a robust hybrid symbolic-numerical environment based on Mathematica® and highly optimised code (C/Fortran) to enable the simulation of highly non-linear phenomena such as post-buckling arising in a wide range of surface instabilities. The method makes use of a typical finite element discretisation and the principle is to follow the non-linear solution branch by applying a perturbation technique in a stepwise manner. The solution can be represented by a succession of local Padé approximations of high order (typically 20). This offers significant advantages over traditional predictor-corrector methods such as the Newton-Raphson method: robustness, full automation, computing time. Alternative approximation methods of the solution branch will be explored and the implementation of fast asymptotic numerical solvers on GPU architecture will be essential for the project. Multiphysics isogeometric structural and solid finite elements will also be extended/developed to study biological differential growth phenomena and the formation of ageing skin wrinkles.

The successful candidate will work in a stimulating research environment, supported by world-leading organisations such as Procter & Gamble, Rolls Royce and the US Air Force and will be encouraged to work with our international academic and industrial collaborators in Europe, South Africa, New Zealand and the USA.

If you wish to discuss any details of the project informally, please contact Georges Limbert, nCATS and Bioengineering research group, Email:, Tel: +44 (0) 2380 592381.

This project is run through participation in the EPSRC Centre for Doctoral Training in Next Generation Computational Modelling ( For details of our 4 Year PhD programme, please see

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