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NGCM-0108: Generalised asymptotic numerical methods for surface instability problems in biological systems

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  • Full or part time
    Dr G. Limbert
  • Application Deadline
    Applications accepted all year round
  • Competition Funded PhD Project (European/UK Students Only)
    Competition Funded PhD Project (European/UK Students Only)

Project Description

Surface instabilities (e.g. wrinkling, folding, creasing) in biological systems play a critical role in processes such as morphogenesis, growth, ageing and mechanobiological adaptation. Understanding the mechanistic principles behind these highly non-linear phenomena is key in unravelling organ and tissue functions in health and disease (e.g. brain folding, skin wrinkles, airway wall remodeling) and also in developing better products designed to interact with the body. For example, unveiling the underlying mechanical principles that condition the morphologies and patterns of skin wrinkles are essential in predicting how an aged skin interacts with its environment (e.g. medical and personal care products, sport equipment, tactile electronic surfaces).

The project: In the study of surface instabilities, and considering the structural and material complexity of biological systems, one need to have access to robust finite element methods and solvers capable of handling highly non-linear coupled phenomena.
Current available numerical tools are hindering research in this field as they 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 orginal method first proposed by Cochelin [1] 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 (using open-source numerical libraries) will be essential for the project. Multiphysics isogeometric structural and solid finite elements will also be extended/developed to study biological differential growth phenomena in skin and the formation of ageing skin wrinkles.

[1] Cochelin, B. 1994 A path-following technique via an asymptotic-numerical method. Comput. Struct. 53, 1181-1192.
We are looking for an applicant with a background in physics, engineering mechanics, mathematics, or computer science, and an appetite to learn and research across conventional discipline boundaries.
The stipend is at the standard EPSRC levels. More details on facilities and computing equipment are available

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, Singapore and the USA.

If you wish to discuss any details of the project informally, please contact Georges Limbert, Email: [email protected] 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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