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  Upscaling morphing in biological structures

   School of Engineering

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  Dr Matteo Taffetani, Dr Marcelo Dias  No more applications being accepted  Funded PhD Project (Students Worldwide)

About the Project

Continuum mechanics approaches have been used to model the mechanical behaviour of biological (and active) systems at length scales that are large enough.

For example, when analysed at the micron-scale, biological membranes can be treated as continuum objects that deform regulated by effective properties such as curvature mismatch or active forces. Those effective properties depend on how their fundamental constituents, such as lipids and proteins, evolve at the nano-scale.

Thus, continuum modelling approaches have been able to improve the understanding of the behaviour of biological materials, showing the critical role of mechanics in processes like growth and remodelling, but they have two also major limitations:

1.   They rely heavily on phenomenological assumptions, such as the parameters that describe the mechanical properties or the active behaviour.

2.   Biological and active materials are fundamentally discrete, thus making the continuum approaches fail when moving at length scales that are not large enough, i.e. the micro-to-nano boundary in the case of biological membranes.

The project focuses on providing a link between the microscopic (discrete) nature and the macroscopic (continuum) modelling of biological structures with the double-pronged aim to improve the understanding of the two limitations described above: (i) to provide a quantitative relation between the lumped parameters used in the continuum description and the microscopic mechanics from which they originate them; (ii) to reveal what scale is large enough for the continuum approaches cannot be used.

The project aims to develop new theories to understand the root causes of the active morphing of two-dimensional biological membrane-like structures, like cellular membranes or kinetoplast sheets.

The project involves three main aspects:

1.   Theoretical continuum modelling. Starting from the well-known description of the mechanics of two-dimensional bodies, we update this passive description by using effective modelling (like negative capillarity or curvature control) to investigate the competition between bulk elasticity and active control on the global morphing of slender objects.

2.   Theoretical discrete modelling. Providing potential modelling ways to couple microscopic features, like the distribution of proteins, the evolution of chemicals and the presence of defects, and macroscopic mechanics.

3.   Numerical study. Implementation of numerical codes to investigate morphing beyond the limitations introduced to gain analytical advancements.

As a potential late-stage target, the understanding gained by the development of the new theories can be used to design table-top experiments able to reproduce the relevant features of the morphing seen at the microscopic level.

A suitable candidate has expertise in mathematical modelling and implementing numerical codes using either commercial codes or open-source suites. Although preferable, knowledge of mechanical concepts (like elasticity or equilibrium equations) is not essential provided some familiarity with partial differential equations and conservation laws is available.

Familiarity with biological or active materials is not essential.

During this project, you will be part of the Institute for Infrastructure and Environment. You will join a vibrant community of PhD students, postdoctoral research associates and academics. This is a collaborative and friendly environment and strong teamwork and communication skills are therefore required.


Minimum entry qualification - an Honours degree at 2:1 or above (or International equivalent) in a relevant science or engineering discipline, possibly supported by an MSc Degree. Further information on English language requirements for EU/Overseas applicants.

This project would potentially suit candidates from backgrounds in Structural and Mechanical Engineering, Engineering Mathematics, Applied Mathematics and Physics.

We are particularly interested to hear from applicants with experience in mathematical modelling and who are keen to develop numerical codes (or improve numerical codes already available) to support the analytical conducted. Moreover, the applicant should have an interest in applying their studies to experimental evidence gathered from literature or tabletop experiments.  

Further Information

The University of Edinburgh is committed to equality of opportunity for all its staff and students, and promotes a culture of inclusivity. Please see details here:

Engineering (12) Mathematics (25) Physics (29)

Funding Notes

Tuition fees + stipend are available for Home/EU and International students
Further information and other funding options:

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