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PhD study

We are always looking for talented students wanting to undertake challenging research in Computational Engineering. For more information - contact us.

Possible research topics are listed below. The School of Engineering has a limited number of scholarships to offer to excellent candidates.  Find additional information on postgraduate study.

PhD projects

Computational cardiovascular biomechanics

Supervisor: Dr. Ankush Aggarwal (

Summary: Almost 30% of all deaths globally are related to cardiovascular diseases. The overall aim of computational cardiovascular biomechanics is to help improve the diagnosis of these diseases (faster, earlier, more precise), provide better surgical outcomes, and design devices that last longer. To achieve that aim, we study the biomechanical properties of tissues and cells comprising the cardiovascular system using a combination of in-vivo imaging, ex-vivo and in-vitro testing, and in-silico modeling. The projects can be divided into model development (at organ and cellular scales) and method development (based on imaging and using data science approaches). A few examples of specific projects are:

1) Multiscale modeling of the heart muscle
2) Modeling of endothelial cells based on in-vitro experiments
3) Developing methods for biomechanical characterisation of tissues from ultrasound images
4) Designing optimal experiments for cardiovascular tissues under uncertainty

During this project, the student will have opportunities to:

  • Develop skills necessary to work at the interface of engineering and biomedical science
  • Publish papers in high-quality journals
  • Present research results at international conferences
  • Learn about nonlinear finite element analysis, nonlinear mechanics, multiscale modeling, image-based analysis, data science, and other numerical techniques
  • Learn about experimental and clinical validation
  • Collaborate with our international academic and industrial partners
  • Interact within the Glasgow Centre for Computational Engineering with other researchers (GCEC) and across departments with biomedical scientists and clinicians

Eligibility: Candidates must have an undergraduate degree in a relevant field, such as Mechanical Engineering, Biomedical Engineering, Civil Engineering or Mathematics, with a minimum 2.1 or equivalent final grade. A background in mechanics and knowledge of finite element modeling would be necessary. Programming skills will be required for computational modeling.

Application: The deadline for applications is 31 January 2022, and the application process consists of two parts:
1) On-line academic application: Go to and click on the ‘Apply now’ tab. Applicants should attach relevant documents such as CV, transcripts, references and a research proposal.
2) The scholarship application: Complete the application form found at the following webpage: and attach a letter of support from a potential supervisor.  Both the application form and supporting letter should be emailed to

Further information: If you are interested or want more information, please contact Dr. Ankush Aggarwal ( before starting the formal application. Please visit Computational Biomechanics Research Group page for more information on our research.

Modelling large deformations in growing soft biological tissues

Understanding mechanical behaviour of biological tissues is becoming increasingly important to understand biological function as well as to design effective treatments for medical conditions. Tissues such as human skin are highly deformable and demonstrate nonlinearity in their mechanical response. Phenomena such as wrinkling are associated with mechanical instabilities caused due to large strains. Furthermore all living tissues constantly remodel themselves by replacing old cells and growth of new cells – leading to changes in their mechanical properties.

This project aims at studying the various forms of mechanical instabilities that can occur in tissues due to growth and remodelling. The scope is fairly open and the exact project aims will be finalised in conjunction with your interests. You will have the opportunity to work closely with all the team members at the Glasgow Computational Engineering Centre (GCEC) as well as colleagues in other schools and universities.

This PhD project is suitable for students with interests in topics such as solid mechanics, structural engineering, computational mechanics, applied mathematics, or biomechanics.

Supervisor: Prashant Saxena

Mechanics of smart magneto-active and electro-active materials

Electro- and magneto-active smart materials are types of advanced composites that can undergo large deformations in the presence of external electromagnetic fields. Being lightweight and possessing capability of extreme deformations before any fracture, they are excellent candidates to be used as sensors, actuators, vibration suppressors, and in other structural mechanics applications. Modelling of these composites requires dealing with the mechanical and electromagnetic fields simultaneously thereby resulting in a coupled “multi-physics” problem.

This project aims at studying the behaviour of these smart materials close to instability (buckling) – a point where the electro-mechanical or magneto-mechanical behaviour of material changes drastically resulting in extreme deformations. A major outcome of this project will be the prediction of post-buckling response of smart materials. These insights will provide significant value towards design of various devices made of these composites. You will have the opportunity to work closely with all the team members at the Glasgow Computational Engineering Centre (GCEC) as well as colleagues in other schools and universities.

This PhD project is suitable for students with interests in topics such as solid mechanics, structural engineering, computational mechanics, applied mathematics, or electromagnetics.

Supervisor: Prashant Saxena

Constitutive modelling of the time effects on mechanical behaviour of sand

The mechanical behaviour of sand is time-dependent. Time effects in granular materials comprise rate effects and aging effects. Rate effects include rate dependent stress-strain relation, creep (time-delayed accumulation of strain at constant stress) and stress relaxation (stress change at constant strain). The aging effects, which are used to describe changes in engineering properties (e.g., stiffness and stress-strain relation) of sand with time, could be attributable to changes in internal structure of sand associated with static fatigue at particle contacts, contact force homogenization, formation of interlocking or cementing agents and/or time-delayed particle movement. These time effects has significant influence on practical geotechnical design. For instance, long term observations showed that sand creep can induce large settlement of foundations built on sand. The settlement after construction may reach 35% of the total one. Neglecting such settlement can result in dangerous designs. Consideration of aging effects on mechanical properties of sand can lead to safer and more cost-efficient design. Abundant experimental and field tests indicate that the bearing capacity of driven piles in sand increase with time, which is known as pile setup. In some cases, the increase can reach 100% in just 3 months. This is attributable to sand aging. This project aims to develop a comprehensive constitutive model to describe time effects on mechanical behaviour of sand. The main objectives are:

(a) Development of an elasto-visco-plastic constitutive model for describing the time effects on mechanical behaviour of sand. Since the time effects on mechanical behaviour of sand cannot be described by a conventional rate-dependent model which assumes that all the time effects are due to time-delayed accumulation of strain, distinction between the rate and aging effects will be made in the proposed model.

(b) After the model is developed, it will be implemented in the finite element package Abaqus to solve practical boundary value problems associated with time-dependent mechanical behaviour of sand. Examples are back analysis on increase of bearing capacity of driven piles with time, increase of liquefaction resistance of sand with time and long term deformation of sand embankments/dams.

Supervisor: Zhiwei Gao

A method for predicting rock fall in 3D

Rock fall is a type of landslide consisting of detachment, fall, rolling, and bouncing of rock fragments. Increasing occurrence of weather events have caused more and more rock fall hazards in both the UK and the world. Catch fence systems consisting of wire meshes, cables and supporting posts are frequently used to control rock fall and debris flow from unstable rock and soil slopes along railways and roads. These systems have been found effective and cost-efficient and there is increasing use of them. For instance, the Network Rail will invest over £5 million on installation of rock catch fences in the coming five years. To date, however, these systems have been designed primarily by empirical methods, engineering judgment, field tests and experience. Recently, geotechnical specialists and some contractors have found that certain system elements may be over-designed. Meanwhile, some systems have failed under various impact conditions, indicating that the system were not properly designed for their desired applications. One of the major reasons for the inappropriate designs is that the potential rock fall trajectory and energy were not properly estimated. Though some 2D methods have been developed for rock fall prediction, there is limit success in 3D prediction. The 2D methods are not sufficient for a real catch fence design in which the rock fall will definitely not occur in a 2D plane. This project aims to develop a method for prediction rock fall in 3D. The major objectives are:

(a) Development of a method for predicting rock fall in 3D. Randomness is one of the main characteristics of rock fall, and therefore, a statistic approach will be used to develop the method.

(b) Small scale model tests will be carried out to study the rock fall in a real site. The tests will be recorded by high speed camera.

(c) Application of the prediction method. The method will be used to predict the rock fall observed in both model tests and full scale tests.

(d) Knowledge transfer of the project. The knowledge generated in this project will be transferred to industry to improve the current design of rock catch fences.

Supervisor: Zhiwei Gao

3D Printable Granular Materials

Granular materials are ubiquitous and vital for our everyday life. They are seen in the form of both natural and engineering materials, such as sand, sugar, food grains and powders in agricultural, pharmaceutical, energy and chemical industries. Granular materials are the second-most manipulated material in industry next to water. Sand is a typical example of granular media, and is important to a wide range of key infrastructures pertaining to the quality and safety of our daily life and the economy of many countries around the world including the UK. Many new infrastructures, such as wind turbines, high-speed railways, tunnels, pipelines and earth dams which are lifelines to the economy of the UK, will be built on/in sand. The mechanical behaviour of sand underpins the critical performance and serviceability of these structures and is a key factor to be considered in their design, construction, operation and maintenance. Until now, many aspects of the mechanical behaviour of granular materials remain mystery to Human. The particle shape is the major factor which controls the mechanical behaviour of sand, including the stiffness, shear strength and volumetric change in shear. This project aims to use 3D printing to create particles with different morphology and use them in experimental tests. The major objectives of this project are:

(a) Development of a numerical scheme for generating 3D granular particles with desired morphology;

(b) 3D printing of the granular particles;

(c) Use of the particles in triaxial compression tests to study the effect of particle shape on mechanical behaviour of granular materials.

Supervisor: Zhiwei Gao

A stable multi-physics modelling framework for the Finite Element analysis of materials and structures

Multi-physics is one of the predominant research challenges dominating international research efforts in computational mechanics. A computationally tractable solution of strongly coupled physical systems requires the simultaneous solution of multiple fields and the interactions of these fields. Such problems frequently suffer from solution instability, resulting in non-physical and spurious results. 

The project will investigate novel techniques that have the potential of guaranteeing stability for any choice of approximation space. The successful implementation, testing and demonstration of this investigation will be a major advance in the field of computational mechanics for achieving solution stability for multi-physics problems.

The project will also consider the application of this framework to materials and structures exposed to elevated temperatures, investigating the interaction between the mechanical, thermal and moisture response. The project will either consider either (a) materials and structures relevant to the nuclear industry, e.g. concrete, graphite, steel, possibly including fracture propagation, or (b) biological materials, depending on the background and interest of the research student.

This fundamental research will be implemented in our group’s FEA software (MoFEM), utilising the latest advances in scientific computing to enable the development of scalable algorithms to maximise efficient use of computer architectures.

Supervisors: Chris Pearce and Lukasz Kaczmarczyk

Liquefaction of sand with fines

Liquefaction causes the ground to undergo dramatic reductions in strength and stiffness and commonly occurs in sandy soils subject to shaking by earthquakes.  An example of the hazard posed by liquefaction is the 2011 Christchurch earthquake, which caused 185 deaths and lead to damage totalling an estimated $40 billion.

The processes which cause liquefaction, such as an increase in water pressure in the pores of the sandy soil, operate at the grain-scale. To develop more effective risk assessment procedures these grain-scale processes must be better understood. Liquefaction is particularly poorly understood for sandy soils containing fines and this will be the focus of this project.

This project will use discrete element modelling (DEM), a numerical method which allows detailed analysis of granular materials to be carried out at the grain/particle scale. It is effectively a virtual laboratory test which allows a wide range of variables unavailable to experimentalists to be measured. The open source DEM code LAMMPS ( will be used and this will be coupled with lattice-Boltzmann methods to simulate the particle-fluid interaction which leads to liquefaction. LAMMPS is designed for use with high performance supercomputers such as the national supercomputer ARCHER and Archie-West at Glasgow University. DEM simulations will be carried out for a range of sandy soil states with varying amounts of finer material and the results will be used to answer the following questions:

  • What are the fundamental grain-scale mechanisms which cause liquefaction of sands with fines?
  • How well do current theories derived from experimental work (e.g. Rahman and Lo, 2011) capture the mechanics of liquefaction?
  • How can analysis techniques be given a more fundamental scientific basis?

The focus of this project is liquefaction but it should appeal to all engineers and physicists interested in granular materials. Therefore, in addition to civil engineers, applications from students from other disciplines (e.g. mechanical and chemical engineering, physics and applied mathematics) are welcomed.

Supervisor: Tom Shire

A first order conservation law framework for solids, fluids and fluid structure interaction

The computational analysis of fluid structure interaction phenomena is widely used these days for a wealth of industrial and physical applications. In particular, the field of biomechanics has observed a surge over the last decade in the application of these computational techniques for the modelling of biological tissues (i.e. heart valves) interacting with biological fluids (i.e. blood). Some of these problems are highly challenging, requiring the modelling of highly deformable (nearly incompressible) solids immersed within a surrounding incompressible Newtonian viscous fluid. In this case, a fast and robust computational framework becomes essential for a successful simulation.

Building upon very recent discoveries (i.e. first order conservation law for solid dynamics) made by the supervisory team, the objective of this PhD is the further development of a novel 3D computational framework with significantly improved properties with respect to the current state of the art. Initial implementation has been carried out in Matlab platform, with very promising results in some extremely challenging solid dynamics problems. Interestingly, the methodology will borrow concepts from Computational Fluid Dynamics and apply them to Computational Solid Dynamics in a way that will greatly enhance the robustness and accuracy of the simulations, with the final aim to handle fluid-structure interaction.

The recruited PhD candidate will become a member of an active research group working on the development and application of cutting edge computational techniques for large strain solid dynamics, fluid structure interaction and computational multi-physics.

Project summary

Traditional low-order finite element formulations are typically employed in Industry when simulating complex engineering large strain fluid structure interaction problems. However, this approach presents a number of well-known shortcomings, namely: (1) unable to accurately capture the initiation and propagation of strong discontinuities in solids/fluids, (2) a reduced order of convergence for strains and stresses, (3) poor performance in nearly incompressible solids and (4) numerical artefacts in the form of shear/bending locking, volumetric locking and spurious pressure modes. 

The aim of this thesis is to develop a unified computational framework for the numerical analysis of fluid structure interaction problems. In this work, a very competitive vertex centred finite volume algorithm will be employed. The solid-fluid coupling conditions on the interface will be solved via a physically based Riemann solver. In addition, for problems involving extremely massive deformations, it may be necessary to re-adapt the mesh to maintain both the mesh quality and the solution accuracy.

Sister project

The sister project, in collaboration between Swansea University and University of Glasgow, will focus on the development of OpenFOAM finite volume solver for fluid structure interaction. Details of this collaborative project can be found at the following link:


  • To have a strong undergraduate and MSc degree (or equivalent) in Engineering, Mathematics, Physics or a related field 
  • To have an enthusiastic attitude to conduct research, being hard-worker and critic 
  • To have a strong background in nonlinear continuum mechanics
  • To demonstrate experience with numerical methods (Finite Volume/Finite Element) 
  • To have a good knowledge of some programming languages such as Matlab and/or C/C++ 
  • To demonstrate experience with parallel programming

Supervisor: Chun Hean Lee (

Improving the dynamic response of reinforced concrete structures

Critical infrastructure, such as bridges, high rise buildings and nuclear reactors, should be designed to resist extreme loading events in the form of blast and high-speed impact. Reinforced concrete structures subjected to dynamic loading exhibit complex failure processes, whereby the response of connections between members are often critical for the resilience of the entire system. Understanding how the performance of structural members and their connections can be improved is highly desirable so that resilient structures can be designed.

The aim of this project is to investigate how cementitious materials can be enhanced by tuning fibres and other inclusions to create materials with exceptional mechanical properties. For these new materials, we aim to develop damage-plasticity constitutive models together with small scale physical experiments. Nonlinear finite element techniques for dynamic analysis of structures together with the new constitutive models will be used to assess the effect of the new materials on the failure process of structural members.

Supervisor: Peter Grassl (

Particle tracking in PEPT using machine learning

Positron emission tomography (PET) is a nuclear imaging technique commonly used in nuclear medicine to produce three-dimensional images of functional processes within the body. PET scanners and their underlying algorithms have been adapted to explore the complex flow exhibited by granular systems. In positron emission particle tracking (PEPT), one particle within the system is tagged with a radionuclide. The radionuclide undergoes β+ decay, during which a position and a neutrino are produced. When the position comes into the neighborhood of an electron in the surrounding medium, an annihilation event occurs resulting in the emission of back-to-back photons. The PET scanner detects this pair of back-to-back photons and a line of response is constructed. After sampling over a small time increment, an algorithm determines the position of the particle from multiple lines of response. The trajectory of the particle in 3D space can then be reconstructed.

PEPT provides valuable insight into a range of industrial processes. Examples include the mixing of pharmaceutical powders and the milling of rock. A key assumption is that the behavior of the whole system can be described by that of an individual particle tracked for a sufficiently long time. The ability to track more than one particle simultaneously is therefore of significant value.

Project Summary

The algorithms used to reconstruct the trajectory of a single particle are relatively mature. Recently work has been done to track multiple tagged particles. This provides a far richer data set but presents many challenges. The objective of this research project is to apply recent advances in machine learning to track multiple particles within a laboratory-scale tumbling mill. The generated algorithm should be robust and efficient. Granular flow simulations, using the discrete element method, will be used to augment the experimental data set.

Supervisor: Andrew McBride

Transient simulation of triboelectric nanogenerators considering surface roughness

Background: Triboelectric nanogenerators (TENG) are modern devices that use repeated cycles of contact between suitably chosen surfaces to transform mechanical energy into electrical energy. TENG have attracted significant attention in recent years as autonomous clean energy harvesters. Various sources of mechanical energy can be used: from human motion (wearable textile systems for charging medical sensors) to ocean waves (large-scale networks for "blue energy" harvesting). 

Optimisation of TENG performance is an active area of research requiring a combination of experimental and computational approaches. Experiments show that TENG output depends on the frequency of contact-separation cycles and the applied mechanical load. At the same time, accurate simulation of TENG is challenging and includes coupling of contact mechanics and electrostatics. It is further complicated if the surface roughness and the material heterogeneity are taken into account.

Objectives: The primary objective of this project is to develop a numerical model of an actual TENG, which requires solving a nonlinear, multi-scale, multi-physical, and time-dependent problem. This work will be underpinned by advanced scientific computing tools available in MoFEM, an open-source finite element library developed at GCEC. As a result, the framework will enable massively parallel simulations with 10-100M of unknowns required to demonstrate the model's predictive capabilities.

Moreover, the project will include collaboration with colleagues at the Materials & Manufacturing Research Group who are doing experimental research on TENG. Therefore, the second objective is to create a "virtual engineering lab" for TENG based on the developed numerical framework, accelerating the design and prototyping of new devices. 

SupervisorAndrei Shvarts (