Continuum Mechanics PhD projects

This page provides a (partial) list of specific (and not so specific) PhD projects currently offered around the Continuum Mechanics topic.

Identifying an interesting, worthwhile and do-able PhD project is not a trivial task since it depends crucially on the interests and abilities of the student (and the supervisor!) The list below therefore contains a mixture of very specific projects and fairly general descriptions of research interests across the School. In either case you should feel free to contact the potential supervisors to find out more if you're interested.

You should also explore the School's research groups' pages, and have a look around the homepages of individual members of staff to find out more about their research interests. You may also contact us for general enquiries.

Title

Thermo-visco-acoustic metamaterials for underwater applications

Group Continuum Mechanics
Supervisor
Description

The ability to control underwater noise has been of practical interest for decades. Such noise, radiating from e.g. offshore wind farms, turbines, and merchant vessels, frequently needs to be attenuated artificially given the close proximity of its generation to sensitive marine environments for example.

Over the last century a number of materials have been designed to assist with underwater noise attenuation. However, recently there has been an explosion of interest in the topic of acoustic metamaterials and metasurfaces. Such media have special microstructures, designed to provide overall (dynamic) material properties that natural materials can never hope to attain and lead to the potential of negative refraction, wave redirection and the holy grail of cloaking. Many of the mechanisms to create these artificial materials rely on the notion of resonance, which in turn gives rise to the possibility of low frequency sound attenuation. This is extremely difficult to achieve with normal materials.

The mechanisms of sound attenuation, i.e. thermal and viscous, have not yet been properly understood for the many metamaterials under study, particularly in an underwater context. The aim of this project is to study this aspect via mathematical analysis and then to optimize designs in order to design and employ metamaterials for use in underwater noise reduction applications. Although there has been some initial interest over the last few years in the “in-air” context, the parameter regime underwater gives rise to new effects that need to be explored and understood thoroughly.

Initially canonical geometries such as simple apertures and infinite and semi-infinite ducts shall be considered before moving on to more complex, realistic scenarios and geometries where resonance plays a key role.

Mathematical modelling using the method of matched asymptotics shall be employed. This is ideally suited to the scenarios considered given the low frequency regime. Comparisons shall be drawn with direct numerical simulations using finite element methods in e.g. COMSOL.

Title

Convective mass transfer for cleaning and decontamination

Group Continuum Mechanics
Supervisors
Description

Cleaning and decontamination processes can rely on different mechanisms to remove a patch of alien substance attached to a substrate. A shear flow covering the substrate can remove the substance through mechanical forces, potentially combined with chemical surfactant agent decreasing the adhesion of the substance onto the surface. However, this project is concerned with a second type of mechanism which is based on the dissolution of the substance into the cleaning fluid flow covering the substance.

This second type of cleaning process establishes a convective mass transfer between the alien phase and the cleaning phase. Several applications rely on this process, particularly when the dispersion of the substance is unwanted, such as in the decontamination process of toxic chemical spills. In our daily life, the cleaning mechanism more and more favoured in dishwashers relies also on a convective mass transfer as it has been shown empirically to reduce energy and water consumption.

This project will focus on the case of a film flow covering a single droplet containing several substances. Many fundamental questions are still unresolved in this multiphase convective mass transfer problem. In particular, we will study how advection processes inside the drop can influence the convective mass transfer. Effect of solubility and surface tension on the overall mass transfer can also be analysed. The project will explore these questions using a combination of experimentation, numerical simulations and theoretical analysis.

The project is suitable for an enthusiastic and creative candidate who has good knowledge in fluid mechanics and some experience in experimentation and numerical simulations.

Reference: J. R. Landel, A. L. Thomas, H. McEvoy and S. B. Dalziel. Convective mass transfer from a submerged drop in a thin falling film, Journal of Fluid Mechanics, 2016.

 

Title

Turbulent particle-laden jets

Group Continuum Mechanics
Supervisors
Description

Turbulent particle-laden jets are relevant to many geophysical and industrial applications: from volcanic eruptions, to sediment resuspension, fluidisation processes and chemical reactors. Much work has been done on the dilute regime of these two-phase flows, where the particles have a small impact on the fluid and can often be considered as passive tracers. In this experimental project, we focus on the poorly understood dense regime, where the coupling between the solid particles and the fluid is more complex.

Many fundamental questions, of high relevance to the applications mentioned above, are still unresolved. This project will explore the impact of the particle density on turbulent entrainment processes. Entrainment processes during an explosive volcanic eruption have a considerable impact on the extent of the damages. They determine whether the eruption will collapse and form a pyroclastic flow, with local implications, or whether the eruption column will rise and form an ash cloud spreading over extended regions, such as in the case of the 2010 eruption of the Icelandic volcano Eyjafjallajökul. This project will also explore the effect on mixing processes, which are very important for instance in chemical reactors where the efficiency of the reaction depends strongly on the efficiency of the mixing.

These dense particle-laden jets are still poorly understood due to the considerable challenges faced analytically and numerically. Technical difficulties have also prevented progress on the experimental side for a long time. New experimental techniques, based on novel experimental design and imaging techniques, recently developed in the laboratory have allowed to probe much further into the complex dynamics of these dense particle laden jet. The main goal of this project is to pursue the development of these techniques in order to address the questions on entrainment and mixing described above.

The project is suitable for an enthusiastic and creative candidate who has some experience in experimentation and good knowledge in fluid mechanics. Some knowledge in imaging analysis technique is desired but not necessary. The motivation and readiness of the candidate to learn new techniques and develop them to explore fundamental scientific questions will be key to the success of this project.

Title

Efficient solvers for multi-physics problems in drilling

Group Continuum Mechanics
Supervisor
Description

This EPSRC Industrial Case Studentship is suitable for students with a strong applied mathematics background, particular in fluid and/or solid mechanics, and good computer programming skills.

Drilling mud motors work in extreme environments with strong coupling between complex fluid (mud) and mechanical components.  Efficient numerical simulation is a key engineering design tool, but fast solvers for these multi-physics systems are lacking. The aim of this project is to develop such solvers for modern multi-core desktops and supercomputers.

The solvers will be developed within the framework of our in-house open-source finite element library (oomph-lib).

Title

Modelling the formation of uranium hydride blisters

Group Continuum Mechanics
Supervisor
Description

An industrially-sponsored applied mathematics project that aims to develop quantitative models describing the corrosion of uranium by hydrogen via the formation and growth of discrete uranium hydride blisters. This project is closely related to another industrially-sponsored project on mathematical modelling of diffusion-driven oxidation in metals. The proposed PhD will study the blister-formation problem at a fundamental level using continuum mechanical models that couple the transport and reaction of chemicals, transport and conversion of heat and deformation of the material.

Typically, the timescales of each process are well separated so that dynamic deformation effects (oscillations) on the order of seconds are faster than the transport of heat which is faster than the diffusion of chemicals.

The project will contain a strong modelling component and will pursue analytical and numerical approaches for the solution of the resulting model equations. The initial model development will be performed in a low-dimensional framework to allow rapid assessment of the influence of different assumptions. The later stages of the project will extend the framework to a realistic three-dimensional geometry. The project is suitable for any student with a strong applied mathematics background.

Title

Interactions between rocks and ice

Group Continuum Mechanics
Supervisor
Description

Many glaciers are covered by a debris layer whose presence has multiple, competing effects on the glacier's melt rate. The debris layer shields the ice from incoming solar radiation and thus reduces its melt rate. However, since the albedo of the debris layer is much smaller than that of the ice, the debris layer is heated up very rapidly by the solar radiation, an effect that is likely to increase the melt rate.

The project aims to develop theoretical/computational models to study how solid objects (rocks) which are placed on (or embedded in) an ice layer affect the ice's melt rate. The work will employ (and contribute to) the object-oriented multi-physics finite-element library oomph-lib, developed by M. Heil and A.L. Hazel and their collaborators, and available as open source software at http://www.oomph-lib.org.

The project would suit students with an interest in mathematical modelling, continuum mechanics and scientific computing and will be performed in close collaborations with Glaciologists at the University of Sheffield and the Bavarian Academy of Science.

Title

Plant tissue mechanics

Group Continuum Mechanics
Supervisor
Description

Plant growth arises through the coordinated expansion of individual cells, allowing a plant to adapt to its environment to harness light, water and essential nutrients.  Growth is driven by the high internal turgor pressure of cells and is regulated by physical and biochemical modifications of plant cell walls.  Many features of this immensely complex process remain poorly understood, despite its profound societal and environmental importance.  Mathematical models describing the mechanical properties of a growing plant tissue integrate features ranging from molecular interactions within an individual cell wall to the expansion, bending or twisting of a multicellular root or stem.  Building on current biological understanding, this project will address the development and analysis of new multiscale models for plant tissues, exploiting a variety of computational and asymptotic techniques.

Background references:

  1. Dyson, RJ & Jensen, OE (2010) J Fluid Mech 655, 472
  2. Dyson, RJ, Band, L & Jensen, OE (2012) J Theor Biol 307, 125
  3. Baskin, TI & Jensen, OE (2013) J Exp Bot 64, 4697
  4. Dyson, RJ et al. (2014) New Phytologist 202, 1212
Title

Flow and transport in the placenta

Group Continuum Mechanics
Supervisor
Description

The placenta provides an interface beween fetal and maternal blood, supplying essential nutrients to the growing fetus.  Within the placenta, fetal blood is confined to a tree-like network of blood vessels that are bathed in a pool of maternal blood.  The placenta's effectiveness as a transporter of oxygen, glucose, and other molecules is critically determined by its complex geometric structure;  this may be compromised in disease, with adverse consequences for fetal growth and development.  This project will build on recent studies of the maternal circulation [1-3], developing analogies with models flow through porous media and exploring new multiscale approximation techniques.  The project offers opportunities for analysis, computation and interaction with experimentalists.

References:

  1. Chernyavsky, IL, Jensen, OE et al. (2010) Placenta 31, 44
  2. Chernyavsky, IL, Leach, L et al.  (2011) Phil Trans Roy Soc A 369, 4162
  3. Chernyavsky, IL, Dryden, IL et al. (2012) IMA J Appl Math 77, 697
Title

Microstructural models of the constitutive behaviour of soft tissue

Group Continuum Mechanics
Supervisors
Description

Soft tissue such as tendon, ligament, skin, and the brain possess complex nonlinear viscoelastic constitutive behaviour which arises due to the intricate microstructures inherent in such materials. The majority of existing models for the constitutive behaviour of soft tissue are phenomenological so that the parameters involved in the model are not derivable from experiments.

In this project the objective is to build models that are based on the microstructure and we will liaise with experimentalists, particularly those in imaging science, in order to ensure that the parameters involved can be directly measured.

This project would suit those with a strong background in continuum mechanics and modelling and although not essential some background knowledge in nonlinear elasticity would be useful.

Title

Environmental fluid mechanics

Group Continuum Mechanics
Supervisor
Description

Many problems of environmental significance require the effective prediction of particulate (contaminant) transport in a fluid system (which constitutes a `two-phase' fluid/particle problem). The primary focus of this project is a suspension of solid particles (dust/ash) in a viscous incompressible fluid. Most practical cases of interest have particles that are typically fractions of a millimetre in size, but still occupy a non-small fraction of the total mixture mass and exist in large numbers. The simultaneous treatment of all individual particles (and the correspondingly complicated fluid domain) is computationally impractical, a state of affairs that will remain for the foreseeable future.

Furthermore, the behaviour of a single particle cannot be solved in isolation of the other particles, owing to particle-particle interactions through the motion of the interstitial fluid, or by direct particle collisions at high concentration levels.  In such cases, both phases of the mixture exchange momentum with the other, so that the fluid motion and the particle motion remain coupled together. Furthermore, the presence of bounding surfaces for the fluid mixture can have crucial consequences for the structural and temporal development of the flow and the distribution of suspended material.

This project aims to continue the development of existing macro scale models, in which both phases are treated as co-existing (coupled) continua, through a combination of analytical and computational methods.

Title

Stability and separation in R>>1 flows

Group Continuum Mechanics
Supervisor
Description

I have several projects available in the area of  high Reynolds number flows, including the study of laminar separation and stability of thin films, cavity flows, break-up of separation bubbles, cross-flow instability. The work can be theoretical, numerical or a mixture of both.

Title

Fractional differential equations and anomalous transport

Group Continuum Mechanics
Supervisor
Description

This project is concerned with anomalous transport, which cannot be described by standard calculus. Instead it requires the use of fractional differential equations involving fractional derivatives of non integer order. This is a new, exciting area of research because anomalous transport is a widespread natural phenomenon. Examples include flight of albatross, stock prices, human migration, social networks, transport on fractal geometries, proteins on cell membranes, bacterial motion, and signalling molecules in the brain.

Title

Mathematical theory of diffraction

Group Continuum Mechanics
Supervisor
Description

There is a long history of mathematicians working on canonical diffraction (or scattering) problems. The mathematical theory of diffraction probably started with the work of Sommerfeld at the end of the 19th century and his famous solution to the diffraction of acoustic waves by a solid half-plane. Since, some very ingenious mathematical methods have been developed to tackle such problems. One of the most famous being the Wiener-Hopf technique.

However, despite tremendous efforts in this field, some canonical problems remain open, in the sense that no clear analytical solution is available for them.

One of this problem is the quarter-plane problem, the problem of diffraction of acoustic waves by a solid quarter-plane. Thus far, it has not been possible to apply classical methods such as the Wiener-Hopf method successfully in that case, and hence some new mathematical methods need to be developed in order to tackle this problem. This makes it very interesting as it implies that many different types of mathematics can be used and it makes the subject intrinsically multidisciplinary.

Many industrial problems can be linked to the theory of diffraction, for example the noise generated by a jet engine (acoustic waves) or radar detection (electro-magnetic waves) and defect detection in materials (elastic waves).

PhD projects are available in this field.

References:
-- R. C. Assier and N. Peake. On the diffraction of acoustic waves by a quarter-plane. Wave Motion, 49(1):64-82, 2012
-- R. C. Assier and N. Peake. Precise description of the different far fields encountered in the problem of diffraction of acoustic waves by a quarter-plane. IMA J. Appl. Math., 77(5):605-625, 2012.

Title

Combustion instabilities

Group Continuum Mechanics
Supervisor
Description

Combustion is essential to energy generation and transport needs, and will remain so for the foreseeable future. Mitigating its impact on the climate and human health, by reducing its associated emissions, is thus a priority. One suggested strategy to reduce NOx is to operate combustors at lean conditions. Unfortunately, combustion instability is more likely to occur in the lean regime, and may have catastrophic consequences on the components of combustion chambers, such as vibrations and structural fatigue.

Ramjet engines, rocket engines and in general any type of gas turbine engines may be subject to this detrimental instability. The ability to predict and control the instability is crucial for implementing the lean burn strategy. Combustion instability involves an intricate interplay of several key physical processes, which take place in regions of different length scales. Due to this multi-scale, multi-physics nature of the problem, direct numerical simulations of realistic combustors are extremely challenging. For this reason, simplified mathematical models capturing qualitatively and quantitatively the main characteristics of combustion instability are essential. In particular, by exploiting the scale disparity, systematic asymptotic analyses may be carried out to derive relevant models on first principles, and to provide guidance for developing reliable and efficient numerical algorithms.

Recent progress have been made in the mathematical modelling of such instabilities, using refining and implementing this model would make a good PhD project.

Reference:
R. C. Assier and X. Wu. Linear and weakly nonlinear instability of a premixed curved flame under the influence of its spontaneous acoustic field. J. Fluid Mech. (2014), vol. 758, pp. 180-220

Title

Complex deformations of biological soft tissues

Group Continuum Mechanics
Supervisors
Description

The answers to many open questions in medicine depend on understanding the mechanical behaviour of biological soft tissues. For example, which tendon is most appropriate to replace the anterior cruciate ligament in reconstruction surgery? what causes the onset of aneurysms in the aorta? and how does the mechanics of the bladder wall affect afferent nerve firing? Current work at The University of Manchester seeks to  understand how the microstructure of a biological soft tissue affects its macroscale mechanical properties. Most of the work to date has focused on simple deformations (e.g. longitudinal extension under tension) for which analytical solutions can be found. However, the geometry and deformation of many soft tissues in vivo is sufficiently complex to prohibit analytical solutions.

In this project, we will use our “in house” finite element software oomph-lib  to investigate complex deformations of biological soft tissues. The work will require development and implementation of novel strain energy functions as well as formulation of non-standard problems in solid mechanics. The project is likely to appeal to students with an interest in continuum mechanics, computational mathematics and interdisciplinary science. The work will be carried out in close collaboration with the School of Materials Science, and the student will have the opportunity to perform experiments at the state-of-the-art Henry Moseley X-ray Imaging Facilities.

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