"PhD Studentship: Multiscale modelling of polymer network constitutive behaviour"

The University of Manchester - Mathematics

Department: Mathematics

Title: Multiscale modelling of polymer network constitutive behaviour

Application deadline: All year round

Research theme: Applied Mathematics

How to apply: Click the 'Apply' button above.

This 3.5-year PhD project is fully funded and home students are eligible to apply. The successful candidate will receive an annual tax-free stipend set at the UKRI rate (£20,780 for 2025/26) and tuition fees will be paid. We expect the stipend to increase each year. The start date is October 2026.

We recommend that you apply early as the advert may be removed before the deadline.

Fibre networks are ubiquitous in both natural and engineered materials. They are manufactured for many reasons: from the nonwoven fabrics used for insulation, clothing and filtration to the rubberlike polymer-based materials used in applications ranging from plumbing to transport. They are also nature's preferred way of providing structural scaffolding within cells (the cytoskeleton), and within tissues (the extracellular matrix). The mechanical behaviour of these materials is heterogeneous, complex and diverse and it is only by means of predictive mathematical modelling that the underlying processes that govern their behaviour can be fully understood.

In this industry-funded project, we will model stochastic fibre networks, with a particular focus on rubberlike polymer networks, seeking to connect microscopic mechanical models formulated using a discrete calculus formalism with macroscopic (continuum) descriptions. The aim will be to determine how the microscopic constitutive properties of the fibres and the geometry and topology of the network influence the strain energy functions that can be used to describe their behaviour on the macroscale. We will combine techniques from discrete calculus, linear algebra and finite strain continuum mechanics to improve upon current methods, producing new constitutive equations that capture the network properties in a mathematically tractable way. The student will work closely with our industrial collaborators and will have the opportunity to spend time on site with them.

Applicants should have, or expect to achieve, at least a 2.1 honours degree or a master’s (or international equivalent) in a relevant science or engineering related discipline.

To apply, please contact the main supervisor; Dr Shearer - tom.shearer@manchester.ac.uk. Please include details of your current level of study, academic background and any relevant experience and include a paragraph about your motivation to study this PhD project.