University College London (UCL)
Development of new effective models for multi-scale lattice materials using mathematical homogenisation
University College London (UCL)
The 2011 UCL Research Strategy calls for a transformation of the understanding of the role of our comprehensive research-intensive university in the 21st century.
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Published: 1 year ago
Application deadline: Unspecified
Location: London , United Kingdom
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Development of new effective models for multi-scale lattice materials using mathematical homogenisation

PhD Studentship Department of Mechanical Engineering

University College London
SALARY: £15.363 per annum (for 3 years)
Reporting To: Co-supervisors Dr P J Tan & Dr Rebecca Shipley
Based at: Department of Mechanical Engineering, University College London, Robert’s Building, Torrington Place, London WC1E 7JE & 132 Hampstead Road, London.
Eligibility: Funding requirements dictate ONLY UK and EU passport holders need apply. Please DO NOT enquire about this project if you are ineligible.

The Faculty:

The Faculty of Engineering Sciences currently comprises eleven academic departments that undertake research and training across a broad range of disciplines. Our teaching programmes are focused on subjects that have the greatest impact on the world around us, and their content is informed by internationally leading research.

The Department:

The history of Mechanical Engineering at UCL began in 1847 with the appointment of a “Professor of Mechanical Principles of Engineering”, the first mechanical engineering chair in the country. Mechanical engineering activities at UCL flourished under Alexander Blackie William Kennedy who was appointed to the chair of Mechanical Principles of Engineering at UCL in 1874. Alexander Kennedy soon established a teaching laboratory which became the prototype for every university teaching laboratory in use today. In recent years, the Department has developed world-leading strengths in a number of new areas, including biomedical engineering, fluid mechanics, materials and manufacturing, computational modelling, combustion and energy, as well as a very strong and internationally recognised presence in multidisciplinary research. These research directions, which have already yielded excellent academic innovation and technology transfer, supplement and interact with traditional areas of expertise in Mechanical Engineering. Currently, close to 150 PhD students (along with numerous postdoctoral fellows) conduct pioneering research in the Department, many of whom are supervised collaboratively with other Departments and hospitals at UCL.

The Research:

Man-made lattices use a combination of material and space in defined configurations, and with nodal connectivities, to achieve enhanced performance. Lattice materials comprise of uniform lattice elements (slender beams or rods) generated by tessellating a unit cell through space. Nature, too, makes extensive use of lattice construction, often in a hierarchical arrangement whereby the material within each strut of the lattice comprises another lattice of a successively finer scale. Understanding the relationship(s) that link the microstructural phenomena at different length scales upon the macroscopic deformation response is essential to tailor-make lattice materials with specific macroscopic requirements. This project is concerned with deriving quantitative relations to link the different length scales by energy equivalence concepts and also homogenisation techniques. When several scales are present in space and/or time, the approach is first to construct micro-scale models, using appropriate representative volume elements (RVEs), and then to deduce macro-laws and the constitutive relations that relate effective behaviour to micro-scale geometry and physics by exploiting, for example, separation of length scales. The perturbation method of multiple scales is typically employed to derive these averaged equations. However, the application of homogenisation to problems involving fracture, nonlocal elasto-plastic response, localised instability and/or microstructural imperfections, such as missing cells or non-periodic microstructure, within an appropriate multi-scale framework remains a considerable challenge and this is to be addressed in the project. The project will be divided into three key aims. Each involves the development of new macroscale models that incorporate more realistic micro-scale geometries and physical effects:

  • Relaxation of micro-scale periodicity assumptions (including a periodic length scale that varies globally, and coupled macro-scale models that incorporate different micro-scale features in different zones of the macro-domain);
  • Locally non-linear stress-strain relationships;
  • Large-deformation mechanics on the micro-scale.

Person specification:

Applicants should have a background in Applied Mathematics or Engineering (with a high theoretical content only), and familiarity with Perturbation Methods and Continuum Mechanics. Experience with ABAQUS (finite-element software) will be an advantage. Depending on the background of the applicant, the degree awarded may either be in Applied Mathematics, Theoretical Mechanics or Applied Mechanics. Position will remain open until filled with start date by mutual agreement.

Application Procedure:

See for information. A CV, full transcript of results (listing all subjects taken and their corresponding grades/marks) and a cover letter stating how the project meets your research interests must be included.


Prospective candidates are strongly encouraged to contact Dr. PJ Tan ( for an informal discussion before applying. This project is co-supervised by an applied mathematician, Dr. R. Shipley ( Please attach your CV and transcript of exam results in your email.

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