Studentship Development of new effective models for multi-scale lattice materials using mathematical homogenisation

Duration of Studentship: 3 years
Stipend: £15,363

Vacancy Information

UCL’s Department of Mechanical Engineering is offering a three year studentship focussing on the development of new effective models for multi-scale lattice materials using mathematical homogenisation.

The Studentship offers full tuition fees and a stipend of up to £15,363 per annum (for 3 years). Funding is provided through a UCL Impact Scheme and the MOD.

Studentship Description

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.

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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: 

(1) 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); 

(2) Locally non-linear stress-strain relationships; 

(3) 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) is an advantage. Only students with a UK-equivalent First Class Honours degree, or are expected to receive one, will be considered.


Funding requirements dictate ONLY UK and EU passport holders need apply. Please DO NOT enquiry about this project if you are ineligible.

Contact name: Dr. PJ Tan
Contact details:

UCL Taking Action for Equality

Closing Date: 30 May 2014
Studentship Start Date: Position is open until filled with start date by mutual agreement.

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