Multi-level topology optimization of architected metamaterial structures

About the Project

Supervisory Team: Dr Haris Moazam Sheikh

About the project

Mechanical metamaterials are engineered structures with extraordinary properties driven by geometry, not composition. This PhD project will pioneer a multi-scale framework combining topology morphing and surrogate modeling to streamline design and enable defect engineering, unlocking real-world metamaterial applications in ultralight, reconfigurable, and high-performance materials.

Mechanical metamaterials are architected artificial materials, purposefully designed to possess unusual combination of mechanical properties not found in natural materials, such as ultralight weight, high energy absorption, and reconfigurability. These properties arise from their internal geometry rather than the material composition itself. Recent research has indicated that strategically introducing localized topological imperfections, or defects, in the metamaterial structures, can significantly enhance these properties. However, despite the aggressive advancement in recent years, the exploration of novel topologies is severely limited by the high computational cost of simulating complex geometries and the vast design space involved. Traditional design approaches rely heavily on human intuition and inspiration from nature or art, which, while creative, are not scalable or systematic.

This PhD project will seek to bridge this gap by developing an integrated, multi-scale framework to systematically address these challenges. This framework will introduce a topology morphing technique that can dramatically reduce the design complexity involved with topology optimization, as well as a novel multi-level surrogate modeling technique that can fuse information from cheaper small-scale structures with data from expensive large-scale structure simulations. This multi-scale framework would allow efficient defect engineering of large-scale metamaterial structures by significantly reducing the computational overhead that currently prohibits it. This research will unlock the potential of metamaterials in critical engineering applications—from aerospace to robotics—where performance, weight, and adaptability are paramount. The fusion of geometric innovation with computational efficiency will pave the way for next-generation material design.

You will be joining a collaborative group dedicated to addressing complex real-world engineering problems. The group is focused on conceptualizing cutting-edge data-driven topology and optimization methodologies. These techniques are specifically developed with the aim of solving real-world engineering challenges such as fluid structures, turbomachinery, meta-materials, etc.

The University of Southampton boasts extensive HPC and experimental facilities making this a unique opportunity to conduct high fidelity, multi-disciplinary research and collaborate with world-class researchers.

Entry requirements

We are actively searching for a highly motivated candidate with the following qualifications:

• a UK 2:1 honours degree, or its international equivalent masters/undergraduate degree in mechanical engineering, mathematics, physics, computer sciences, or a related field
• proficiency in at least one high level scientific computing language such as MATLAB, Python, etc
• capability to conduct research independently and collaboratively
• a passion for exploring new scientific ideas, solving problems with scientific rigor and producing high-impact research

Fees and funding

Full scholarships include tuition fees, a stipend at the UKRI rate plus 10% ORC enhancement tax-free per annum for up to 3.5 years (totalling £22,858 for 2025/26, rising annually) and a budget of £4200 for things like conference travel. UK, EU and Horizon Europe students are eligible for scholarships. Chinese Scholarship Council funded students are eligible for fee waivers. Funding for other international applicants is very limited and highly competitive. Overseas students who have secured or are seeking external funding are welcome to apply.

How to apply

Please apply via the online portal and select:

• Programme type: Research
• Academic year: 2026/27
• If you will be full time or part time
• Faculty: Engineering and Physical Sciences
• Search for programme PhD Engineering & the Environment (7175)
• Please add the name of the supervisor in section 2 of the application.

Applications should include:

• your CV (resumé)
• 2 academic references
• degree transcripts/ certificates to date
• English language qualification (if applicable)