[Picture of me]

Dr. Vivien Challis

Phone: +61 7 3365 2302

Office: Room 703, Priestly Building, UQ St Lucia campus

I'm a post-doctoral research fellow in the School of Mathematics and Physics at The University of Queensland, Brisbane, Australia.

I received my PhD in mathematics from The University of Queensland in 2009. My PhD thesis was titled "Multi-Property Topology Optimisation with the Level-Set Method" (email me if you'd like a copy). My PhD supervisors were Dr. A. P. Roberts and Dr. A. H. Wilkins (now at CSIRO).

Before moving to Brisbane to study towards my PhD, I obtained a Bachelor of Applied Science (Hons I) in computational modelling from the University of Otago, New Zealand.

Note that I am also known as Vivien Foster - I am married to Chris Foster.

Competitive Grants

ARC Discovery Project DP170104307: Prof Timothy B Sercombe, A/Prof Anthony P Roberts, Prof Xiaozhi Hu, Dr Vivien J Challis, Prof Joseph F Grotowski, Predicting strength of porous materials: A microstructure-based approach. Awarded funding: $347,000 over 2017-2019.

ARC Discovery Project DP110101653: Prof Timothy B Sercombe, Dr Anthony P Roberts, Dr Vivien J Challis, Dr Lai Chang Zhang, A/Prof Joseph F Grotowski, Asst Prof James K Guest, Prof Dr Jurgen Eckert, Porous beta-titanium bone implants optimised for strength and bio-compatibility: design and fabrication. Awarded funding: $330,000 over 2011-2013. I am an ARC Postdoctoral Fellow on this Discovery Project.

UQ Major Equipment and Infrastructure Grant: A/Prof Anthony Roberts, A/Prof Matthew Davis, Dr Jamie Alcock, Dr Holger Baumgardt, Dr Ben Burton, Dr Vivien Challis, A/Prof Joseph Grotowski, Dr Dirk Kroese, New-generation parallel-computing cluster for the mathematical and physical sciences. Awarded funding: $122,000 for 2011, plus $35,000 from the Faculty of Science and $35,000 from the School of Mathematics and Physics.

UWA-UQ Bilateral Research Collaboration Award: Dr Vivien J Challis, Prof Timothy B Sercombe, Dr Anthony P Roberts, A/Prof Joseph F Grotowski, Dr Lai Chang Zhang, Manufacturing high strength-to-weight materials via topology optimization and solid freeform fabrication. Awarded funding: $10,790 for 2011.

Optimised Scaffold

Scaffold optimised for bulk modulus and diffusivity with an isotropy requirement, see [6], [3].

Fabricated Scaffold

Scaffold design above fabricated from bronze via selective laser melting.

2D Wheel Design

Simple compliance minimisation of a "wheel", see [5].

Optimised Diffuser

Optimised 3D diffuser, see [4].

Research Interests

My main research interest is developing and using the level set method for topology optimisation. I've applied the level set method to various new engineering optimisation problems and developed the algorithms for doing so.

In my current post-doctoral position, I'm working on the topology optimisation problems behind the design of customisable, optimised bone implant scaffolds. I've been compression testing several of our designs that have been fabricated from metal powder by an additive manufacturing technique called selective laser melting.

I'm also interested in using topology optimisation for more general microstructural design problems and for problems involving fluid flow.

As well as having this major research focus, I enjoy opportunities to apply my mathematical skills to problems from other fields. For example, I have worked with anaesthesiologists from the Royal Brisbane and Women's Hospital (see [7]) and have worked on problems from industry (see [a]).


You can also see my list of publications at my ORCiD, ResearcherID and Google Scholar profiles.

[14] A.D. Cramer, V.J. Challis, A.P. Roberts, Physically Realisable Three-Dimensional Bone Prosthesis Design with Interpolated Microstructures, Journal of Biomechanical Engineering 139(3), 031013, 2017, doi:10.1115/1.4035481.

[13] A.D. Cramer, V.J. Challis, A.P. Roberts, Microstructure interpolation for macroscopic design, Structural and Multidisciplinary Optimization 53(3), 489-500, 2016, doi:10.1007/s00158-015-1344-7.

[12] T.B. Sercombe, X. Xu, V.J. Challis, R. Green, S. Yue, Z. Zhang, P.D. Lee, Failure modes in high strength and stiffness to weight scaffolds produced by Selective Laser Melting, Materials & Design 67, 501-508, 2015, doi:10.1016/j.matdes.2014.10.063.

[11] V.J. Challis, X. Xu, L.C. Zhang, A.P. Roberts, J.F. Grotowski, T.B. Sercombe, High specific strength and stiffness structures produced using Selective Laser Melting, Materials & Design 63, 783-788, 2014, doi:10.1016/j.matdes.2014.05.064.

[10] V.J. Challis, A.P. Roberts, J.F. Grotowski, High resolution topology optimization using Graphics Processing Units (GPUs), Structural and Multidisciplinary Optimization 49(2), 315-325, 2014, doi:10.1007/s00158-013-0980-z.

[9] V.J. Challis, J.K. Guest, J.F. Grotowski, A.P. Roberts, Computationally generated cross-property bounds for stiffness and fluid permeability using topology optimization, International Journal of Solids and Structures 49, 3397-3408, 2012, doi:10.1016/j.ijsolstr.2012.07.019.

[8] A.P. Roberts, G. Grayson, V.J. Challis, L.C. Zhang, J.F. Grotowski, G.B. Schaffer, T.B. Sercombe, Elastic moduli of sintered powders with application to components fabricated using selective laser melting, Acta Materialia 59(13), 5257-5265, 2011, doi:10.1016/j.actamat.2011.05.002.

[7] K. Greenland, M. J. Edwards, N. J. Hutton, V. J. Challis , M. G. Irwin and J. Sleigh, Changes in airway configuration with different head and neck positions using magnetic resonance imaging of normal airways: a new concept with possible clinical applications, British Journal of Anaesthesia 105(5), 683-690, 2010, doi:10.1093/bja/aeq239.

[6] V. J. Challis, A. P. Roberts, J. F. Grotowski, L. C. Zhang and T. B. Sercombe, Prototypes for bone implant scaffolds designed via topology optimization and manufactured by solid freeform fabrication, Advanced Engineering Materials 12(11), 1106-1110, 2010, doi:10.1002/adem.201000154.

[5] V. J. Challis, A discrete level-set topology optimization code written in Matlab, Structural and Multidisciplinary Optimization 41(3), 453-464, 2010, doi:10.1007/s00158-009-0430-0.

[4] V. J. Challis and J .K. Guest, Level-set topology optimization of fluids in Stokes flow, International Journal for Numerical Methods in Engineering 79, 1284-1308, 2009, doi:10.1002/nme.2616.

[3] V. J. Challis, A. P. Roberts and A. H. Wilkins, Design of three dimensional isotropic microstructures for maximized stiffness and conductivity, International Journal of Solids and Structures 45, 4130-4146, 2008, doi:10.1016/j.ijsolstr.2008.02.025.

[2] V. J. Challis, A. P. Roberts and A. H. Wilkins, Fracture resistance via topology optimization, Structural and Multidisciplinary Optimization 36, 263-271, 2008, doi:10.1007/s00158-007-0160-0.

[1] M. Hegland, J. Garke and V. Challis, The combination technique and some generalisations, Linear Algebra and its Applications 420, 249-275, 2007, doi:10.1016/j.laa.2006.07.014.

Conference Articles

[d] V. J. Challis, A. P. Roberts and A. H. Wilkins, Topological design of isotropic composites, in Proceedings of the XXII International Congress of Theoretical and Applied Mechanics, 2008.

[c] V. J. Challis, A. P. Roberts and A. H. Wilkins, Optimal bone implants and cermets, in Proceedings of the 7th World Congress on Structural and Multidisciplinary Optimization, 2007.

[b] A. H. Wilkins, V. J. Challis and A. P. Roberts, Isotropic, stiff, conducting structures via topology optimization, in Proceedings of the 7th World Congress on Structural and Multidisciplinary Optimization, 2007.

[a] K. Russell, P. Cerone and V. Challis, Integral Energy: Calculation of a risk measure for the net system load profile, in Proceedings of the 2007 Mathematics and Statistics in Industry Study Group, 2007.


Semester 2, 2011: Lecturer for half of the course MECH3750 - Engineering Analysis II.

Summer semester, 2010: Coordinator and lecturer for MATH1052 - Multivariate Calculus and ODEs.

Semester 2, 2010: Lecturer of the L3 stream for MATH1052 - Multivariate Calculus and ODEs, and lecturer for half of the course MECH3750 - Engineering Analysis II.