# 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.

### 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]).

### Publications

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**.

### Teaching

** 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.