# Dr Angela Mihai

Lecturer in Applied Mathematics

- Email:
- mihaila@cardiff.ac.uk
- Telephone:
- +44 (0)29 2087 5570
- Location:
- M/2.14, 2nd Floor, Mathematics Institute, Senghennydd Road, Cardiff, CF24 4AG

I am a mathematician working on developing new mathematical tools for applications in physical, engineering and life sciences. My primary area of expertise is in theoretical and computational solid mechanics, including multiscale modelling, limit states analysis, and computer simulations for applications. Current application areas inlude the fundamental mechanics of cellular bodies and soft tissue biomechanics.

I am especially interested in the mechanical responses of nonlinear elastic materials which cannot be represented by constants but are generally described by parameters which are scalar functions of the deformation. For these materials, the aim is to determine constitutive parameters that capture nonlinear elastic behaviours which play significant roles in applications.

An important application area is the mathematical modelling and mechanical analysis of load- and non-load-bearing cellular structures operating under large strain deformation. Cellular structures are the subject of significant research efforts in biomedical applications, where the development of new flexible scaffolds for tissue re-growth is a rapidly growing multidisciplinary area of biomaterials and tissue engineering. Cellular bodies are also ubiquitous in nature and can be found in most things where light-weight, shock-absorbing, multi-functional materials are required, in everyday life as well as in several industrial areas (e.g., microelectronics, aerospace, pharmaceutical and food processes). Although, in many cases, it is hard to estimate their precise cost or the exact value of those protected by them, it is not difficult to appreciate their overwhelming significance for the economy and society. For these complex materials to be understood and optimised with respect to their mechanical responses, reliable models that take into account the interplay between the geometry and the mechanical qualities of the constituents across the scales are needed and may also open the way to new applications.

For further details, see my research publications, or view my research profle at Google Scholar, ORCID, ResearcherID, or ResearchGate.

### Career overview

I am a Senior Lecturer in Applied Mathematics at the Cardiff School of Mathematics since August 2016. Prior to this, I was a Lecturer in Applied Mathematics at the same institution, from October 2011. Before joining Cardiff University, I worked as a postdoctoral researcher at the Universities of Oxford, Cambridge, and Strathclyde in Glasgow.

### Education and qualifications

I hold a DPhil in Numerical Analysis from the University of Durham, UK, a Certificate of Advanced Study in Mathematics (Part III of the Mathematical Tripos) from the University of Cambridge, UK, and a BSc in Mathematics from the University of Bucharest, Romania.

### Anrhydeddau a Dyfarniadau

- Outstanding Contribution Award, Cardiff University, Wales, UK, 2015.
- Postdoctoral Researcher Presentation Prize, UK Association for Computational Mechanics, Queen's University Belfast, Ireland, UK, 2006.
- The Euan Squires Memorial Prize, University of Durham, England, UK, 2003.
- SIAM-UKIE Student Presentation Prize, Society for Industrial and Applied Mathematics, University of Durham, England, UK, 2002.
- Shell Centenary Scholarship, Shell Group & Cambridge University Trust, England, UK, 1999-2000.

### Aelodaethau proffesiynol

- Member of the Society for Industrial and Applied Mathematics (SIAM), 2012 - Present.
- Secretary & Treasurer of the UK and Republic of Ireland Section of the Society for Industrial and Applied Mathematics (SIAM-UKIE), 2014 - 2016.

- Co-founder and Faculty Adviser of the SIAM-IMA Student Chapter at Cardiff University, 2012- Present.
- Cardiff Students Hold First SIAM Chapter Day, SIAM News, April 2013.
- First Meeting of Cardiff SIAM Student Chapter, January 2013.

- Secretary & Treasurer of the UK and Republic of Ireland Section of the Society for Industrial and Applied Mathematics (SIAM-UKIE), 2014 - 2016.
- Member of the International Society for the Interaction of Mechanics and Mathematics (ISIMM), 2017- Present.

### Ymrwymiadau siarad cyhoeddus

- Nonlinear Elasticity Minisynposium, 10th European Solid Mechanics Conference (ESMC), Bologna, Italy, July 2018.
- International Workshop on Modelling of Nonlinear Continua, Centro Internacional de Encuentros Matematicos, Castro Urdiales, Spain, June 2017.
- Elasticity Day, the 7th in a series of one-day events for the solid mechanics community, School of Engineering, Cardiff University, Wales, UK, May 2017.
- Applied Mathematics Seminar, School of Mathematics, University of Glasgow, Scotland, UK, March 2017.
- Applied Mathematics Seminar, School of Mathematics, Cardiff University, Wales, UK, February 2017.
- Applied Mathematics Seminar, Department of Mathematics, University College London, England, UK, January 2017.
- 21st Annual Meeting of SIAM-UKIE, University of Strathclyde, Scotland, UK, January 2017.
- Residential Workshop on Computational Sciences for Medical Simulation: Surgical Training and Guidance, University of Luxembourg, Luxembourg, December 2016.
- Emerging Trends in Applied Mathematics and Mechanics International Conference, University of Perpignan, France, June 2016.
- SIAM Student Chapter Annual Meeting, School of Mathematics, University of Manchester, England, UK, May 2016.
- Fluids and Materials Seminar, School of Mathematics, University of Bristol, England, UK, April 2016.
- Mathematical Mechanical Biology Minisymposium, British Applied Mathematics Colloquium (BAMC), University of Oxford, England, UK, April 2016.
- Applied Mathematics Seminar, School of Mathematics, University of Birmingham, England, UK, February 2016.
- Applied Mechanics Seminar, Faculty of Engineering and the Environment, University of Southampton, England, UK, December 2015.
- EPSRC-DST Indo-UK Workshop: Mathematics, Mechanics and Physics for Tomorrow's Materials, International Centre for Mathematical Sciences, Edinburgh, Scotland, UK, October 2015.
- International Workshop on Modelling Across the Biology-Mechanics Interface, Centro Internacional de Encuentros Matematicos, Castro Urdiales, Spain, September 2015.
- 2nd Workshop on Soft Tissue Modelling, University of Glasgow, Scotland, UK, June 2015.
- Applied Mathematics Seminar, School of Mathematics, University of Manchester, England, UK, April 2015.
- LMS Prospects in Mathematics, Mathematical Institute, University of Oxford, England, UK, December 2014.
- Numerical Analysis Seminar, Department of Mathematical Sciences, University of Bath, England, UK, December 2014.
- LMS-WIMCS Applied Analysis Day, Aberystwyth University, Wales, UK, May 2014.
- Newport & District Materials Society, The Institute of Materials, Minerals and Mining (IOM3), Cardiff University, Wales, UK, March 2014.
- Mechanics Research Seminar, School of Engineering and Computing Sciences, University of Durham, England, UK, February 2014.

### Pwyllgorau ac adolygu

- Member of the Research Committee, School of Mathematics, Cardiff University, 2013 - Present.
- Deputy Research Director, 2016 - Present.

- Member of the Engineering and Physical Sciences Research Council Peer Review College, 2017 - Present.
- Reviewer for Mathematical Reviews/MathSciNet, American Mathematical Society, 2017 - Present.

### 2020

- Schweickert, E.et al. 2020. A note on non-homogeneous deformations with homogeneous Cauchy stress for a strictly rank-one convex energy in isotropic hyperelasticity. International Journal of Non-Linear Mechanics 119, article number: 103282. (10.1016/j.ijnonlinmec.2019.103282)

### 2019

- Mihai, L. A.et al. 2019. Likely cavitation in stochastic elasticity. Journal of Elasticity 137(1), pp. 27-42. (10.1007/s10659-018-9706-1)
- Mihai, L. A., Woolley, T. and Goriely, A. 2019. Likely chirality of stochastic anisotropic hyperelastic tubes. International Journal of Non-Linear Mechanics 114, pp. 9-20. (10.1016/j.ijnonlinmec.2019.04.004)
- Mihai, L. A.et al. 2019. Likely equilibria of stochastic hyperelastic spherical shells and tubes. Mathematics and Mechanics of Solids 24(7), pp. 2066-2082. (10.1177/1081286518811881)
- Mihai, L. A., Woolley, T. and Goriely, A. 2019. Likely equilibria of the stochastic Rivlin cube. Philosophical Transactions of the Royal Society of London. Series A: Mathematical and Physical Sciences 377(2144), article number: 20180068. (10.1098/rsta.2018.0068)
- Mihai, L.et al. 2019. Likely oscillatory motions of stochastic hyperelastic solids. Transactions of Mathematics and Its Applications 3(1), article number: tnz003. (10.1093/imatrm/tnz003)
- Wyatt, H.et al. 2019. Nonlinear scaling effects in the stiffness of soft cellular structures. Royal Society Open Science 6(1), article number: 181361.
- Mihai, L. A. 2019. Power in numbers: The rebel women of mathematics by Talithia Williams [Book Review]. London Mathematical Society Newsletter
- Fitt, D.et al. 2019. Uncertainty quantification of elastic material responses: testing, stochastic calibration and Bayesian model selection. Mechanics of Soft Materials

### 2018

- Schweickert, E., Mihai, L. A. and Neff, P. 2018. Homogeneous Cauchy stress induced by non-homogeneous deformations. Presented at: 89th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Munich, Germany, 19-23 March 2018. Proceedings in Applied Mathematics and Mechanics (PAMM) Vol. 1. Wiley pp. 1-2., (10.1002/pamm.201800185)
- Safar, A. and Mihai, L. A. 2018. The nonlinear elasticity of hyperelastic models for stretch-dominated cellular structures. International Journal of Non-Linear Mechanics 106, pp. 144-154. (10.1016/j.ijnonlinmec.2018.08.006)
- Mihai, L. A., Safar, A. and Wyatt, H. L. 2018. Debonding of cellular structures with fibre-reinforced cell walls under shear deformation. Journal of Engineering Mathematics 109(1), pp. 3-19. (10.1007/s10665-016-9894-2)
- Mihai, L. A. and Neff, P. 2018. Hyperelastic bodies under homogeneous Cauchy stress induced by three-dimensional non-homogeneous deformations. Mathematics and Mechanics of Solids 23(4), pp. 606-616. (10.1177/1081286516682556)
- Mihai, L. A., Woolley, T. and Goriely, A. 2018. Stochastic isotropic hyperelastic materials: constitutive calibration and model selection. Proceedings of the Royal Society A 474(2211), article number: 201708. (10.1098/rspa.2017.0858)

### 2017

- Mihai, L. A. and Goriely, A. 2017. How to characterize a nonlinear elastic material? A review on nonlinear constitutive parameters in isotropic finite elasticity. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473(2207), article number: 607. (10.1098/rspa.2017.0607)
- Mihai, L. A.et al. 2017. A family of hyperelastic models for human brain tissue. Journal of the Mechanics and Physics of Solids 106, pp. 60-79. (10.1016/j.jmps.2017.05.015)
- Mihai, L. A., Wyatt, H. and Goriely, A. 2017. A microstructure-based hyperelastic model for open-cell solids. Siam Journal on Applied Mathematics 77(4), pp. 1397-1416. (10.1137/16M1098899)
- Safar, A., Wyatt, H. L. and Mihai, L. A. 2017. Debonding of cellular structures under shear deformation. Presented at: 25th Conference of the UK Association for Computational Mechanics, University of Birmingham, Birmingham, UK, 11-13 April 2017.
- Mihai, L. A., Wyatt, H. L. and Goriely, A. 2017. Microstructure-based hyperelastic models for closed-cell solids. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473(2200), article number: 20170036. (10.1098/rspa.2017.0036)
- Neff, P. and Mihai, L. A. 2017. Injectivity of the Cauchy-stress tensor along rank-one connected lines under strict rank-one convexity condition. Journal of Elasticity 127(2), pp. 309-315. (10.1007/s10659-016-9609-y)
- Lee, C.et al. 2017. Strain smoothing for compressible and nearly-incompressible finite elasticity. Computers & Structures 182, pp. 540-555. (10.1016/j.compstruc.2016.05.004)
- Mihai, L. A. and Neff, P. 2017. Hyperelastic bodies under homogeneous Cauchy stress induced by non-homogeneous finite deformations. International Journal of Non-Linear Mechanics 89, pp. 93-100. (10.1016/j.ijnonlinmec.2016.12.003)
- Mihai, L. A. 2017. The ascent of Mary Somerville in 19th century society by Elisabetta Strickland [Book Review]. London Mathematical Society Newsletter March(467), pp. 29-30.
- Mihai, L. A., Alayyash, K. and Wyatt, H. L. 2017. The optimal density of cellular solids in axial tension. Computer Methods in Biomechanics and Biomedical Engineering 20(7), pp. 701-713. (10.1080/10255842.2017.1292352)
- Wyatt, H. L.et al. 2017. Optical strain measurement techniques for soft cellular structures. Presented at: BSSM 12th International Conference on Advances in Experimental Mechanics, Sheffield, UK, 29 - 31 August 2017.

### 2016

- Wyatt, H. L.et al. 2016. Computer modelling of cellular structures under uniaxial loading. Presented at: 24th Conference of the UK Association on Computational Mechanics, Cardiff University, Cardiff, UK, 31 March - 1 April 2016. Cardiff: pp. 184-187.
- Mihai, L. A. and Goriely, A. 2016. Guaranteed upper and lower bounds on the uniform load of contact problems in elasticity. Siam Journal on Applied Mathematics 76(4), pp. 1558-1576. (10.1137/15M1046563)
- Wyatt, H. L., Alayyash, K. and Mihai, L. A. 2016. Optimising material density of cellular bodies in high elastic deformations. Presented at: 24th International Congress of Theoretical and Applied Mechanics, Montreal, Canada, 21-25 August 2016.

### 2015

- Mihai, L. A.et al. 2015. A comparison of hyperelastic constitutive models applicable to brain and fat tissues. Journal of the Royal Society Interface 12(10), pp. 1-12. (10.1098/rsif.2015.0486)
- Mihai, L. A., Alayyash, K. and Goriely, A. 2015. Paws, pads, and plants: The enhanced elasticity of cell-filled load-bearing structures. Proceedings of the Royal Society of London Series A 471(2178), article number: 20150107. (10.1098/rspa.2015.0107)
- Mihai, L. A. and Goriely, A. 2015. Finite deformation effects in cellular structures with hyperelastic cell walls. International Journal of Solids and Structures 53, pp. 107-128. (10.1016/j.ijsolstr.2014.10.015)

### 2014

- Mihai, L. A. and Goriely, A. 2014. Nonlinear Poisson effects in soft honeycombs. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470(2169), article number: 20140363. (10.1098/rspa.2014.0363)

### 2013

- Mihai, L. A. 2013. Cardiff students hold first SIAM Chapter Day. SIAM News 2013(1 Apr)
- Mihai, L. A. and Goriely, A. 2013. Numerical simulation of shear and the Poynting effects by the finite element method: An application of the generalised empirical inequalities in non-linear elasticity. International Journal of Non-Linear Mechanics 49, pp. 1-14. (10.1016/j.ijnonlinmec.2012.09.001)

### 2011

- Mihai, L. A. and Goriely, A. 2011. Positive or negative Poynting effect? The role of adscititious inequalities in hyperelastic materials. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 467(2136), pp. 3633-3646. (10.1098/rspa.2011.0281)

### 2010

- Mihai, L. A. 2010. A fixed-point approach to the limit load analysis of multibody structures with Coulomb friction. Computers & Structures 88(13-14), pp. 859-869. (10.1016/j.compstruc.2010.04.005)

### 2009

- Mihai, L. A. and Ainsworth, M. 2009. A finite element procedure for rigorous numerical enclosures on the limit load in the analysis of multibody structures. Computer Methods in Applied Mechanics and Engineering 199(1-4), pp. 48-60. (10.1016/j.cma.2009.09.018)
- Mihai, L. A. and Ainsworth, M. 2009. An adaptive multi-scale computational modelling of Clare College Bridge. Computer Methods in Applied Mechanics and Engineering 198(21-26), pp. 1839-1847. (10.1016/j.cma.2008.12.030)
- Ainsworth, M. and Mihai, L. A. 2009. An adaptive multi-scale approach to the modelling of masonry structures. International Journal for Numerical Methods in Engineering 78(10), pp. 1135-1163. (10.1002/nme.2520)
- Mihai, L. A. and Craig, A. W. 2009. Alternate slice-based substructuring in three dimensions. Ima Journal of Numerical Analysis 29(3), pp. 508-538. (10.1093/imanum/drn023)

### 2007

- Ainsworth, M. and Mihai, L. A. 2007. Modeling and numerical analysis of masonry structures. Numerical Methods for Partial Differential Equations 23(4), pp. 798-816. (10.1002/num.20253)

### 2006

- Ainsworth, M. and Mihai, L. A. 2006. A comparison of solvers for linear complementarity problems arising from large-scale masonry structures. Applications of Mathematics 51(2), pp. 93-128. (10.1007/s10492-006-0008-8)
- Mihai, L. A. and Craig, A. W. 2006. Alternate strip-based substructuring algorithms for elliptic PDEs in two dimensions. Ima Journal of Numerical Analysis 26(2), pp. 354-380. (10.1093/imanum/dri025)

### 2005

- Mihai, L. A. and Craig, A. W. 2005. A two-grid alternate strip-based domain decomposition strategy in two-dimensions. In: Kornhuber, R. et al. eds. Domain Decomposition Methods in Science and Engineering.. Springer-Verlag Berlin Heidelberg, pp. 661-668., (10.1007/3-540-26825-1_71)

### Academic affiliation and training

- Fellow of the UK Higher Education Academy, 2014 - Present.
- Postgraduate Certificate in University Teaching and Learning, Cardiff University, Wales, UK, 2014.

### Undergraduate teaching

- MA4012 Finite Elasticity (22 lectures + 11 example classes), 2014 - Present (Spring Semester).
- MA2701 Numerical Analysis (22 lectures + 6 example classes), 2013 - Present (Autumn Semester).
- MA1300 Mechanics I (22 lectures + 6 example classes + 5 tutorials), 2012 - 2017 (Spring Semester).

### Undergraduate projects

- Nonlinear constitutive parameters for hyperelastic materials with uncertainties - Adair Paez-Bastia (BSc), Cardiff School of Mathematics, 2017 - 2018.
- Instabilities in hyperelastic models for adipose tissue - Aaron English (MMath), Cardiff School of Mathematics, 2015 - 2016.

### Research group & interdisciplinary team

- Applied and Computational Mathematics Research Group
- Discrete Mathematics and Data Science Research Team

### Research interests

- Mathematics and mechanics of solids and structures (elasticity, contact problems, limit states analysis)
- Mathematical modelling in materials science (soft solids, foams, soft tissues)
- Numerical analysis and scientific computing (finite elements, optimisation, uncertainty quantification)

### Grants awarded

- College of Physical Sciences and Engineering, Cardiff University, UK, full research scholarship for a postgraduate student under my supervision, 2015 - 2019.
- Engineering and Physical Sciences Research Council of Great Britain (EPSRC) first grant EP/M011992/1, 2015 - 2017.
- Institute of Mathematics and its Applications (IMA) - UK small grant SGS10/13, 2013.

### Postgraduate students & research associates

**Mr Alexander Safar**, DPhil student, School of Mathematics, Cardiff University, 2015 - Present.- UKACM 2017 - Mike Crisfield Prize (University of Birmingham, UK)
- SNSCC 2017 - Best Talk Prize (NUI Galway, Ireland)
- Cardiff Spark Ideas Competition 2017 - Award (Cardiff University, UK)

**Ms Khulud Alayyash**, DPhil student, School of Mathematics, Cardiff University, 2013 - 2017.**Dr Hayley Wyatt**, Postdoctoral research associate, School of Mathematics, Cardiff University, 2015 - 2017.

### Public outreach & media coverage

- Structures within Nature and Modern Engineering Applications, Western Mail (Cardiff, Wales), June 6, 2016. In this newspaper article, Dr Hayley Wyatt, research associate on EPSRC funded project led by Dr Angela Mihai, explains the significance of fundamental research in the mathematics and mechanics of cellular structures, following her presentation at the first Soapbox Science public outreach event in Cardiff.

### Events organising

**Elasticity Day 2017**, the 7th in a series of one-day events for the solid mechanics community. Jointly with Prof Massimiliano Gei and Dr Lorenzo Morini, School of Engineering, Cardiff University, Wales, UK.