# Dr Angela Mihai

Reader in Applied Mathematics

- mihaila@cardiff.ac.uk
- 5.14, Abacws, Senghennydd Road, Cathays, Cardiff, CF24 4AG

## Overview

### Groups, teams and networks

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

### Research interests

- Mathematics of solid mechanics
- Mathematical modelling of soft materials
- Numerical analysis and scientific computing

### Administrative roles

- Director of Research and Innovation, Cardiff School of Mathematics (2022 - Present)
- Deputy Director of Research and Innovation, Cardiff School of Mathematics (2016 - 2021)

## Biography

### Career overview

I am a Reader (Associate Professor) in Applied Mathematics at the School of Mathematics, Cardiff University. I received a DPhil for research in numerical analysis from the University of Durham, UK, in 2005, and worked as a postdoctoral researcher at the Universities of Strathclyde, Cambridge, and Oxford where I developed my expertise in nonlinear elasticity. I joined Cardiff as a University Lecturer in 2011.

### Honours and awards

Outstanding Contribution Award, Cardiff University (2015)

### Professional memberships

- Faculty Adviser of SIAM-IMA Student Chapter at Cardiff University
- Secretary & Treasurer of SIAM-UKIE Section (2014 - 2016)
- Member of SIAM, IBMTL and ISIMM

### Committees and reviewing

- Member
- EPSRC Peer Review College
- UKRI Future Leaders Peer Review College
- Editorial Advisory Board for International Journal of Non-Linear Mechanics (Elsevier)

- Associate Editor
- IMA Journal of Applied Mathematics (OUP)
- Transactions of Mathematics and Its Applications (OUP)
- Mathematics and Mechanics of Solids (SAGE)
- Special Issue in Honor of Prof Alain Goriely FRS (2023)

- Journal of Elasticity: The Physical and Mathematical Science of Solids (Springer)

- Reviewer for a wide range of scientific journals

## Publications

### 2022

- Mihai, L. A., Mistry, D., Raistrick, T., Gleeson, H. F. and Goriely, A. 2022. A mathematical model for the auxetic response of liquid crystal elastomers. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 380, article number: 20210326. (10.1098/rsta.2021.0326)
- Buze, M., Woolley, T. E. and Mihai, L. A. 2022. A stochastic framework for atomistic fracture. SIAM Journal on Applied Mathematics 82(2), pp. 526-548. (10.1137/21M1416436)
- Goriely, A., Moulton, D. E. and Mihai, L. A. 2022. A rod theory for liquid crystalline elastomers. Journal of Elasticity (10.1007/s10659-021-09875-z)
- Mihai, L. A. 2022. Stochastic elasticity: a nondeterministic approach to the nonlinear field theory. Interdisciplinary Applied Mathematics. Switzerland: Springer. (10.1007/978-3-031-06692-4)

### 2021

- Mihai, L. A. and Goriely, A. 2021. Instabilities in liquid crystal elastomers. MRS Bulletin 46, pp. 784-794. (10.1557/s43577-021-00115-2)
- Mihai, L. A., Wang, H., Guilleminot, J. and Goriely, A. 2021. Nematic liquid crystalline elastomers are aeolotropic materials. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 477(2253), article number: 20210259. (10.1098/rspa.2021.0259)
- Goriely, A. and Mihai, L. A. 2021. Liquid crystal elastomers wrinkling. Nonlinearity 34(8), article number: 5599. (10.1088/1361-6544/ac09c1)
- Mihai, L. A. and Alamoudi, M. 2021. Likely oscillatory motions of stochastic hyperelastic spherical shells and tubes. International Journal of Non-Linear Mechanics 130, article number: 103671. (10.1016/j.ijnonlinmec.2021.103671)

### 2020

- Mihai, L. A. and Goriely, A. 2020. A plate theory for nematic liquid crystalline solids. Journal of the Mechanics and Physics of Solids 144, article number: 104101. (10.1016/j.jmps.2020.104101)
- Mihai, L. A. and Goriely, A. 2020. A pseudo-anelastic model for stress softening in liquid crystal elastomers. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476(2243), article number: 20200558. (10.1098/rspa.2020.0558)
- Mihai, L. A. and Goriely, A. 2020. Likely striping in stochastic nematic elastomers. Mathematics and Mechanics of Solids 25(10), pp. 1851-1872. (10.1177/1081286520914958)
- Mihai, L. A., Woolley, T. and Goriely, A. 2020. Likely cavitation and radial motion of stochastic elastic spheres. Nonlinearity 33(5), article number: 1987. (10.1088/1361-6544/ab7104)
- Schweickert, E., Mihai, L. A., Martin, R. J. and Neff, P. 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

- Fitt, D., Wyatt, H., Woolley, T. and Mihai, L. A. 2019. Uncertainty quantification of elastic material responses: testing, stochastic calibration and Bayesian model selection. Mechanics of Soft Materials 1, article number: 13. (10.1007/s42558-019-0013-1)
- Mihai, L. A. 2019. Power in numbers: The rebel women of mathematics by Talithia Williams [Book Review]. London Mathematical Society Newsletter 485, pp. 49-50.
- Mihai, L. A., Fitt, D., Woolley, T. and Goriely, A. 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., Fitt, D., Woolley, T. E. and Goriely, A. 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. E. and Goriely, A. 2019. Likely equilibria of the stochastic Rivlin cube. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 377(2144), article number: 20180068. (10.1098/rsta.2018.0068)
- Mihai, L., Fitt, D., Woolley, T. and Goriely, A. 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., Safar, A., Clarke, A., Evans, S. and Mihai, L. A. 2019. Nonlinear scaling effects in the stiffness of soft cellular structures. Royal Society Open Science 6(1), article number: 181361.

### 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., Budday, S., Holzapfel, G., Kuhl, E. and Goriely, A. 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)
- Lee, C., Mihai, L. A., Hale, J. S., Kerfriden, P. and Bordas, S. P. A. 2017. Strain smoothing for compressible and nearly-incompressible finite elasticity. Computers & Structures 182, pp. 540-555. (10.1016/j.compstruc.2016.05.004)
- 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)
- 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., Clarke, A., Evans, S. L. and Mihai, L. A. 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., Alayyash, K., Evans, S. L. and Mihai, L. A. 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., Chin, L., Janmey, P. A. and Goriely, A. 2015. A comparison of hyperelastic constitutive models applicable to brain and fat tissues. Journal of the Royal Society Interface 12(110), pp. -., article number: 20150486. (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)

## Teaching

I am a fellow of the UK Higher Education Academy. My teaching at Cardiff University is in Applied Mathematics.

### Courses taught

**Numerical Analysis**- Year 2 Mathematics (2013 - Present)

**Finite Elasticity**- Year 3 Mathematics (2020 - 2022)
- Year 4 MMath (2015 - 2020)

**Classical Mechanics**- Year 1 Mathematics (2012 - 2017)

I am generally interested in applied and computational mathematics at the interface with engineering and natural sciences. My primary expertise is in the mathematics of solid mechanics, including multiscale modelling, limit states analysis, optimisation, and uncertainty quantification. Important application fields include biomechanics and materials science. For further details, please see my Google Scholar, MathSciNet, ORCID and ResearchGate profiles.

### Funded projects

- Full PhD studentship, College of Physical Sciences and Engineering, Cardiff University (2022 - 2026) - jointly with Dr Yasemin Sengul Tezel
- Uncertainty quantification and stochastic modelling of materials, Issac Newton Institute for Mathematical Sciences, Cambridge (Summer 2023) - jointly with Dr Johann Guilleminot and Prof Alain Goriely
- Retreat for women in applied mathematics, International Centre for Mathematical Sciences (ICMS), Edinburgh (9-13 January 2023) - jointly with Prof Apala Majumdar
- Limit analysis of debonding states in multi-body systems of stochastic hyperelastic material, EPSRC (2019 - 2022)
- Full PhD studentship, College of Physical Sciences and Engineering, Cardiff University (2015 - 2019)
- Limit analysis of collapse states in cellular solids, EPSRC (2015 - 2017)

### Mottoes to papers

- "The task of the theorist is to bring order into the chaos of the phenomena of nature, to invent a language by which a class of these phenomena can be described efficiently and simply." - C. Truesdell (1965) (doi: 10.1098/rspa.2017.0607)
- "This task is made more difficult than it otherwise would be by the fact that some of the test-pieces used have to be moulded individually, and it is difficult to make two rubber specimens having identical properties even if nominally identical procedures are followed in preparing them." - R. S. Rivlin & D. W. Saunders (1951) (doi: 10.1007/s42558-019-0013-1)
- "Instead of stating the positions and velocities of all the molecules, we allow the possibility that these may vary for some reason - be it because we lack precise information, be it because we wish only some average in time or in space, be it because we are content to represent the result of averaging over many repetitions [...] We can then assign a probability to each quantity and calculate the values expected according to that probability." - C. Truesdell (1984) (doi: 10.1177/1081286520914958)
- "It is a problem of mechanics, highly complicated and irrelevant to probability theory except insofar as it forces us to think a little more carefully about how probability theory must be formulated if it is to be applicable to real situations.” - E. T. Jaynes (1996) (doi: 10.1088/1361-6544/ab7104)
- "Denominetur motus talis, qualis omni momento temporis t praebet configurationem ca- pacem aequilibrii corporis iisdem viribus massalibus sollicitati, ‘motus quasi aequilibratus’. Generatim motus quasi aequilibratus non congruet legibus dynamicis et proinde motus verus corporis fieri non potest, manentibus iisdem viribus masalibus.” - C. Truesdell (1962) (doi: 10.1093/imatrm/tnz003)

### Cover image

- A molecular dynamics simulation of liquid crystal elastomers, Proceedings of the Royal Society A 477, issue 2253, September 2021.

### Recorded talks

- Mathematics and mechanics of liquid crystal elastomers, Journal of Engineering Mathematics Webinar (October 2022)
- Mathematics and mechanics of liquid crystal elastomers, Cardiff Applied and Computational Mathematics Seminar (November 2021)
- The mathematics and continuum mechanics of liquid crystal elastomers, LMS Prospects in Mathematics (September 2021)

## Supervision

### Postdoctoral researchers

**Dr Thomas Raistrick**, Postdoctoral research associate, EP/S028870/1 (2022)**Dr Maciej Buze**, Postdoctoral research associate, EP/S028870/1 (2019 - 2022)**Dr Hayley Wyatt**, Postdoctoral research associate, EP/M011992/1 (2015 - 2017)

### Past projects

**Dr Manal Alamoudi**, PhD thesis (2018 - 2022): Stochastic finite strain analysis of inhomogeneous hyperelastic solids**Dr Danielle Fitt**, PhD thesis (2018 - 2020): Stochastic modelling and analysis of homogenoues hyperelastic solids**Dr Alexander Safar**, PhD thesis (2015 - 2019): Debonding and stretching of biogenic celular structures- Mike Crisfield Prize, UK Association for Computational Mechanics (2017)

**Dr Khulud Alayyash**, PhD thesis (2013 - 2017): The nonlinear elasticity of cellular bodies under large defomations