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 received my DPhil for research in numerical analysis from the University of Durham, UK, in 2005, then worked as a postdoctoral researcher at the Universities of Strathclyde, Cambridge, and Oxford where I developed my expertise in nonlinear elasticity. I have been on the faculty of the Cardiff School of Mathematics since 2011, and a Reader (Associate Professor) in Applied Mathematics from 2019.
Honours and awards

Outstanding Contribution Award, Cardiff University (2015)
Professional memberships
 Faculty Adviser of SIAMIMA Student Chapter at Cardiff University
 Secretary & Treasurer of SIAMUKIE 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 NonLinear Mechanics (Elsevier)
 Associate Editor
 Reviewer for a wide range of scientific journals
Publications
2022
 Buze, M., Woolley, T. E. and Mihai, L. A. 2022. A stochastic framework for atomistic fracture. SIAM Journal on Applied Mathematics 82(2), pp. 526548. (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/s1065902109875z)
 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
 Mihai, L. A. 2022. Stochastic elasticity: a nondeterministic approach to the nonlinear field theory. Springer.
2021
 Mihai, L. A. and Goriely, A. 2021. Instabilities in liquid crystal elastomers. MRS Bulletin 46, pp. 784794. (10.1557/s43577021001152)
 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. (10.1088/13616544/ac09c1)
 Mihai, L. A. and Alamoudi, M. 2021. Likely oscillatory motions of stochastic hyperelastic spherical shells and tubes. International Journal of NonLinear 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 pseudoanelastic 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. 18511872. (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. (10.1088/13616544/ab7104)
 Schweickert, E., Mihai, L. A., Martin, R. J. and Neff, P. 2020. A note on nonhomogeneous deformations with homogeneous Cauchy stress for a strictly rankone convex energy in isotropic hyperelasticity. International Journal of NonLinear 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/s4255801900131)
 Mihai, L. A. 2019. Power in numbers: The rebel women of mathematics by Talithia Williams [Book Review]. London Mathematical Society Newsletter 485, pp. 4950.
 Mihai, L. A., Fitt, D., Woolley, T. and Goriely, A. 2019. Likely cavitation in stochastic elasticity. Journal of Elasticity 137(1), pp. 2742. (10.1007/s1065901897061)
 Mihai, L. A., Woolley, T. and Goriely, A. 2019. Likely chirality of stochastic anisotropic hyperelastic tubes. International Journal of NonLinear Mechanics 114, pp. 920. (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. 20662082. (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 nonhomogeneous deformations. Presented at: 89th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Munich, Germany, 1923 March 2018. Proceedings in Applied Mathematics and Mechanics (PAMM) Vol. 1. Wiley pp. 12., (10.1002/pamm.201800185)
 Safar, A. and Mihai, L. A. 2018. The nonlinear elasticity of hyperelastic models for stretchdominated cellular structures. International Journal of NonLinear Mechanics 106, pp. 144154. (10.1016/j.ijnonlinmec.2018.08.006)
 Mihai, L. A., Safar, A. and Wyatt, H. L. 2018. Debonding of cellular structures with fibrereinforced cell walls under shear deformation. Journal of Engineering Mathematics 109(1), pp. 319. (10.1007/s1066501698942)
 Mihai, L. A. and Neff, P. 2018. Hyperelastic bodies under homogeneous Cauchy stress induced by threedimensional nonhomogeneous deformations. Mathematics and Mechanics of Solids 23(4), pp. 606616. (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. 6079. (10.1016/j.jmps.2017.05.015)
 Mihai, L. A., Wyatt, H. and Goriely, A. 2017. A microstructurebased hyperelastic model for opencell solids. SIAM Journal on Applied Mathematics 77(4), pp. 13971416. (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, 1113 April 2017.
 Mihai, L. A., Wyatt, H. L. and Goriely, A. 2017. Microstructurebased hyperelastic models for closedcell 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 nearlyincompressible finite elasticity. Computers & Structures 182, pp. 540555. (10.1016/j.compstruc.2016.05.004)
 Neff, P. and Mihai, L. A. 2017. Injectivity of the Cauchystress tensor along rankone connected lines under strict rankone convexity condition. Journal of Elasticity 127(2), pp. 309315. (10.1007/s106590169609y)
 Mihai, L. A. and Neff, P. 2017. Hyperelastic bodies under homogeneous Cauchy stress induced by nonhomogeneous finite deformations. International Journal of NonLinear Mechanics 89, pp. 93100. (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. 2930.
 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. 701713. (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. 184187.
 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. 15581576. (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, 2125 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 cellfilled loadbearing 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. 107128. (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 nonlinear elasticity. International Journal of NonLinear Mechanics 49, pp. 114. (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. 36333646. (10.1098/rspa.2011.0281)
2010
 Mihai, L. A. 2010. A fixedpoint approach to the limit load analysis of multibody structures with Coulomb friction. Computers & Structures 88(1314), pp. 859869. (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(14), pp. 4860. (10.1016/j.cma.2009.09.018)
 Mihai, L. A. and Ainsworth, M. 2009. An adaptive multiscale computational modelling of Clare College Bridge. Computer Methods in Applied Mechanics and Engineering 198(2126), pp. 18391847. (10.1016/j.cma.2008.12.030)
 Ainsworth, M. and Mihai, L. A. 2009. An adaptive multiscale approach to the modelling of masonry structures. International Journal for Numerical Methods in Engineering 78(10), pp. 11351163. (10.1002/nme.2520)
 Mihai, L. A. and Craig, A. W. 2009. Alternate slicebased substructuring in three dimensions. Ima Journal of Numerical Analysis 29(3), pp. 508538. (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. 798816. (10.1002/num.20253)
2006
 Ainsworth, M. and Mihai, L. A. 2006. A comparison of solvers for linear complementarity problems arising from largescale masonry structures. Applications of Mathematics 51(2), pp. 93128. (10.1007/s1049200600088)
 Mihai, L. A. and Craig, A. W. 2006. Alternate stripbased substructuring algorithms for elliptic PDEs in two dimensions. Ima Journal of Numerical Analysis 26(2), pp. 354380. (10.1093/imanum/dri025)
2005
 Mihai, L. A. and Craig, A. W. 2005. A twogrid alternate stripbased domain decomposition strategy in twodimensions. In: Kornhuber, R. et al. eds. Domain Decomposition Methods in Science and Engineering. SpringerVerlag Berlin Heidelberg, pp. 661668., (10.1007/3540268251_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
 Mathematics of liquid crystal elastomers, EPSRC DTP studentship, 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
 Limit analysis of debonding states in multibody systems of stochastic hyperelastic material, EPSRC (2019  2022)
 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 testpieces 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/s4255801900131)
 "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: 10.1088/13616544/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
 The 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
Research students
 Dr Manal Alamoudi, PhD student (2018  2022)
 Dr Danielle Fitt, PhD student (2018  2020)
 Dr Alexander Safar, PhD student (2015  2019)
 Dr Khulud Alayyash, PhD student (2013  2017)
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)