# List

# In Press

Bergh J, Snedden GC, and Dunn DI, **Optimization of non-axisymmetric endwall contours for the rotor of a low speed, 1 1/2 stage research turbine with unshrouded blades - Optimization and Experimental Validation.** *ASME Journal of Turbomachinery *doi: https://doi.org/10.1115/1.4045988

Ebobisse F, Neff P and Reddy BD, **Existence results in dislocation based rate-independent isotropic gradient plasticity with kinematical hardening and plastic spin: the case with symmetric local backstress.** *Quarterly Journal of Mechanics and Applied Mathematics*

Reddy BD and van Huyssteen, **Alternative approaches to the stabilization of virtual element formulations for hyperelasticity. ***Current trends and Open Problems in Computational Mechanics (eds Springer, Berlin) (2021)*

# 2021

## Articles

Reddy BD, Steinmann P and Kergassner A, **A thermodynamically consistent theory of stress-gradient plasticity. ***Journal of the Mechanics and Physics of Solids ***147 **(2021) 1094266

Reddy BD, **Science literacy, public engagement, and responsibility in science. ***Cultures in Science (2021) *__https://doi.org/10.1177/20966083211009646__

Sysala S, Haslinger J, Reddy BD and Repin S, **An abstract inf-sup problem inspired by limit analysis in perfect plasticity and related applications.** *Mathematical Models and Methods in Applied Sciences *Vol.31, No.8 (2021) 1593-1623.

Alheit B, Bargmann S and Reddy BD, **Dynamic mechanical behaviour of suture interfaces as inspiration for architectured hierarchical interlocking composites.*** Journal of the Mechanics and Physics of Solids ***157 **(2021) 104620.

van Huyssteen D and Reddy BD, **A virtual element method for transversely isotropic hyperelasticity ***Computer Methods in Applied Mechanics and Engineering ***386** (2021) 114108.

# 2020

## Articles

Reddy BD, **Analysis and computation in solid mechanics.** *Notices of the South African Mathematical Society ***51 **(1) (2020) 9-30

Bergh J, Snedden G and Reddy BD, **Development of an automated non-axisymmetric endwall contour design system for the rotor of a 1-stage research turbine – Part 2 computed and experimental results.** *Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy* **234 **(2020) 1084-1100

Grieshaber BJ, Reddy BD and Rasolofoson F, **Discontinuous Galerkin approximations for near-incompressible and near-inextensible transversely isotropic bodies.** *Computers and Mathematics with Applications ***79 **(2020) 1914–1935.

Griffiths E, Wilmers J, Bargmann S and Reddy BD, **Nanoporous metal based composites: giving polymers strength and making metals move.** *Journal of the Mechanics and Physics of Solids ***137 **(2020) 103848.

Djoko JK, Gidey HH and Reddy BD, **Multilevel finite volume methods for 2D incompressible Navier-Stokes equations.** *International Journal of Numerical Analysis and Modeling ***17 (4) **485 - 516.

van Huyssteen D and Reddy BD, **A virtual element method for isotropic hyperelasticity.** *Computer Methods in Applied Mechanics and Engineering* **367** (2020) 113134.

Grieshaber B, McBride A and Reddy BD, **Convergence in the incompressible limit of new discontinuous Galerkin methods with general quadrilateral and hexahedral elements**. *Computer Methods in Applied Mechanics and Engineering ***370 **(2020) 113233

Reddy BD and Sysala S, **Bounds on the elastic threshold for problems of dissipative strain-gradient plasticity.** *Journal of the Mechanics of Physics of Solids* **143** (2020) 104089

Bergh J, Snedden G and Reddy BD, **Development of an automated non-axisymmetric endwall contour design system for the rotor of a 1-stage research turbine ‐ Part 1 System design.** *Proceedings* *of* *the **Institution of Mechanical Engineering, Part A: Journal of Power and Energy ***234 **(2020) 565 - 581

Griffiths E, Soyarslan C, Bargmann S and Reddy BD, **Insights into fracture mechanisms in nanoporous gold and polymer impregnated nanoporous gold.** *Extreme Mechanics Letters ***39 **(2020) 100815

Alheit B, Bargmann S and Reddy BD, **Computationally modelling the mechanical behaviour of turtle shell sutures - a natural interlocking structure**. *Journal of the Mechanical Behaviour of Biomedical Materials ***110** (2020) 103973

# 2019

## Articles

Mhlongo NP and Reddy BD, **Numerical investigations of strain-gradient plasticity with reference to non-homogeneous deformations.** *European Journal of Mechanics - A/Solids ***76 **(2019) 300 - 307* *

Ebobisse F, Hackl K, and Neff P, **A canonical rate-independent model of geometrically linear isotropic gradient plasticity with isotropic hardening and plastic spin accounting for Burgers vector. ***Continuum Mechanics and Thermodynamics ***31 **(2019) 1477-1502. https://doi.org/10.1007/s00161-019-00755-5

Rasolofoson F, Grieshaber B and Reddy BD, **Finite element approximations for near-incompressible and near-inextensible transversely isotropic bodies.** *International Journal for Numerical Methods in Engineering ***117 **(2019) 693 - 712

Reddy BD, **Modelling, analysis and computation in plasticity.** *Acta Mathematica Sinica ***35 **(2019) 64 - 82

Shirzadi M, Appa H and Reddy BD, **Development of a patient-specific finite element model of the transcatheter aortic valve implantation (TAVI) procedure.** (2019) Available at: http://arxiv.org/abs/1910.00297

Gidey HH and Reddy BD, **Operator-splitting methods for the 2D convective Cahn-Hilliard equation.** *Computers and Mathematics with Applications* **77** (2019) 3128 - 3153

Reddy BD and van Huyssteen D, **A virtual element method for transversely isotropic elasticity. ***Computational Mechanics ***64** (2019) 971 - 988

Wakeni MF and Reddy BD, **Space-time Galerkin methods for simulation of laser heating using the generalized nonlinear model. ***Computer Methods in Applied Mechanics and Engineering ***357 **(2019) 112586

Vundla, N. and Reddy BD, **A computational study of viscoelastic blood flow in an arteriovenous fistula **(2019)** **Available at: http://arxiv.org/abs/2003.08176.

Ebobisse F and Neff P, **Invariance conditions at work: A fourth order gradient plasticity model based on Kroner's incompatibility tensor ***Proceedings of the GAMM Seminar on Microstructures *(2019)

# 2018

## Articles

Ebobisse F, Neff P, Aifantis EC,** Existence result for a dislocation based model of single crystal gradient plasticity with isotropic or linear kinematic hardening, ***The Quarterly Journal of Mechanics and Applied Mathematics*, **71(1) **(2018) 99-124.

McBride AT, Reddy BD and Steinmann P, **Dissipation-consistent modelling and classification of extended plasticity formulations.** *Journal of the Mechanics and Physics of Solids* **119** (2018) 118-139.

Pond D, McBride AT, Davids JM, Reddy BD and Limbert G, **Constitutive modeling of the skin accounting for ageing.** *Journal of Theoretical Biology ***444** (2018) 108—123.

Musehane NM, Oxtoby OF and Reddy BD, **Multi-scale simulation of droplet-droplet interaction and coalescence**. *Journal of Computational Physics* **373 **(2018) 924 – 939.

de Villiers AM, McBride AT, Reddy, BD, Franz T and Spottiswoode BS, **A validated patient-specific FSI model for vascular access in haemodialysis ***Biomechanics and Modeling in Mechanobiology ***17 **(2018) 479 - 497

Ebobisse F, Neff P, Forest S, **Well-posedness for the microcurl model in both single and polycrystal gradient plasticity.** *International Journal of Plasticity ***107 **(2018) 1 - 26.

Malahe M, **An efficient spectral crystal plasticity solver for GPU architectures. ***Computational Mechanics ***62 (6) **1311 - 1326.

# 2017

## Articles

Carstensen C, Ebobisse F, McBride AT, Reddy BD and Steinmann P, **Some properties of the dissipative model of strain-gradient plasticity**. *Philosophical Magazine* **97 **(2017) 693-717. http://dx.doi.org/10.1080/14786435.2016.1274836

Wriggers P, Reddy BD, Rust W and Hudobivnik B, **Efficient virtual element formulations for compressible and incompressible finite deformations**. *Computational Mechanics ***60 **(2017) 253-268. http://dx.doi.org/10.1007/s00466-017-1405-4

Griffiths E, Bargmann S and Reddy BD, **Elastic behaviour at the nanoscale of innovative composites of nanoporous gold and polymer** *Extreme Mechanics Letters ***17 **(2017) 16 - 23

Guess WP, Reddy BD, McBride A, Spottiswoode B, Downs J and Franz T, **Fluid-structure interaction modelling and stabilisation of a patient-‐specific arteriovenous access fistula.** __https://arxiv.org/abs/1704.07753__

Ebobisse F, Neff P and Aifantis EC, **Existence result for a dislocation based model of single crystel gradient plasticity with isotropic or linear kinematic hardening ***Quarterly Journal of Mechanics and Applied Mechanics *Vol.71 No.1 (2017) 99-124

## In book

Carstensen C, Ebobisse F, McBride AT, Reddy BD and Steinmann P, **Flow relations and yield functions for dissipative strain-gradient plasticity**. In *Mathematical Modelling in Solid Mechanics *(dell'Isol F, Sofonea M and Steigmann D (eds.)), Springer, Berlin (2017) 31-42. DOI: 10.1007/978-981-10-3764-1_3

Reddy BD, **Mathematical foundations of elastoplastic deformations in solids**. In *Encyclopedia of Computational Mechanics*, *Second Edition* (Stein E, de Borst R and Hughes TJR, eds), John Wiley **1** (2017) 1-27. Online ISBN: 9781119176817. DOI: 10.1002/9781119176817

# 2016

## Articles

Bayerschen E, McBride A, Reddy BD and Böhlke T, **Review on slip transmission criteria in experiments and crystal plasticity models**. *Journal of Materials Science ***55, **2243 - 2258, 2016 [DOI: http://10.1007/s10853-015-9553-4]

Bogaers AEJ, Kok S, Reddy BD and Franz T, **An evaluation of quasi-Newton methods for application to FSI problems involving free surface flow and solid body contact**. *Computers and Structures*** 173** (2016) 71 – 83.

Carstensen C, Reddy BD and Schedensack M, **A natural nonconforming method for the Bingham flow problem is quasi-optimal**. Numerische Mathematik 133 (2016) 37 – 66. http://dx.doi.org/10.1007/s00211-015-0738-1

De Lorenzis L, McBride A and Reddy BD, **Phase-field modeling of fracture in single crystal plasticity**. *GAMM Mitteilungen* **39 **(2016) 7 – 34.

Gottschalk D, McBride A, Reddy BD, Javili A, Wriggers P, Hirschberger CB, **Computational and theoretical aspects of a grain-boundary model that accounts for grain misorientation and grain-boundary orientation**. *Computational Materials Science*, Vol. 111, pp. 443-459, 2016. [DOI: 10.1016/j.commatsci.2015.09.048]

Gurtin ME and Reddy BD, **Some issues associated with the intermediate space in single--crystal plasticity**. *Journal of the Mechanics and Physics of Solids ***95 **(2016) 230 – 238*.*

McBride AT, Gottschalk D, Reddy BD, Wriggers P and Javili A, **Computational and theoretical aspects of a grain-boundary model at finite deformations**. *Technische Mechanik ***36** (2016) 102–119.

Reddy BD, **Mathematical foundations of elastoplastic deformations in solids**. In *Encyclopedia of Computational Mechanics* (Stein E, de Borst R and Hughes TJR, eds), John Wiley (2016) (in press).

Reddy BD, **Functional Analysis, Boundary Value Problems, and Finite Elements**. In *Advanced Finite Element Technologies* (Wriggers P and Schröder J, eds) CISM Course and Lecture Notes, Springer, Wien (2016) 1–15.

Reddy BD, **Three-Field Mixed Finite Element Methods in Elasticity**. In *Advanced Finite Element Technologies* (Wriggers P and Schröder J, eds) CISM Course and Lecture Notes, Springer, Wien (2016) 53 –68.

Reddy BD, **Theoretical and Numerical Elastoplasticity**. In *Advanced Finite Element Technologies* (Wriggers P and Schröder J, eds) CISM Course and Lecture Notes, Springer, Wien (2016) 177–194.

Ssozi EN, Reddy BD and van Zyl JE,** Effect of viscoelastic deformation on the pressure-leakage behavior of plastic pipes**. *Journal of Hydraulic Engineering ***142 (3), **2016

Wakeni MF, Reddy BD and McBride AT, **An unconditionally stable algorithm for generalized thermoelasticity based on operator-splitting and time-discontinuous Galerkin finite element methods**. *Computer Methods in Applied Mechanics and Engineering* 306 (2016) 427–451.

Wakeni MF, Reddy BD, McBride AT, **A thermodynamically consistent formulation of generalized thermoelasticity at finite deformations. ***International Journal of Engineering Science, *108, 1 - 8, 2016

Wriggers P, Rust W and Reddy BD, **A virtual element method for contact.** In *Computational Mechanics *58, 1039 - 1050, 2016

## In book

Reddy BD, **Three-Field Mixed Finite Element Methods in Elasticity**. In *Advanced Finite Element Technologies *(Wriggers P and Schröder J, eds) CISM Course and Lecture Notes, Springer, Wien, 1 - 15, 2016

Reddy BD, **Theoretical and Numerical Elastoplasticity**. In *Advanced Finite Element Technologies *(Wriggers P and Schröder J, eds) CISM Course and Lecture Notes, Springer, Wien, 77 - 194, 2016

Reddy BD, **Three-Field Mixed Finite Element Methods in Elasticity**. In *Advanced Finite Element Technologies *(Wriggers P and Schröder J, eds) CISM Course and Lecture Notes, Springer, Wien, 1 - 15, 2016

# 2015

## Articles

Carstensen C, Reddy BD and Schedensack M, **A natural nonconforming method for the Bingham flow problem is quasi-optimal**. *Numerische Mathematik* [DOI: 10.1007/s00211-015-0738-1]

T. Chinyoka and O.D. Makinde, **Unsteady and porous media flow of reactive non-Newtonian fluids subjected to buoyancy and suction/injection**. *International Journal of Numerical Methods for Heat and Fluid Flow*** 25**, 1682 -1704, 2015a

T. Chinyoka and O.D. Makinde, **Buoyancy effects on unsteady MHD flow of a reactive third-grade fluid with asymmetric convective cooling**. *Journal of Applied Fluid Mechanics ***8**, 931 - 941, 2015b

L. Anand, M. Gurtin and B. Reddy, **The stored energy of cold work, thermal annealing, and other thermodynamic issues in single crystal plasticity at small length scales**. *International Journal of Plasticity* , Vol. 64, pp. 1 - 25, 2015. [DOI: 10.1016/j.ijplas.2014.07.009 ]

A.E.J. Bogaers, S. Kok, B.D. Reddy and T. Franz, **Extending the robustness and efficiency of artificial compressibility for partitioned fluid-structure interactions**. *Computer Methods in Applied Mechanics and Engineering* , Vol. 283, pp. 1278-1295, 2015. [DOI: 10.1016/j.cma.2014.08.021 ]

Grieshaber BJ, McBride AT and Reddy BD, **Uniformly convergent interior penalty methods using multilinear approximations, for problems in elasticity**. *SIAM Journal on Numerical Analysis* 53 (2015) 2255–2278. [DOI: 10.1137/140966253]

A. Javili, G. Chatzigeorgiou, A.T. McBride, P. Steinmann and C. Linder, **Computational homogenization of nano-materials accounting for size effects via surface elasticity**. *GAMM-Mitteilungen* , Vol. 38, pp. 285-312, 2015. [DOI: 10.1002/gamm.201510016 ]

A. McBride, S. Bargmann and B. Reddy, **A computational investigation of a model of single-crystal gradient thermoplasticity that accounts for the stored energy of cold work and thermal annealing**. *Computational Mechanics* , 2015. [DOI: 10.1007/s00466-015-1134-5 ]

R. Pauck and B. Reddy, **Computational analysis of the radial mechanical performance of PLLA coronary artery stents **. *Medical Engineering & Physics * , Vol. 37, pp. 7-12, 2015. [DOI: 10.1016/j.medengphy.2014.09.014 ]

M.S. Sirry, N.H. Davies, K. Kadner, L. Dubuis, M.G. Saleh, E.M. Meintjes, B.S. Spottiswoode, P. Zilla and T. Franz, **Micro-structurally detailed model of a therapeutic hydrogel injectate in a rat biventricular cardiac geometry for computational simulations**. *Computer Methods in Biomechanics and Biomedical Engineering* , Vol. 18, pp. 325-331, 2015. [DOI: 10.1080/10255842.2013.793765 ]

S. Skatulla, C. Sansour and M. Hjiaj, **On computational shells with scale effects**. *Computer Methods in Applied Mechanics and Engineering* , Vol. 283, pp. 46-73, 2015. [DOI: 10.1016/j.cma.2014.08.001 ]

## In book

Reddy BD, **Functional Analysis, Boundary Value Problems, and Finite Elements**. In *Advanced Finite Element Technologies* (Wriggers P and Schröder J, eds) CISM Course and Lecture Notes, Springer, Wien, 53 - 68, 2015

# 2014

## Articles

H. Appa, D.A. Deglon and C.J. Meyer, **Numerical modelling of mass transfer in an autoclave**. *Hydrometallurgy* , Vol. 147, pp. 234-240, 2014. [DOI: 10.1016/j.hydromet.2014.04.014 ]

S. Bargmann, B. Reddy and B. Klusemann, **A computational study of a model of single-crystal strain-gradient viscoplasticity with an interactive hardening relation**. *International Journal of Solids and Structures * , Vol. 51, pp. 2754 - 2764, 2014. [DOI: 10.1016/j.ijsolstr.2014.03.010 ]

A. Bogaers, S. Kok, B. Reddy and T. Franz, **Quasi-Newton methods for implicit black-box FSI coupling**. *Computer Methods in Applied Mechanics and Engineering * , Vol. 279, pp. 113 - 132, 2014. [DOI: 10.1016/j.cma.2014.06.033 ]

A. Chama and B. Reddy, **Stability and convergence of two three-field finite element formulations for elasticity**. *Computational Methods in Applied Mathematics* , Vol. 14, pp. 305-316, 2014. [DOI: 10.1515/cmam-2014-0014 ]

T. Chinyoka, S. Dhliwayo, L. Marabini, K. Dutlow, G. Matope and D.M. Pfukenyi, **Serological survey of Brucella canis in dogs in urban Harare and selected rural communities in Zimbabwe**. *Journal of the South African Veterinary Association-Tydskrif Van Die Suid-Afrikaanse Veterinere Vereniging* , Vol. 85, 2014. [DOI: 10.4102/jsava.v85i1.1087 ]

T. Chinyoka and O.D. Makinde, **Analysis of non-Newtonian flow with reacting species in a channel filled with a saturated porous medium**. *Journal of Petroleum Science and Engineering* , Vol. 121, pp. 1-8, 2014. [DOI: 10.1016/j.petrol.2014.07.004 ]

T. Chinyoka and O.D. Makinde, **Computational dynamics of arterial blood flow in the presence of magnetic field and thermal radiation therapy**. *Advances in Mathematical Physics* , 2014. [DOI: 10.1155/2014/915640 ]

T.J. Cloete, G. Paul and E.B. Ismail, **Hopkinson bar techniques for the intermediate strain rate testing of bovine cortical bone**. *Philosophical Transactions of the Royal Society, A* , Vol. 372, 2014. [DOI: 10.1098/rsta.2013.0210 ]

I. Donev and B. Reddy, **Time-dependent finite element simulations of a shear-thinning viscoelastic fluid with application to blood flow**. *International Journal for Numerical Methods in Fluids* , Vol. 75, pp. 668-686, 2014. [DOI: 10.1002/fld.3914 ]

T. Franz, **Computational mechanics and electro-mechanics in cardiovascular physiology and disease**. *International Journal for Numerical Methods in Biomedical Engineering* , pp. 0, 2014. [DOI: 10.1002/cnm.2617 ]

T. Franz, **Does cell mechanics in adipogenesis offer new keys for the prevention and management of obesity?**. *Biophysical Journal* , Vol. 106, pp. 1231-1232, 2014. [DOI: 10.1016/j.bpj.2014.01.004 ]

M. Gurtin and B. Reddy, **Gradient single-crystal plasticity within a Mises-Hill framework based on a new formulation of self- and latent-hardening**. *Journal of the Mechanics and Physics of Solids* , Vol. 68, pp. 134 - 160, 2014. [DOI: 10.1016/j.jmps.2014.01.002 ]

A. Javili, A. McBride, P. Steinmann and B. Reddy, **A unified computational framework for bulk and surface elasticity theory: a curvilinear-coordinate-based finite element methodology**. *Computational Mechanics* , Vol. 54, pp. 745-762, 2014. [DOI: 10.1007/s00466-014-1030-4 ]

J. Kortsmit, N. Davies, R. Miller, P. Zilla and T. Franz, **Computational predictions of improved of wall mechanics and function of the infarcted left ventricle at early and late remodelling stages: comparison of layered and bulk hydrogel injectates**. *Advances in Biomechanics and Applications* , Vol. 1, 2014. [DOI: 10.12989/aba.2013.1.1.041 ]

D. Legner, S. Skatulla, J. MBewu, R. Rama, B. Reddy, C. Sansour, N. Davies and T. Franz, **Studying the influence of hydrogel injections into the infarcted left ventricle using the element-free Galerkin method**. *International Journal for Numerical Methods in Biomedical Engineering* , Vol. 30, pp. 416-429, 2014. [DOI: 10.1002/cnm.2610 ]

M.M. MacDevette, T.G. Myers and B. Wetton, **Boundary layer analysis and heat transfer of a nanofluid**. *Microfluidics and Nanofluidics * , Vol. 17, pp. 401-412, 2014. [DOI: 10.1007/s10404-013-1319-1 ]

T.G. Myers, M.M. MacDevette, F. Font and V. Cregan, **Continuum mathematics at the nanoscale**. *Journal of Mathematics in Industry* , Vol. 4, pp. 11, 2014

J.-P. Pelteret and B. Reddy, **Development of a computational biomechanical model of the human upper-airway soft-tissues toward simulating obstructive sleep apnea**. *Clinical Anatomy* , Vol. 27, pp. 182-200, 2014. [DOI: 10.1002/ca.22313 ]

T. Povall, A. McBride and B. Reddy, **Finite element simulation of large-strain single-crystal viscoplasticity: An investigation of various hardening relations **. *Computational Materials Science * , Vol. 81, pp. 386-396, 2014. [DOI: 10.1016/j.commatsci.2013.08.043 ]

J. van Zyl and A. Cassa, **Modeling elastically deforming leaks in water distribution pipes**. *Journal of Hydraulic Engineering* , Vol. 140, pp. 182-189, 2014. [DOI: 10.1061/(ASCE)HY.1943-7900.0000813 ]

## Books

T. Franz, **Cardiovascular and Cardiac Therapeutic Devices**. , 2014. [DOI: 10.1007/978-3-642-53836-0 ]

## In book

T. Franz, M.H. de Vaal, J. Neville, J. Scherman, M. Litow and P. Zilla, **In Vivo Mechanical Loading Conditions of Pectorally Implanted Cardiac Pacemakers**. Edited by T. Franz , Springer , pp. 27-38, 2014. [DOI: 10.1007/8415_2013_160 ]

H. Krynauw, L. Bruchmller, D. Bezuidenhout, P. Zilla and T. Franz, **Constitutive Effects of Hydrolytic Degradation in Electro-Spun Polyester-Urethane Scaffolds for Soft Tissue Regeneration**. Edited by P.R. Fernandes and J.R. Bartolo , Springer , pp. 49-67, 2014. [DOI: 10.1007/978-94-007-7073-7_3 ]

M.S. Yeoman, B.D. Reddy, D. Bezuidenhout, H.C. Bowles, P. Zilla and T. Franz, **Development of a Fabric-Reinforced Porous Graft for Vascular Tissue Engineering using Finite Element Methods and Genetic Algorithms**. Edited by T. Franz , Springer , pp. 29-62, 2014. [DOI: 10.1007/8415_2013_162 ]

## In proceedings

B. Reddy, **Numerical approximation of variational inequalities arising in elastoplasticity**. *Proceedings of the International Congress of Mathematicians*, 2014

# 2013

## Articles

H. Appa, D.A. Deglon and C.J. Meyer, **Numerical modelling of hydrodynamics and gas dispersion in an autoclave**. *Hydrometallurgy*, Vol. 131, pp 67-75, 2013. [DOI: 10.1016/j.hydromet.2012.10.006]

M. Bracher, D. Bezuidenhout, M.P. Lutolf, T. Franz, M. Sun, P. Zilla and N.H. Davies, **Cell specific ingrowth hydrogels **. *Biomaterials *, Vol. 34, pp 6797-6803, 2013. [DOI: 10.1016/j.biomaterials.2013.05.057]

A.M. Cassa and J.E. van Zyl, **Predicting the pressure-leakage slope of cracks in pipes subject to elastic deformations**. *Journal of Water Supply: Research and Technology - AQUA*, Vol. 62, pp 214-223, 2013. [DOI: 10.2166/aqua.2013.094]

A. Chama and B.D. Reddy, **New stable mixed finite element approximations for problems in linear elasticity**. *Computer Methods in Applied Mechanics and Engineering*, Vol. 256, pp 211-223, 2013. [DOI: 10.1016/j.cma.2012.12.006]

T. Chinyoka, S.P. Goqo and B.I. Olajuwon, **Computational analysis of gravity driven flow of a variable viscosity viscoelastic fluid down an inclined plane **. *Computers & Fluids*, Vol. 84, pp 315-326, 2013. [DOI: 10.1016/j.compfluid.2013.06.022]

T. Chinyoka and O.D Makinde, **Computational analysis of CO2 emission, O2 depletion and thermal decomposition in a cylindrical pipe filled with reactive materials **. *Communications in Nonlinear Science and Numerical Simulation*, Vol. 18, pp 2448-2461, 2013. [DOI:10.1016/j.cnsns.2013.01.018]

T. Chinyoka and O.D. Makinde, **Viscoelastic modeling of the diffusion of polymeric pollutants injected into a pipe flow**. *Acta Mechanica Sinica*, Vol. 29, pp 166-178, 2013. [DOI: 10.1007/s10409-013-0016-3]

T. Chinyoka and O.D. Makinde, **Numerical investigation of entropy generation in unsteady MHD generalized couette flow with variable electrical conductivity**. *The Scientific World Journal*, 2013. [DOI: 10.1155/2013/364695]

T. Chinyoka and O.D. Makinde, **Analysis of entropy generation rate in an unsteady porous channel flow with navier slip and cooling, convective cooling**. *Entropy*, Vol. 15, pp 2081-2099, 2013. [DOI: 10.3390/e15062081]

I. Govender, P.W. Cleary and A.N. Mainza, **Comparisons of PEPT derived charge features in wet milling environments with a friction-adjusted DEM model**. *Chemical Engineering Science*, Vol. 97, pp 162-175, 2013. [DOI: 10.1016/j.ces.2013.04.023]

I.E. Ireka and T. Chinyoka, **Non-isothermal flow of a Johnson-Segalman liquid in a lubricated pipe with wall slip**. *Journal of Non-Newtonian Fluid Mechanics*, Vol. 192, pp 20-28, 2013. [DOI: 10.1016/j.jnnfm.2012.11.001]

A. Javili, A. McBride, J. Mergheim, P. Steinmann and U. Schmidt, **Micro-to-macro transitions for continua with surface structure at the microscale **. *International Journal of Solids and Structures *, Vol. 50, pp 2561-2572, 2013. [DOI: 10.1016/j.ijsolstr.2013.03.022]

A. Javili, A. McBride and P. Steinmann, **Numerical modelling of thermomechanical solids with highly conductive energetic interfaces**.*International Journal for Numerical Methods in Engineering*, Vol. 93, pp 551-574, 2013. [DOI: 10.1002/nme.4402]

Y. Kajee, J-P.V. Pelteret and B.D. Reddy, **The biomechanics of the human tongue**. *International Journal for Numerical Methods in Biomedical Engineering*, Vol. 29, pp 492-514, 2013. [DOI: 10.1002/cnm.2531]

J. Kortsmit, N.H. Davies, R. Miller, J.R. Macadangdang, P. Zilla and T. Franz, **The effect of hydrogel injection on cardiac function and myocardial mechanics in a computational post-infarction model**. *Computer Methods in Biomechanics and Biomedical Engineering*, Vol. 16, pp 1185-1195, 2013. [DOI: 10.1080/10255842.2012.656611]

Bishnu P. Lamichhane, A.T. McBride and B.D. Reddy, **A finite element method for a three-field formulation of linear elasticity based on biorthogonal systems **. *Computer Methods in Applied Mechanics and Engineering *, Vol. 258, pp 109-117, 2013. [DOI:10.1016/j.cma.2013.02.008]

O.D. Makinde and T. Chinyoka, **Numerical investigation of buoyancy effects on hydromagnetic unsteady flow through a porous channel with suction/injection**. *Journal of Mechanical Science and Technology*, Vol. 27, pp 1557-1568, 2013. [DOI: 10.1007/s12206-013-0221-9]

O.D. Makinde, T. Chinyoka and A.S. Eegunjobi, **Numerical investigation of entropy generation in an unsteady flow through a porous pipe with suction**. *International Journal of Exergy*, Vol. 12, pp 279-297, 2013. [DOI: 10.1504/IJEX.2013.054114]

O.D. Makinde, W.D. Khan and T. Chinyoka, **New developments in fluid mechanics and its engineering applications**. *Mathematical Problems in Engineering*, Vol. 2013, 2013. [DOI: 10.1155/2013/797390]

R. Miller, N.H. Davies, J. Kortsmit, P. Zilla and T. Franz, **Outcomes of myocardial infarction hydrogel injection therapy in the human left ventricle dependent on injectate distribution**. *International Journal for Numerical Methods in Biomedical Engineering*, Vol. 29, pp 870-884, 2013. [DOI: 10.1002/cnm.2551]

J-P.V. Pelteret and B.D. Reddy, **Development of a computational biomechanical model of the human upper-airway soft-tissues toward simulating obstructive sleep apnea**. *Clinical Anatomy*, Vol. 27, pp 182-200, 2013. [DOI: 10.1002/ca.22313]

B.D. Reddy, **Variational formulations for single-crystal strain-gradient plasticity at large deformations**. *GAMM Mitteilungen*, Vol. 36, pp 149-160, 2013. [DOI: 10.1002/gamm.201310009]

B.D. Reddy, **Some theoretical and computational aspects of single-crystal strain-gradient plasticity**. *ZAMM*, Vol. 93, pp 844-867, 2013. [DOI: 10.1002/zamm.201200101]

C. Sansour, S. Skatulla and M. Hjiaj, **A shell theory with scale effects and higher order gradients **. *International Journal of Solids and Structures*, Vol. 50, pp 2271-2280, 2013. [DOI: 10.1016/j.ijsolstr.2013.03.031]

C. Sansour, S. Skatulla and M. Hjiaj, **A shell theory with scale effects and higher order gradients **. *International Journal of Solids and Structures *, Vol. 50, pp 2271-2280, 2013. [DOI: 10.1016/j.ijsolstr.2013.03.031]

M.S. Sirry, N.H. Davies, K. Kadner, L. Dubuis, M.G. Saleh, E.M. Meintjes, B.S. Spottiswoode, P. Zilla and T. Franz, **Micro-structurally detailed model of a therapeutic hydrogel injectate in a rat biventricular cardiac geometry for computational simulations**. *Computer Methods in Biomechanics and Biomedical Engineering*, 2013. [DOI: 10.1080/10255842.2013.793765]

S. Skatulla and C. Sansour, **A formulation of a Cosserat-like continuum with multiple scale effects **. *Computational Materials Science*, Vol. 67, pp 113-122, 2013. [DOI: 10.1016/j.commatsci.2012.08.040]

## Books

W. Han and B.D. Reddy, **Plasticity: Mathematical Theory and Numerical Analysis**. Springer, New York, 2013. [DOI: 10.1007/978-1-4614-5940-8]

## In Book

D. Davydov, A. Javili, P. Steinmann and A. McBride, **Surface Effects in Solid Mechanics: A Comparison of Atomistic and Surface Enhanced Continuum Approaches at Finite Temperature**. Edited by H. Altenbach and N.F. Morozov. Springer-Verlag, 2013, pp 43-57. [DOI: 10.1007/978-3-642-35783-1_4]

S.C. Jasinoski, M.A. Cluver, A. Chinsamy and B.D Reddy, **Anatomical plasticity in the snout of Lystrosaurus**. Edited by C.F. Kammerer, K.D. Angielczyk and J. Frobisch. Springer, New York, 2013, Chapter 8, pp 139-149. [DOI: 10.1007/978-94-007-6841-3_8]

M.S. Yeoman, B.D. Reddy, D. Bezuidenhout, H.C. Bowles, P. Zilla and T. Franz, **Development of a fabric-reinforced porous graft for vascular tissue engineering using finite element methods and genetic algorithms**. Edited by A. Gefen. Springer, 2013. [DOI:10.1007/8415_2013_162]

## In Proceedings

M. Essack and S. Skatulla, **Identification of nonlinear hyperelastic material parameters for healthy myocardial tissue via an inverse method based on modelling the passive filling stage of the cardiac cycle**. *Proceedings of the V International Conference on Structural Engineering, Mechanics and Computation, Cape Town, South Africa,*, 2013.

S. Goqo, R. Tait, S. Skatulla and T. Becker, **Optimisation of the double torsion test geometry**. *Proceedings of the V International Conference on Structural Engineering, Mechanics and Computation, Cape Town, South Africa,*, 2013.

K. Sack, S. Skatulla and C. Sansour, **Biological tissue mechanics with fibres modelled as one-dimensional Cosserat continua: Applications to cardiac tissue in healthy and diseased states**. *Proceedings of the V International Conference on Structural Engineering, Mechanics and Computation, Cape Town, South Africa,*, 2013.

K. Sack, S. Skatulla and C. Sansour, **Biological tissue mechanics with fibres modelled as one-dimensional Cosserat Continua. Applications to cardiac tissue in healthy and diseased states**. *Proceedings of the 3rd African Conference on Computational Mechanics, Livingstone, Zambia*, 2013.

S. Skatulla, D. Legner, R.R. Rama, J. Mbewu, C. Sansour, B.D. Reddy, N. Davies and T. Franz, **Studying the impact of the Injection therapy for myocardial infarction on the heart's performance**. *Proceedings of 3rd South-East European Conference on the Computational Mechanics (SEECCM III), Kos, Greece*, 2013.

S. Skatulla, D. Legner, R.R. Rama, J. Mbewu, N. Sansour, C., Davies and T. Franz, **Computational study of the injection therapy for myocardial infarction during the necrotic stage**. *Proceedings of 10th IASTED International Conference on Biomedical Engineering, Innsbruck, Austria*, 2013. [DOI: 10.2316/P.2013.791-066]

J.E. Van Zyl, M.O.A. Alsaydalani, C.R.I. Clayton, T. Bird and A. Dennis, **Soil fluidisation outside leaks in water distribution pipes - preliminary observations**. *Proceedings of the Institution of Civil Engineers: Water Management*, 2013.

# 2012

## Articles

A.R. Appadu, **Investigating the shock-capturing properties of some composite numerical schemes for the 1-D linear advection equation**.*International Journal of Computer Applications in Technology*, Vol. 43, pp 79-79, 2012. [DOI: 10.1504/IJCAT.2012.046038]

A.R. Appadu, **Comparison of some optimisation techniques for numerical schemes discretising equations with advection terms**.*International Journal of Innovative Computing and Applications*, Vol. 4, pp 12-12, 2012. [DOI: 10.1504/IJICA.2012.045701]

A.R. Appadu, **Optimised composite numerical schemes in 2-D for hyperbolic conservation laws**. *International Journal for Numerical Methods in Fluids*, Vol. 69, pp 1522-1549, 2012. [DOI: 10.1002/fld.2652]

M. Bickell, A. Buffler, I. Govender and D.J. Parker, **A new line density tracking algorithm for PEPT and its application to multiple tracers**. *Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment *, Vol. 682, pp 36-41, 2012. [DOI: 10.1016/j.nima.2012.04.037]

T. Chinyoka and O.D. Makinde, **On transient flow of a reactive variable viscosity third-grade fluid through a cylindrical pipe with convective cooling**. *Meccanica*, Vol. 47, pp 667-685, 2012. [DOI: 10.1007/s11012-011-9476-3]

T. Chinyoka and O.D. Makinde, **Unsteady hydromagnetic flow of a reactive variable viscosity third-grade fluid in a channel with convective cooling**. *International Journal for Numerical Methods in Fluids*, Vol. 69, pp 353-365, 2012. [DOI: 10.1002/fld.2562]

K.E. Cole, A. Buffler, N.P. van der Meulen, J.J. Cilliers, J-P. Franzidis, I. Govender, C. Liu and M.R. van Heerden, **Positron emission particle tracking measurements with 50 micron tracers **. *Chemical Engineering Science *, Vol. 75, pp 235-242, 2012. [DOI:10.1016/j.ces.2012.02.053]

J.K. Djoko and BD Reddy, **Existence results for a polymer melt with an evolving natural configuration**. *Mathematical Models and Methods in Applied Sciences*, Vol. 22, pp 1150004-1150004, 2012. [DOI: 10.1142/S0218202512005873]

T. Franz, **Computational and numerical modelling in neuromechanics and biomechanics.**. *International Journal for Numerical Methods in Biomedical Engineering*, Vol. 28, pp 1001-1001, 2012. [DOI: 10.1002/cnm.2514]

S.C. Jasinoski and B.D. Reddy, **Mechanics of cranial sutures during simulated cyclic loading **. *Journal of Biomechanics *, Vol. 45, pp 2050-2054, 2012. [DOI: 10.1016/j.jbiomech.2012.05.007]

A. Javili, A.T. McBride, J. Mergheim, P Steinmann and U. Schmidt, **Micro-to-macro transitions for continua with surface structure at the microscale**. *PAMM*, Vol. 12, pp 23-26, 2012. [DOI: 10.1002/pamm.201210007]

A. Javili, A. McBride and P. Steinmann, **Numerical modelling of thermomechanical solids with mechanically energetic (generalised) Kapitza interfaces**. *Computational Materials Science*, Vol. 65, pp 542-551, 2012. [DOI: 10.1016/j.commatsci.2012.06.006]

A. Javili, A. McBride and P. Steinmann, **Thermomechanics of solids with lower-dimensional energetics: on the importance of surface, interface and curve structures at the nanoscale. A unifying review**. *Applied Mechanics Reviews*, Vol. 65, 2012. [DOI: 10.1115/1.4023012]

A. Javili, A. McBride, P. Steinmann and B.D. Reddy, **Relationships between the admissible range of surface material parameters and stability of linearly elastic bodies**. *Philosophical Magazine*, Vol. 92, pp 3540-3563, 2012. [DOI: 10.1080/14786435.2012.682175]

K. Kadner, S. Dobner, T. Franz, D. Bezuidenhout, M.S. Sirry, P. Zilla and N.H. Davies, **The beneficial effects of deferred delivery on the efficiency of hydrogel therapy post myocardial infarction **. *Biomaterials *, Vol. 33, pp 2060-2066, 2012. [DOI:10.1016/j.biomaterials.2011.11.031]

O.P. Layeni and J.V. Johnson, **Hybrids of the heat balance integral method **. *Applied Mathematics and Computation *, Vol. 218, pp 7431-7444, 2012. [DOI: 10.1016/j.amc.2012.01.001]

O.D. Makinde and T. Chinyoka, **Analysis of unsteady flow of a variable viscosity reactive fluid in a slit with wall suction or injection**.*Journal of Petroleum Science and Engineering*, Vol. 94, pp 1-11, 2012. [DOI: 10.1016/j.petrol.2012.06.023]

A. McBride, J. Mergheim, A. Javili, P. Steinmann and S. Bargmann, **Micro-to-macro transitions for heterogeneous material layers accounting for in-plane stretch**. *Journal of the Mechanics and Physics of Solids*, Vol. 60, pp 1221-1239, 2012. [DOI:10.1016/j.jmps.2012.01.003]

J-P.V. Pelteret and B.D. Reddy, **Computational model of soft tissues in the human upper airway**. *International Journal for Numerical Methods in Biomedical Engineering*, Vol. 28, pp 111-132, 2012. [DOI: 10.1002/cnm.1487]

B.D. Reddy, **Mixed finite element methods**. *Notices of the South African Mathematical Society*, Vol. 43, pp 57-88, 2012.

B.D. Reddy, C. Wieners and B. Wohlmuth, **Finite element analysis and algorithms for single-crystal strain-gradient plasticity**.*International Journal for Numerical Methods in Engineering*, Vol. 90, pp 784-804, 2012. [DOI: 10.1002/nme.3347]

M. Saleh, S-K. Sharp, A. Alhamud, B.S. Spottiswoode, A.J.W. van der Kouwe, N.H. Davies, T. Franz and E.M. Meintjes, **Longterm left ventricular remodelling in rat model of non-reperfused myocardial infarction: sequential MR imaging using a 3t clinical scanner.**.*Journal of Biomedicine and Biotechnology*, 2012. [DOI: 10.1155/2012/504037]

S. Skatulla, C. Sansour and A. Arockiarajan, **A multiplicative approach for nonlinear electro-elasticity **. *Computer Methods in Applied Mechanics and Engineering *, Vol. 245, pp 243-255, 2012. [DOI: 10.1016/j.cma.2012.07.002]

P. Steinmann, A.T. McBride, S. Bargmann and A. Javili, **A deformational and configurational framework for geometrically non-linear continuum thermomechanics coupled to diffusion**. *International Journal of Non-Linear Mechanics*, Vol. 47, pp 215-227, 2012. [DOI:10.1016/j.ijnonlinmec.2011.05.009]

B. Weed, A. Borazjani, S. Patnaik, R. Prabhu, M.F. Horstemeyer, P.L. Ryan, T. Franz, L.N. Williams and J. Liao, **Stress state and strain rate dependence of the human placenta**. *Annals of Biomedical Engineering*, Vol. 40, pp 2255-2265, 2012. [DOI: 10.1007/s10439-012-0588-2]

## In Book

B.D. Reddy and A.T. McBride, **Introduction to Finite Element Analysis and Recent Developments**. Edited by A. Patnaik and R.D. Anandjiwala. Nova Science Publishers, New York, 2012, Chapter 1, pp 1-28.

## In Proceedings

O.P. Layeni and J.V. Johnson, **Some explicit solutions for a class of one-phase Stefan problems**. , Edited by Theodore E. Simos, George Psihoyios, Ch. Tsitouras and Zacharias Anastassi. 2012. [DOI: 10.1063/1.4756673]

E.M. Smuts, D.A. Deglon and C.J. Meyer, **Methodology for coupled CFD-DEM modeling of particulate suspension rheology**. *Ninth International Conference on Computational Fluid Dynamics in the Minerals and Process Industries*, 2012.

A. Thiart, G. Floweday and C. Meyer, **A CFD Study of Fuel Evaporation and Related Thermo-fluid Dynamics in the Inlet Manifold, Port and Cylinder of the CFR Octane Engine**. *SAE 2012 International Powertrains, Fuels and Lubricants Meeting*, 2012. [DOI: 10.4271/2012-01-1715]

# 2011

## Articles

S. Bargmann, AT McBride and P. Steinmann, **Models of solvent penetration in glassy polymers with an emphasis on case II diffusion. A comparative review**. *Applied Mechanics Reviews*, Vol. 64, 2011.

S. Bargmann and B.D. Reddy, **Modeling of polycrystals using a gradient crystal plasticity theory that includes dissipative micro-stresses**.*European Journal of Mechanics - A/Solids*, Vol. 30, pp 719-730, 2011. [DOI: 10.1016/j.euromechsol.2011.04.006]

D.J. Brinkerhoff, T.W. Meierbachtol, J.V. Johnson and J.T. Harper, **Sensitivity of the frozen/melted basal boundary to perturbations of basal traction and geothermal heat flux: Isunnguata Sermia, western Greenland**. *Annals of Glaciology*, Vol. 52, pp 43-50, 2011. [DOI:10.3189/172756411799096330]

S.P. Carter, H.A. Fricker, D.D. Blankenship, J.V. Johnson, W.H. Lipscomb, S.F. Price and D.A. Young, **Modeling 5 years of subglacial lake activity in the MacAyeal Ice Stream (Antarctica) catchment through assimilation of ICESat laser altimetry**. *Journal of Glaciology*, Vol. 57, pp 1098-1112, 2011. [DOI: 10.3189/002214311798843421]

T. Chinyoka, **Suction-Injection Control of Shear Banding in Non-Isothermal and Exothermic Channel Flow of Johnson-Segalman Liquids**. *Journal of fluids engineering*, Vol. 133, 2011. [URL]

T. Chinyoka, **Two-dimensional flow of chemically reactive viscoelastic fluids with or without the influence of thermal convection**.*Communications in Nonlinear Science and Numerical Simulation*, Vol. 16, pp 1387-1395, 2011. [DOI: 10.1016/j.cnsns.2010.07.006]

T. Chinyoka and O.D. Makinde, **Analysis of transient Generalized Couette flow of a reactive variable viscosity third-grade liquid with asymmetric convective cooling**. *Mathematical and Computer Modelling*, Vol. 54, pp 160-174, 2011. [DOI: 10.1016/j.mcm.2011.01.047]

G. Floweday, S. Petrov, R.B. Tait and J. Press, **Thermo-mechanical fatigue damage and failure of modern high performance diesel pistons**.*Engineering Failure Analysis*, Vol. 18, pp 1664-1674, 2011. [DOI: 10.1016/j.engfailanal.2011.02.002]

Hugo Krynauw, Lucie BruchmÃ¼ller, Deon Bezuidenhout, Peter Zilla and Thomas Franz, **Degradation-induced changes of mechanical properties of an electro-spun polyester-urethane scaffold for soft tissue regeneration**. *Journal of Biomedical Materials Research Part B: Applied Biomaterials*, Vol. 99, pp 359-368, 2011. [DOI: 10.1002/jbm.b.31907]

OD Makinde, T. Chinyoka and RS Lebelo, **Numerical investigation into CO2 emission, O2 depletion and thermal decomposition in a reacting slab**. *Mathematical Problems in Engineering*, Vol. 2011, 2011. [DOI: 10.1155/2011/208426]

O.D. Makinde, T. Chinyoka and L. Rundora, **Unsteady flow of a reactive variable viscosity non-Newtonian fluid through a porous saturated medium with asymmetric convective boundary conditions**. *Computers & Mathematics with Applications*, Vol. 62, pp 3343-3352, 2011. [DOI: 10.1016/j.camwa.2011.08.049]

A.T. McBride, A. Javili, P. Steinmann and S. Bargmann, **Geometrically nonlinear continuum thermomechanics with surface energies coupled to diffusion**. *Journal of the Mechanics and Physics of Solids*, Vol. 59, pp 2116-2133, 2011. [DOI: 10.1016/j.jmps.2011.06.002]

MN Ngoepe, BD Reddy, D. Kahn, C. Meyer, P. Zilla and T. Franz, **A Numerical Tool for the Coupled Mechanical Assessment of Anastomoses of PTFE Arterio-venous Access Grafts**. *Cardiovascular Engineering and Technology*, Vol. 2, pp 160-172, 2011. [DOI:10.1007/s13239-011-0045-7]

B.D. Reddy, **The role of dissipation and defect energy in variational formulations of problems in strain-gradient plasticity. Part 2: single-crystal plasticity**. *Continuum Mechanics and Thermodynamics*, Vol. 23, pp 551-572, 2011. [DOI: 10.1007/s00161-011-0195-8]

B.D. Reddy, **The role of dissipation and defect energy in variational formulations of problems in strain-gradient plasticity. Part 1: polycrystalline plasticity**. *Continuum Mechanics and Thermodynamics*, Vol. 23, pp 527-549, 2011. [DOI: 10.1007/s00161-011-0194-9]

## In Book

A.T. McBride, S. Bargmann and P. Steinmann, **Lecture Notes in Applied and Computational Mechanics: Advances in Extended and Multifield Theories for Continua**. Edited by B. Markert. Springer-Verlag, 2011, Chapter 5, pp 89-107.

B.D. Reddy and A.T. McBride, **Modeling and Simulation in Fibrous Materials: Techniques and Applications**. Edited by A. Patnaik. Nova Science Publishers, New York, 2011, Chapter 1, pp 1-28.

# 2010

## Articles

C.W. Bakker, C.J. Meyer and D.A. Deglon, **The development of a cavern model for mechanical flotation cells**. *Minerals Engineering*, Vol. 23, pp 968-972, 2010.

L.S. Bbosa, I. Govender, A.N. Mainza and M.S. Powell, **Power draw estimations in experimental tumbling mills using PEPT**. *Journal of Engineering Mining*, 2010. [DOI: 10.1016/j.mineng.2010.10.005]

T. Chinyoka, **Poiseuille flow of reactive Phan-Thien-Tanner liquids in 1D channel flow, Transactions of ASME**. *Journal of Heat Transfer*, Vol. 132, pp 111701-111708, 2010.

T. Chinyoka and O.D. Makinde, **Computational dynamics of unsteady flow of a variable viscosity reactive fluid in a porous pipe**.*Mechanics Research Communications*, Vol. 37, pp 347-353, 2010.

T. Chinyoka and O.D. Makinde, **Analysis of nonlinear dispersion of a pollutant ejected by an external source into a channel flow**.*Mathematical Problems in Engineering*, 2010. [DOI: 10.1155/2010/827363]

P. Ebobisse and P. Neff, **Existence and uniqueness for rate-independent gradient plasticity with isotropic hardening and plastic spin**.*Mathematics and Mechanics of Solids*, Vol. 15, pp 691-703, 2010.

T. Franz, P. Human, S. Dobner, B.D. Reddy, M. Black, H. Ilsley, M.F. Wolf, D. Bezuidenhout, L. Moodley and P. Zilla, **Tailored sizes of constrictive external vein meshes for coronary artery bypass surgery**. *Biomaterials*, Vol. 31, pp 9301-9309, 2010.

T. Franz, B.D. Reddy, P. Human and P. Zilla, **A mathematical method for constraint-based cluster analysis towards optimized constrictive diameter smoothing of saphenous vein grafts**. *Medical and Biological Engineering and Computing*, Vol. 48, pp 519-529, 2010.

I. Govender, N. Mangesana, A.N. Mainza and Franzidis J.-P., **Measurement of shear rates in a laboratory tumbling mill**. *Journal of Mining Engineering*, 2010. [DOI: 10.1016/j.mineng.2010.08.009]

I. Govender, G.B. Tupper and A.N. Mainza, **Towards a mechanistic model for slurry transport in tumbling mills**. *Journal of Mining Engineering*, 2010. [DOI: 10.1016/j.mineng.2010.08.010]

S.C. Jasinoski, B.D. Reddy, K.K. Louw and A. Chinsamy, **Mechanics of cranial sutures using the finite element method**. *Journal of Biomechanics*, Vol. 34, pp 3104-3111, 2010.

C.T. Jayasundara, R.Y. Yang, B.Y. Guo, A.B. Yu, I. Govender, A. Mainza, A. van der Westhuizen and J. Rubenstein, **CFD-DEM modelling of particle flow in IsaMills - comparison between simulations and PEPT measurements**. *Journal of Mining Engineering*, 2010. [DOI:10.1016/j.mineng.2010.07.011]

D.V.V. Kallon, I. Govender and A.N Mainza, **Circulation rate modelling of mill charge using position emission particle tracking**. *Journal of Engineering Mining*, 2010. [DOI: 10.1016/j.mineng.2010.09.006]

T. Koch, B.D. Reddy, P. Zilla and T. Franz, **Aortic valve leaflet mechanical properties facilitate diastolic valve function**. *Computer Methods in Biomechanics and Biomedical Engineering*, Vol. 13, pp 225-234, 2010.

O.D. Makinde and T. Chinyoka, **Numerical investigation of transient heat transfer to hydromagnetic channel flow with radiative heat and convective cooling**. *Communications in Nonlinear Science and Numerical Simulation*, Vol. 15, pp 3919-3930, 2010.

O.D. Makinde and T. Chinyoka, **Transient analysis of pollutant dispersion in a cylindrical pipe with a nonlinear waste discharge concentration**. *Computers and Mathematics with Applications*, Vol. 60, pp 642-652, 2010.

O.D. Makinde and T. Chinyoka, **MHD transient flows and heat transfer of dusty fluid in a channel with variable physical properties and Navier slip condition**. *Computers and Mathematics with Applications*, Vol. 60, pp 660-669, 2010.

Mohamed, H.B.H and B.D. Reddy, **Some properties of models for generalized Oldroyd-B fluids**. *International Journal of Engineering Science*, Vol. 48, pp 1470-1480, 2010.

S.W. Mumenya, R.B. Tait and Alexander M.G., **Mechanical behaviour of textile concrete under accelerated ageing conditions**. *Journal of Cement and Concrete Composites*, Vol. 32, pp 580-588, 2010.

Q.G. Reynolds, R.T. Jones and B.D. Reddy, **Mathematical and computational modelling of the dynamic behaviour of direct current plasma arcs**. *Journal of the South African Institute of Mining and Metallurgy*, Vol. 110, pp 733-742, 2010.

C. Sansour and S. Skatulla, **A micromorphic continuum-based formulation for inelastic deformations at finite strains. Application to shear band formation**. *International Journal of Solids and Structures*, Vol. 47, pp 1546-1554, 2010.

N.K. Schiller, T. Franz, N.S. Weerasekara, P. Zilla and B.D. Reddy, **A simple fluid-structure coupling algorithm for the study of the anastomotic mechanics of vascular grafts**. *Computer Methods in Biomechanics and Biomedical Engineering*, Vol. 13, pp 773-781, 2010.

K. Sichalwe, I. Govender and A.N. Mainza, **Characterising porosity of multi-component mixtures in rotary mills**. *Journal of Mining Engineering*, 2010. [DOI: 10.1016/j.mineng.2010.08.027]

M.S. Sirry, P. Zilla and T. Franz, **A computational study of structural designs for a small-diameter composite vascular graft promoting tissue regeneration**. *Cardiovascular Engineering and Technology*, Vol. 1, pp 269-81, 2010.

T.S. Volkwyn, A. Buffler, I. Govender, J.-P. Franzidis, A.J. Morrison, A. Odo, N.P. van der Meulen and C. Vermeulen, **Studies of the effect of tracer activity on time-averaged positron emission particle tracking measurements on tumbling mills at PEPT Cape Town**. *Journal of Mining Engineering*, 2010. [DOI: 10.1016/j.mineng.2010.08.020]

M.S. Yeoman, B.D. Reddy, H.C. Bowles, D. Bezuidenhout, P. Zilla and T. Franz, **A constitutive model for the warp-weft coupled non-linear behavior of knitted textiles with potential use in tissue regenerative implants**. *Biomaterials*, Vol. 31, pp 8484-8493, 2010.

## In Book

C. Sansour, S. Skatulla and A Arunachalakasi, **A generalized framework and a multiplicative formulation of electro-mechanical coupling in mechanics of generalized continua: One hundred years after the Cosserats**. Edited by G. Maugin and A. Metrikine. Springer, New York, 2010, pp 287-294. [DOI: 10.1007/978-1-4419-5695-8_30]

## In Proceedings

S. Bartle, A.T. McBride and B.D. Reddy, **Proceedings of the 7th South African conference on computational mechanics**. *Shell finite elements, with applications in biomechanics*, Edited by S. Kok, D.N. Wilke, H.M. Inglis and E. Sellers. January, 2010.

S. Braun, S. Skatulla, H.-D. Beushausen and C. Sansour, **Proceedings of the Fourth International Conference on Structural Engineering, Mechanics and Computation**. *A micromorphic theory and its application to elastic size-scale effects*, Edited by A. Zingoni. 2010.

E.B. Ismail and B.D. Reddy, **Proceedings of the 7th South African conference on computational mechanics**. *Smoothed particle hydrodynamics for non-linear solid mechanics*, Edited by S. Kok, D.N. Wilke, H.M. Inglis and E. Sellers. January, 2010.

Y. Kajee, J-P. Pelteret and B.D. Reddy, **Proceedings of the 7th South African conference on computational mechanics**. *Biomechanics of the human tongue*, Edited by S. Kok, D.N. Wilke, H.M. Inglis and E. Sellers. January, 2010.

Morrissey, H.L, A.T. McBride and B.D. Reddy, **Proceedings of the 7th South African conference on computational mechanics**. *The modeling of fibre-reinforced composites using a multi-scale methodology*, Edited by S. Kok, D.N. Wilke, H.M. Inglis and E. Sellers. January, 2010.

# 2009

## Articles

C.W. Bakker, C.J. Meyer and D.A. Deglon, **Numerical modelling of non-Newtonian slurry in a mechanical flotation cell**. *Progess in Computational Fluid Dynamics*, Vol. 9, pp 308-315, 2009.

C.W. Bakker, C.J. Meyer and D.A. Deglon, **Numerical modelling of non-Newtonian slurry in a mechanical flotation cell**. *Minerals Engineering*, Vol. 22, pp 944-950, 2009.

M.E. Gurtin and B.D. Reddy, **Alternative formulations of isotropic hardening for Mises materials, and associated variational inequalities**.*Continuum Mechanics and Thermodynamics*, Vol. 21, pp 237-250, 2009. [DOI: 10.1007/s00161-009-0107-3]

S.K.F. Hattingh and B.D. Reddy, **A finite element approach for modelling single phase compressible flow in dual porosity systems**. *Journal of Petroleum Science and Engineering*, Vol. 69, pp 1-24, 2009.

A.T. McBride and B.D. Reddy, **A discontinuous Galerkin formulation of a model of gradient plasticity at finite strains**. *Comp*, Vol. 198, pp 1805-1820, 2009. [DOI: 10.1016/j.cma.2008.12.034]

Moyo, P and R.B. Tait, **Structural performance assessment and fatigue analysis of a railway bridge**. *Structure and Infrastructure Engineering*, 2009. [DOI: 10.1080/15732470903068912]

C. Sansour and S. Skatulla, **A strain gradient generalised continuum approach for modelling elastic scale-effects**. *Computer Methods in Applied Mechanics and Engineering*, Vol. 198, pp 1401-1412, 2009.

S. Skatulla, A. Arunachalakasi and C. Sansour, **A nonlinear generalized continuum framework for electro-elasticity. Theoretical and Computational Aspects**. *Journal of the Mechanics and Physics of solids*, Vol. 57, pp 137-160, 2009.

M.S. Yeoman, B.D. Reddy, H.C. Bowles, P. Zilla, D. Bezuidenhout and T. Franz, **The use of finite element methods and genetic Algorithms in search of an optimal fabric reinforced porous graft system**. *annal of Biomedical Engineering*, Vol. 37, pp 2266-2287, 2009.

## In Proceedings

F. Ebobisse and B.D. Reddy, **Mathematical aspects of elastoplasticity**. *Multiple scales problems in biomathematics, mechanics, physics and numerics*, Edited by A. Abdulle, J. Banasiak, A. Damlamian and M. Sango. 2009.

# 2008

## Articles

T. Chinyoka, **Computational dynamics of a thermally decomposable viscoelastic lubricant under shear**. *Journal of Fluids Engineering*, Vol. 130, pp 7-7, 2008.

H. van der Merwe, B.D. Reddy, P. Zilla, D. Bezuidenhout and T. Franz, **A computational study of knitted Nitinol meshes for their prospective use as external vein reinforcement**. *Journal of Biomechanics*, Vol. 41, pp 1302-1309, 2008.

S. Nhleko, A. Zingoni and P. Moyo, **A variable mass model for describing load impulses due to periodic jumping**. *Engineering Structures*, Vol. 30, pp 1760-1769, 2008.

M.S. Powell, I. Govender and A.T. McBride, **Applying DEM outputs to the unified comminution model**. *Minerals Engineering*, Vol. 21, pp 744-750, 2008.

B.D. Reddy, F. Ebobisse and A.T. McBride, **Well-posedness of a model of strain-gradient plasticity for plastically irrotational materials**.*International Journal of Plasticity*, 2008. [DOI: 10.1016/j.ijplas.2007.01.013]

R.F. Rickard, C.J. Meyer and D.A. Hudson, **Computational modeling of microarterial anastomoses with size discrepancy**. *Journal of Surgical Research*, Vol. 153, pp 1-11, 2008.

S. Skatulla and C. Sansour, **Essential boundary conditions in meshfree methods via a modified variational principle. Applications to shell computations**. *Computer Assisted Mechanics and Engineering Sciences*, Vol. 15, pp 123-142, 2008.

A. Zingoni, **The case for the Eurocodes for South Africa**. *Civil Engineering*, Vol. 16, pp 16-18, 2008.

A. Zingoni, **What do the Eurocodes mean for South Africa?**. *The Structural Engineer*, Vol. 86, pp 11-13, 2008.

A. Zingoni and V. Balden, **On the buckling strength of stiffened elliptic paraboloidal steel panels. Thin-Walled Structures**. , 2008. [DOI:10.1016/j.tws.2008.11.007]

A. Zongoni, **On group-theoretic computation of natural frequencies for spring-mass dynamic systems with rectilinear motion**.*Communications in Numerical Methods in Engineering*, Vol. 24, pp 973-987, 2008.

## Proceedings

**IUTAM Symposium on Theoretical, Computational and Modelling Aspects of Inelastic Media**. Edited by B.D. Reddy. 2008.

## In Proceedings

C.W. Bakker, C.J. Meyer and D.A. Deglon, **Numerical modelling of non-newtonian slurry in a mechanical flotation cell**. *6th International Conference on CFD in Oil & Gas, Metallurgical and Process Industries*, Trondheim Norway, 10-12 June, 2008.

F. Ebobisse, A.T. McBride and B.D. Reddy, **On the mathematical formulations of a model of strain gradient plasticity**. *IUTAM Symposium on Theoretical, Modelling and Computational Aspects of Inelastic Media*, Edited by B.D. Reddy. 2008.

A.T. McBride and B.D. Reddy, **Some aspects of a Discontinuous Galerkin formulation for gradient plasticity at finite strains**. *IUTAM Symposium on Theoretical, Modelling and Computational Aspects of Inelastic Media*, Edited by B.D. Reddy. 2008.

S. Skatulla, C. Sansour and A. Arunachalakasi, **'A nonlinear generalized continuum approach for electro-mechanical couplin**. *AIP Conference Proceedings*, 2008.

# 2007

## Articles

J.K. Djoko, F. Ebobisse, A.T. McBride and B.D. Reddy, **A Discontinuous Galerkin formulation for classical and gradient plasticity - Part 1: Formulation and analysis**. *Computer Methods in Applied Mechanics and Engineering*, Vol. 196, pp 3881-3897, 2007. [DOI:10.1016/j.cma.2006.10.045]

J.K. Djoko, F. Ebobisse, A.T. McBride and B.D. Reddy, **A Discontinuous Galerkin formulation for classical and gradient plasticity - Part 2: Algorithms and numerical analysis**. *Computer Methods in Applied Mechanics and Engineering*, Vol. 197, pp 1-27, 2007. [DOI:10.1016/j.cma.2007.06.027]

R. Heise, C.J. Meyer and T.W. Von Backstraam, **CFD simulation of helicopter flow fields using an actuator disk main rotor model**. *R&D Journal*, Vol. 23, pp 26-32, 2007.

C.L. Vaughan, B.D. Reddy, T.D. Noakes and V.C. Moran, **A commentary on the intellectual health of the nation**. *South African Journal of Science*, Vol. 103, pp 22-26, 2007.

## In Proceedings

J.K. Djoko and B.D. Reddy, **A generalised Hu-Washizu formulation for elasticity**. *In Proceedings of the Fifth South African Conference on Computational and Applied Mechanics (SACAM)*, Edited by T.M. Harms. Cape Town, January, 2007.

I. Govender and M.S. Powell, **A 3D X-ray vision system for studying discrete particulate behaviour**. *DEM07*, Brisbane, Australia, August, 2007.

I. Govender, M.S. Powell, R. Chandramohan, D.J. Parker, X. Fan and A. Ingram, **Positron emission particle tracking of charge particles in a scaled industrial tumbling mill**. *DEM07*, Brisbane, Australia, August, 2007.

A.T. McBride and M.S. Powell, **Using DEM to inform experimental design**. *DEM07*, Brisbane, Australia, August, 2007.

A.T. McBride and B.D. Reddy, **Primal plasticity within a discontinuous Galerkin framework. Part 2: numerics and comparison with standard formulations**. *In Proceedings of the Fifth South African Conference on Computational and Applied Mechanics (SACAM)*, Edited by T.M. Harms. Cape Town, 2007.

M.S. Powell, I. Govender, C. Kulya and A.T. McbBride, **Applying DEM outputs to the Unified Comminution Model - the SAG mill**.*DEM07*, Brisbane, Australia, August, 2007.

B.D. Reddy and A.T. McBride, **Primal plasticity within a discontinuous Galerkin framework. Part 1: basic formulation**. *Proceedings of the Fifth South African Conference on Computational and Applied Mechanics (SACAM)*, Edited by T.M. Harms. Cape Town, January, 2007.