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Publications - Daya Reddy

BOOKS AND EDITED WORKS

  • Reddy BD, Functional Analysis and Boundary Value Problems: An Introductory Treatment. (Pitman Surveys and Reference Works in Pure and Applied Mathematics, Vol 30) Longman, London and Wiley, New York (1986) 333 pages.
  • Reddy BD, Introductory Functional Analysis with Applications to Boundary-Value Problems and Finite Elements. Springer-Verlag, New York (1998) 471 pages.[link]
  • Reddy BD (editor), Recent Developments in Computational and Applied Mechanics: A Volume in Honour of John B Martin. CIMNE, Barcelona (1997) 432 pages.
  • Lubuma JM-S, Luhandjula MK and Reddy BD, Actes de la Conférence Internationale sur les Problèmes Variationnels en Mathématiques Appliquées Presses de l'Université de Kinshasa (1997) 332 pages.
  • Han W and Reddy BD, Plasticity: Mathematical Theory and Numerical Analysis. Springer-Verlag, New York (1999) 371 pages.[link]
  • Reddy BD (guest editor), Special Issue on Advances in Computational Plasticity, Computer Methods in Applied Mechanics and Engineering 171 (Nos.3-4) (1999) [link]
  • Reddy BD (editor), Theoretical, Modelling and Computational Aspects of Inelastic Media. Proceedings of IUTAM Symposium, Cape Town, 2008. Springer, Berlin (2009) [link]
  • Franz T and Reddy BD (guest editors), Special Issue on Selected Papers from 2nd African Conference on Computational Mechanics (2011), International Journal for Numerical Methods in Biomedical Engineering 28 (No. 1) (2012) .
  • Han W and Reddy BD, Plasticity: Mathematical Theory and Numerical Analysis. 2nd edition, Springer, New York (2013) 421 pages. [link]

ARTICLES IN JOURNALS AND CONFERENCE PROCEEDINGS, AND CHAPTERS IN BOOKS

  • Martin JB and Reddy BD, A programming approach to the solution of the rate problem in elastic, plastic solids. In Mechanics in Engineering (RN Dubey and NC Lind, eds) University of Waterloo Press, Waterloo, Canada (1977) 251 - 270.
  • Baggett J, Martin JB and Reddy BD, Elastic-plastic deformations in plane frames. The Civil Engineer in South Africa 19 (1977) 89 - 93.
  • Reddy BD and Calladine CR, Classical buckling of a thin-walled tube subjected to bending moment and internal pressure. International Journal of Mechanical Sciences 20 (1978) 641 - 650.[link]
  • Reddy BD, An experimental study of the plastic buckling of circular cylinders in pure bending. International Journal of Solids and Structures 15 (1979) 669 - 683.[link]
  • Reddy BD, Plastic buckling of cylindrical shells. International Journal of Mechanical Sciences 21 (1979) 671 - 679.[link]
  • Reddy BD, Discussion of paper `Inelastic buckling of circular tubes in bending' by RM Korol (in Journal of the Engineering Mechanics Division of the ASCE 104 (1978) 939 -952). Journal of the Engineering Mechanics Division of the ASCE 105 (1979) 358 - 359.
  • Reddy BD, Buckling of elastic-plastic discretely stiffened cylinders in axial compression. International Journal of Solids and Structures 16 (1980) 313 - 328.[link]
  • Reddy BD, Dual extremum principles in the dynamics of rigid-plastic bodies undergoing finite deformation. Journal of the Mechanics and Physics of Solids 29 (1981) 199 - 210.[link]
  • Reddy BD, A deformation theory analysis of the bifurcation of pressurised thick-walled cylinders. Quarterly Journal of Mechanics and Applied Mathematics 35 (1982) 183 - 196.
  • Reddy BD, Surface instabilities on an equibiaxially stretched elastic half-space. Mathematical Proceedings of the Cambridge Philosophical Society 91 (1982) 491 - 501.
  • Duffett GA and Reddy BD, Plastic buckling of initially imperfect stiffened cylinders in axial compression. Journal of Applied Mechanics 50 (1983) 88 - 94.[link]
  • Reddy BD, The occurrence of surface instabilities and shear bands in plane strain deformation of an elastic half-space. Quarterly Journal of Mechanics and Applied Mathematics 36 (1983) 337 - 350.
  • Reddy BD and Mitchell GP, The analysis of elastic-plastic plates: a quadratic programming problem and its solution by finite elements. Computer Methods in Applied Mechanics and Engineering 41 (1983) 237 - 248.[link]
  • Duffett GA and Reddy BD, The analysis of incompressible hyperelastic bodies by the finite element method. Computer Methods in Applied Mechanics and Engineering 41 1983) 105 - 120.[link]
  • Reddy BD, The propagation and growth of acceleration waves in constrained thermoelastic materials. Journal of Elasticity 14 (1984) 387 - 402.
  • Reddy BD, Acceleration waves in isotropic constrained thermoelastic materials. In Wave Phenomena: Modern Theory and Applications (TB Moodie and CA Rogers, eds) North-Holland, Amsterdam (1984) 71 - 82.
  • Reddy BD, Griffin TB and Marais MJ, A penalty approach to the rate problem in small-strain plasticity. IMA Journal of Applied Mathematics 34 (1985) 303 - 321.
  • Griffin TB and Reddy BD, Penalty-finite element approximations of the rate problem in plasticity. In Variational Methods in Engineering (CA Brebbia, ed) Springer, Berlin (1985) 8.37 - 8.46.
  • Duffett GA and Reddy BD, The solution of multi-parameter systems of equations, with application to problems in nonlinear elasticity. Computer Methods in Applied Mechanics and Engineering 59 (1986) 179 - 213.[link]
  • Bleach GP and Reddy BD, The influence of constraints on the properties of acceleration waves in isotropic thermoelastic media. Archive for Rational Mechanics and Analysis 98 (1987) 31 - 64.
  • Martin JB, Reddy BD, Griffin TB and Bird WW, Applications of mathematical programming concepts to incremental elastic-plastic analysis. Engineering Structures 9 (1987) 171 - 176.[link]
  • Reddy BD, Martin JB and Griffin TB, Extremal paths and holonomic constitutive laws in elastoplasticity. Quarterly of Applied Mathematics 45 (1987) 487 - 502.
  • Reddy BD and Griffin TB, Variational principles and finite element approximations of a holonomic elastic-plastic problem. Numerische Mathematik 52 (1988) 101 - 117.
  • Reddy BD, Variational and numerical aspects of eigenvalue problems in the stability of fluids. In Mathematics of Finite Elements and Applications 6 (JR Whiteman, ed) Academic Press, London (1988) 397 - 404.
  • Griffin TB, Reddy BD and Martin JB, A numerical study of holonomic approximations to problems in plasticity. International Journal for Numerical Methods in Engineering 26 (1988) 1449 -1466.
  • Reddy BD and Voyé HF, Finite element analysis of the stability of fluid motions. Journal of Computational Physics 79 (1988) 92 - 118.
  • Reddy BD, Convergence of mixed finite element approximations for the shallow arch problem. Numerische Mathematik 53 (1988) 687 - 700.[link]
  • Geveci T, Reddy BD and and Pearce HT, The approximation of the spectrum of the Stokes operator. RAIRO - Modélisation Mathématique et Analyse Numérique 23 (1989) 129 - 136.
  • Eve RA and Reddy BD, Variational principles and finite element approximations to problems in finite strain plasticity. Computational Plasticity: Models, Software and Applications 21 (DRJ Owen, E Oñate and E Hinton (eds)) (Pineridge, Swansea) (1989) 71 - 84.
  • Reddy BD and Tomarelli F, The obstacle problem for an elasto-plastic body. Applied Mathematics and Optimization 21 (1990) 89 - 110.[link]
  • Eve RA, Reddy BD and Rockafellar RT, An internal variable theory of elastoplasticity based on the maximum plastic work inequality. Quarterly of Applied Mathematics 48 (1990) 59 - 84.
  • Martin JB and Reddy BD, Variational principles and solution algorithms for internal variable formulations of problems in plasticity. In Omaggio a Giulio Ceradini (U Andreaus et al (eds)) Università di Roma `La Sapienzà' (Roma) (1988) 465 - 477. [link]
  • Eve RA, Gültop T and Reddy BD, An internal variable finite strain theory of plasticity. Quarterly of Applied Mathematics 48 (1990) 625 - 644.
  • Reddy BD, The impact of continuum mechanics on analysis. Notices of the SA Mathematical Society 21 (1989) 166 - 182.
  • Reddy BD, Book review: Maximum and Minimum Principles (by MJ Sewell) (CUP, 1988). SIAM Review 32 (1990) 182 - 184.[link]
  • Reddy BD, Method and Myth in Applied Mathematics. Inaugural lecture, University of Cape Town, 1989. 12pp.
  • Reddy BD and Martin JB, Finite element approximations and return mapping algorithms for internal variable formulations of problems in plasticity. Computer Methods in Applied Mechanics and Engineering 93 (1991) 253-273.
  • Reddy BD, Mixed finite element methods for one-dimensional problems: a survey. Quaestiones Mathematicae 15 (1992) 233-259.
  • Reddy BD and Volpi MB, Mixed finite element approximations for the circular arch problem. Computer Methods in Applied Mechanics and Engineering 97 (1992) 125 - 145.[link]
  • Reddy BD, Mixed variational inequalities arising in elastoplasticity. Nonlinear Analysis: Theory, Methods and Applications 19 (1992) 1071 - 1089.[link]
  • Reddy BD, Existence of solutions to quasistatic problems in plasticity. In Progress in Partial Differential Equations: Calculus of Variations, Applications. (C Bandle et al. (eds) Pitman Research Notes in Mathematics 267 , Longman, UK (1992) 299 - 311.
  • Eve RA and Reddy BD, Algorithms for the solution of problems of finite-strain elastoplasticity. In Computational Plasticity: Fundamentals and Applications (Proceedings of the 3rd International Conference on Computational Plasticity (DRJ Owen, E Oñate and E Hinton (eds)) (1992) 103 - 115.
  • Arunakirinathar K and Reddy BD, Mixed finite element approximations for the analysis of arbitrarily curved bars. Numerische Mathematik 94 (1993) 13 - 43.
  • Reddy BD, Aspects of the modern theory of elastoplasticity. In Free Boundary Problems Involving Solids. (JM Chadam and H Rasmussen (eds)). Pitman Research Notes in Mathematics 281 Longman, UK (1993) 48 - 56.
  • le Roux C and Reddy BD, The steady Navier-Stokes equations with mixed boundary conditions: applications to free boundary flows. Nonlinear Analysis: Theory, Methods and Applications 20 (1993) 1043 - 1068.[link]
  • Nurick GN, Nates M and Reddy BD, The behaviour of a single particle on the inside of a rotating cylinder. Part I: Theoretical Analysis. nternational Journal of Minerals Processing 38 (1993) 67 - 79.[link]
  • Nurick GN, Nates M and Reddy BD, The behaviour of a single particle on the inside of a rotating cylinder. Part II: Experimental Investigation. International Journal of Minerals Processing 38 (1993) 81 - 91.[link]
  • Martin JB and Reddy BD, Piecewise smooth dissipation and yield functions in plasticity. Meccanica 28 (1993) 169 - 175..[link]
  • Eve RA and Reddy BD, The variational formulation and solution of problems of finite-strain elastoplasticity based on the use of a dissipation function. International Journal for Numerical Methods in Engineering 37 (1994) 1673 - 1695.
  • Hueck U, Reddy BD and Wriggers P, On the stabilization of the rectangular four-node quadrilateral element. Communications in Numerical Methods in Engineering 10 (1994) 555 - 563. [pdf]
  • Reddy BD and Martin JB, Internal variable formulations of problems in elastoplasticity: constitutive and algorithmic aspects. Applied Mechanics Reviews 47 (1994) 429 - 456.
  • Arunakirinathar K and Reddy BD, Enhanced strain finite element methods. In Computational Plasticity: Fundamentals and Applications (DRJ Owen, E Oñate and E Hinton (eds)) (Proceedings of the 4th International Conference on Computational Plasticity, Barcelona, April 1995) Pineridge Press, Swansea (1995) 321 - 332.
  • Arunakirinathar K and Reddy BD, Some geometrical results and estimates for quadrilateral finite elements. Computer Methods in Applied Mechanics and Engineering 122 (1995) 307 - 314.[link]
  • Reddy BD and Simo JC, Stability and convergence of a class of enhanced strain methods. SIAM Journal on Numerical Analysis 32 (1995) 1705 - 1728.
  • Han W and Reddy BD, On the finite element method for mixed variational inequalities arising in elastoplasticity. SIAM Journal on Numerical Analysis 32 (1995) 1778 - 1807.
  • Arunakirinathar K and Reddy BD, Further results for enhanced strain methods with isoparametric elements. Computer Methods in Applied Mechanics and Engineering 127 (1995) 127 - 143.
  • Gültop T and Reddy BD, Acceleration waves in elastic-plastic solids with singular yield surfaces. European Journal of Mechanics/A: Solids 14 (1995) 529 - 551.
  • Han W and Reddy BD, Computational plasticity: the variational basis, and numerical analysis. Computational Mechanics Advances 2 (4) (1995) 283 - 400. [pdf]
  • Han W, Reddy BD and Schroeder GC, Qualitative and numerical analysis of quasistatic problems in elastoplasticity. SIAM Journal on Numerical Analysis 34 (1997) 143 - 177.
  • Han W,Jensen S and Reddy BD, Numerical approximations of problems in plasticity: error analysis and solution algorithms. Numerical Linear Algebra with Applications 4 (1997) 191 - 204.
  • Stülpner MA, Reddy BD, Starke GR and Spirakis A, Finite element analysis of three-dimensional adaptive bone remodelling. Journal of Biomechanics 30 (1997) 1063 - 1066.[link]
  • Reddy BD and Küssner M, The four-noded quadrilateral with a 2 x 1 integration rule: application to plates and other problems. Computer Methods in Applied Mechanics and Engineering 149 (1997) 101 - 112.[link]
  • Reddy BD, John B Martin: a biographical essay. In Recent Developments in Computational and Applied Mechanics: A Volume in Honour of John B Martin. CIMNE, Barcelona (1997) 1 - 10.
  • Reddy BD and Mitchell GP, Finite element approximations of the flow of fibre suspensions. In Recent Developments in Computational and Applied Mechanics: A Volume in Honour of John B Martin. CIMNE, Barcelona (1997) 342 - 356.
  • Reddy BD and Küssner M, Some low-order quadrilateral elements based on novel integration rules. Engineering Computations 15 (1998) 700 - 721.
  • Reddy BD, Acceleration waves. In Encyclopaedia of Mathematics (M Hazewinkel, Ed.) Kluwer Academic Publishers, Dordrecht, Netherlands.
  • Reddy BD, Book review: Limit Analysis of Solids and Structures (JA Kamenjarzh) (CRC Press, 1996). SIAM Review 40 (1998) 173 - 175.
  • Galdi GP and Reddy BD, Well-posedness of the problem of fiber suspension flows. Journal of Non-Newtonian Fluid Mechanics 83 (1999) 205 - 230. [link]
  • Han W and Reddy BD, Convergence analysis of discrete approximations of problems in hardening plasticity. Computer Methods in Applied Mechanics and Engineering 171 (1999) 327 - 340. [link]
  • Childs SJ and Reddy BD, Finite element simulation of the motion of a rigid body in a fluid with a free surface. Computer Methods in Applied Mechanics and Engineering 175 (1999) 99 - 120. [link]
  • Reese S, Küssner M and Reddy BD, A new stabilization technique for finite elements in non-linear elasticity. International Journal for Numerical Methods in Engineering 44 (1999) 1617 - 1652. [link]
  • Reese S, Küssner M, Reddy BD and Wriggers P, Eine neue Stabilisieringstechnik für finite Elemente in der finiten Elastizität. Zeitschrift für angewandte Mathematik und Mechanik. 79 (1999) S573 - 574.
  • Reese S, Wriggers P and Reddy BD, A new locking-free brick element formulation for continuous large deformation problems. Computers and Structures 75 (2000) 291 - 304. [link]
  • Munganga JMW, Reddy BD and Diatezua JK, Aspects of the thermodynamic stability of fibre suspension flows. Journal of Non-Newtonian Fluid Mechanics 92 (2000) 135 - 150. [link]
  • Han W and Reddy BD, Convergence of approximations to the primal problem in plasticity under minimal conditions of regularity. Numerische Mathematik 87 (2000) 283 - 315. [link]
  • Reddy BD and Mitchell GP, Finite element analysis of fibre suspension flows. Computer Methods in Applied Mechanics and Engineering 190 (2001) 2349 - 2368. [link]
  • Küssner M and Reddy BD, The equivalent parallelogram and parallelipiped, and their application to stabilised finite elements in two and three dimensions. Computer Methods in Applied Mechanics and Engineering 190 (2001) 1967 - 1983. [link]
  • Kahn MJ and Reddy BD, Science and Technology in South Africa: regional innovation hub or passive consumer? In Daedalus, Special Issue "Why South Africa Matters", American Academy of Arts and Sciences, Cambridge, MA, 130, No.1 (2001) 205-234.
  • Reddy BD and Ehl O, Enhanced strain finite elements for Mindlin-Reissner plates. In Structural Engineering, Mechanics and Computation. (ed. A Zingoni) Elsevier, Amsterdam, 27 - 38.[link]
  • Munganga JMW and Reddy BD, Local and global existence of solutions to the equations for fibre suspension flows. Mathematical Models and Methods in Applied Sciences 12 (1989) 166 - 182. [link]
  • Arunakirinathar K and Reddy BD, A stable affine-approximate finite element method. SIAM Journal on Numerical Analysis 40 (2002) 180 - 197. [link]
  • Reddy BD, Affine-approximate finite element methods and stabilization techniques in elasticity. Computational Mechanics of Solid Materials at Large Strains (ed. C Miehe et al.), Kluwer, Dordrecht, Netherlands (2003) 395-404. [pdf]
  • Djoko JK and Reddy BD, New mixed formulations for problems in elasticity. Engineering Computations 20 (2003) 659 - 674. [link]
  • Braess D, Carstensen C and Reddy BD, Uniform convergence and a posteriori estimators for the enhanced strain finite element method. Numerische Mathematik 96 (2004), 461 - 479. [link]
  • Ebobisse Bille F and Reddy BD, Some mathematical problems in perfect plasticity. Computer Methods in Applied Mechanics and Engineering 193 (2004) 5071 - 5094. [link]
  • Bostan V, Han W and Reddy BD, A posteriori estimation and adaptive solution of elliptic variational inequalities of the second kind. Applied Numerical Mathematics 52 (2005) 13 - 38. [link]
  • Kleine D and Reddy BD, Finite element analysis of flows in secondary settling tanks. International Journal for Numerical Methods in Engineering 64 (2005) 849 - 876. [link]
  • Lamichhane BP, Reddy BD and Wohlmuth BI, Convergence in the incompressible limit of finite element approximations based on the Hu-Washizu formulation Numerische Mathematik 104 (2006) 151 - 175. [link]
  • Djoko JK, Lamichhane BP, Reddy BD and Wohlmuth BI, Conditions for equivalence between the Hu-Washizu and related formulations, and computational behaviour in the incompressible limit Computer Methods in Applied Mechanics and Engineering 195 (2006) 4161 - 4178. [link]
  • Djoko JK and Reddy BD, An extended Hu-Washizu formulation for elasticity. Computer Methods in Applied Mechanics and Engineering 195 (2006) 6330 - 6346. [link]
  • Kleine D and Reddy BD, Finite element analysis of unsteady flows in secondary settling tanks. Proceedings of the Fifth International Conference on Computational Fluid Dynamics in the Process Industries. CD-ROM, ISBN 0 643 09423 7 (2006).
  • Djoko JK, Ebobisse F, McBride AT and Reddy BD, A Discontinuous Galerkin formulation for classical and gradient plasticity. Part 1: Formulation and analysis. Computer Methods in Applied Mechanics and Engineering 196 (2007) 3881 - 3897. [link]
  • Djoko JK, Ebobisse F, McBride AT and Reddy BD, A Discontinuous Galerkin formulation for classical and gradient plasticity. Part 2: Algorithms and numerical results. Computer Methods in Applied Mechanics and Engineering 21 (2007) 1 - 21. [link]
  • Vaughan CL, Reddy BD, Noakes TD and Moran VC, A commentary on the intellectual health of the nation. South African Journal of Science 103 (2007) 22-26.[pdf]
  • Reddy BD, Ebobisse F and McBride AT, Well-posedness of a model of strain-gradient plasticity for plastically irrotational materials. International Journal of Plasticity 24 (2008) 55-73. [link]
  • van der Merwe H, Reddy BD, Bezuidenhout D, Zilla P and Franz T, A computational study of knitted Nitinol meshes for their prospective use as external vein reinforcement. Journal of Biomechanics 41 (2008) 1302-1309. [link]
  • Ebobisse F, McBride AT and Reddy BD, On the mathematical formulations of a model of strain gradient plasticity. In Theoretical, Modelling and Computational Aspects of Inelastic Media (Proceedings of IUTAM Symposium, ed. BD Reddy), Springer, Berlin (2008) 117-128. [pdf]
  • McBride AT and Reddy BD, Some aspects of a Discontinuous Galerkin formulation for gradient plasticity at finite strains. In Theoretical, Modelling and Computational Aspects of Inelastic Media (Proceedings of IUTAM Symposium, ed. BD Reddy), Springer, Berlin (2008). 237-247. [pdf]
  • Hattingh SKF And Reddy BD, A finite element approach for modelling single phase compressible flow in dual porosity systems. Journal of Petroleum Science and Engineering 69 (2009) 1-24. [link]
  • Yeoman MS, Reddy BD, Bowles H, Bezuidenhout D and Zilla P and Franz T, The use of finite element methods and genetic Algorithms in search of an optimal fabric reinforced porous graft system. Annals of Biomedical Engineering 37 (2009) 2266-2287. [link]
  • McBride AT and Reddy BD, A discontinuous Galerkin formulation for gradient plasticity at finite strains. Computer Methods in Applied Mechanics and Engineering. 198 (2009) 1805-1820. [pdf]
  • Ebobisse Bille F and Reddy BD, Mathematical Aspects of Elastoplasticity. In Multiple Scales Problems in Biomathematics, Mechanics, Physics and Numerics (Proceedings of CIMPA School, Cape Town, August 2007 (ed. A Abdulle, J Banasiak, A Damlamian, M Sango), Gakkotosho, Tokyo, pages 185-220, 2009.
  • Gurtin ME and Reddy BD, Alternative formulations of isotropic hardening for Mises materials, and associated variational inequalities. Continuum Mechanics and Thermodynamics 21 (2009) 237-250. [link]
  • Koch T, Reddy BD, Zilla P and Franz T, Aortic valve leaflet mechanical properties facilitate diastolic valve function. Computer Methods in Biomechanics and Biomedical Engineering. 13 (2010) 225-234. [link]
  • Schiller NK, Franz T, Weerasekara NS, Zilla P and Reddy BD, A simple fluid–structure coupling algorithm for the study of the anastomotic mechanics of vascular grafts. Computer Methods in Biomechanics and Biomedical Engineering13(2010) 773-781. [link]
  • Franz T, Reddy BD, Human P and Zilla P, A mathematical method for constraint-based cluster analysis towards optimized constrictive diameter smoothing of saphenous vein grafts. Medical and Biological Engineering and Computing 48 (2010) 519-529. [link]
  • Reynolds QG, Jones RT and Reddy BD, Mathematical and computational modelling of the dynamic behaviour of direct current plasma arcs. Proceedings of the Twelfth International Ferroalloys Congress, Helsinki, Finland (A Vartiainen, ed.), Outotec Oyj (2010) 789-801. Also published as Journal of the South African Institute of Mining and Metallurgy 110 (2010) 733-742. [pdf]
  • Yeoman MS, Reddy BD, Bowles HC, Bezuidenhout D, Zilla P and Franz T, A constitutive model for the warp-weft coupled non-linear behavior of knitted textiles with potential use in tissue regenerative implants. Biomaterials 31 (2010) 8484-8493. [link]
  • Mohamed HBH and Reddy BD, Some properties of models for generalized Oldroyd-B fluids. International Journal of Engineering Science 48 (2010) 1470-1480. [link]
  • Jasinoski SC, Reddy BD, Louw KK, and Chinsamy A, Mechanics of cranial sutures using the finite element method. Journal of Biomechanics 43 (2010) 3104-3111. [link]
  • Franz T, Human P, Dobner S, Reddy BD, Black M, Ilsley H, Wolf MF, Bezuidenhout D, Moodley L, and Zilla P, Tailored sizes of constrictive external vein meshes for coronary artery bypass surgery. Biomaterials 31 (2010) 9301-9309.[link]
  • Ngoepe MN, Reddy BD, Kahn D, Meyer CJ, Zilla P and Franz T, A numerical tool for the coupled mechanical assessment of anastomoses of PTFE arterio-venous access grafts. Cardiovascular Engineering and Technology 2 (2011) 160-172.[link]
  • Bartle S, McBride AT and Reddy BD, Shell finite elements, with applications in biomechanics. Proceedings of the 7th South African Conference on Computational Mechanics (Pretoria, January 2010) (S Kok, DN Wilke, HM Inglis, E Sellers, editors) (CD-ROM, ISBN 978-0-620-49192-1) (2011) 63-74. [pdf]
  • Morrissey H, Reddy BD, McBride A and Bowles H, The modelling of fibre-reinforced cocmposites using a multi-scale methodology. Proceedings of the 7th South African Conference on Computational Mechanics (Pretoria, January 2010) (S Kok, DN Wilke, HM Inglis, E Sellers, editors) (CD-ROM, ISBN 978-0-620-49192-1) (2011) 86-96.
  • Kajee Y, Pelteret J-P and Reddy BD, Biomechanics of the human tongue. Proceedings of the 7th South African Conference on Computational Mechanics (Pretoria, January 2010) (S Kok, DN Wilke, HM Inglis, E Sellers, editors) (CD-ROM, ISBN 978-0-620-49192-1) (2011) 97-108.
  • Richardson NJN, McBride AT and Reddy BD, An investigation of algorithms for rate-independent single crystal plasticity. Proceedings of the 7th South African Conference on Computational Mechanics (Pretoria, January 2010) (S Kok, DN Wilke, HM Inglis, E Sellers, editors) (CD-ROM, ISBN 978-0-620-49192-1) (2011) 508-517.
  • Bargmann S and Reddy BD, Modeling of polycrystals using a gradient crystal plasticity theory that includes dissipative microstresses. European Journal of Mechanics A: Solid 30 (2011) 1-12. [link]
  • Ismail EB and Reddy BD, Smoothed particle hydrodynamics for nonlinear solid mechanics. Proceedings of the 7th South African Conference on Computational Mechanics (Pretoria, January 2010) (S Kok, DN Wilke, HM Inglis, E Sellers, editors) (CD-ROM, ISBN 978-0-620-49192-1) (2011) 372-381. [pdf]
  • Reddy BD and McBride AT, Introduction to finite element analysis and recent developments. Chapter 1 in Modeling and Simulation in Fibrous Materials: Techniques and Applications (A Patnaik and RD Anandjiwala, editors) Nova Science Publishers, New York (2012) 1-21. [pdf]
  • Djoko JK and Reddy BD, Existence results for a polymer melt with an evolving natural configuration. Mathematical Models and Methods in Applied Sciences22 1150004 (37 pages) (2012). [link]
  • Reddy BD, The role of dissipation and defect energy in variational formulations of problems in strain-gradient plasticity. Part 1: Polycrystalline plasticity. Continuum Mechanics and Thermodynamics 23 (2011) 527–549. [link]
  • Reddy BD, 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 23 (2011) 551-572. [link]
  • Reddy BD, Wieners C and Wohlmuth B, Finite element analysis and algorithms for single-crystal strain-gradient plasticity. International Journal for Numerical Methods in Engineering 90 (2012) 784-804.
  • Pelteret J-PV and Reddy BD, Computational model of soft tissues in the human upper airway computational model of soft tissues in the human upper airway. International Journal for Numerical Methods in Biomedical Engineering 28 (2012) 111-132. [link]
  • Jasinoski SC and Reddy BD, Mechanics of cranial sutures during simulated cyclic loading. Journal of Biomechanics 45 (2012) 2050-2054. [link]
  • Javili A, McBride A, Steinmann P and Reddy BD, The admissibility of negative material parameters for surface elasticity theory. Philosophical Magazine 92 (2012) 3540-3563. [link]
  • Reddy BD, Mixed finite element methods. Notices of the South African Mathematical Society 43 (2012) 57-88.
  • Jasinoski SC, Cluver MA, Chinsamy A, and Reddy BD, Anatomical plasticity in the snout of Lystrosaurus and its functional implications. In C. F. Kammerer, K. D. Angielczyk, and J. Frobisch, eds. Early Evolutionary History of the Synapsida. Springer, New York (2013).
  • Chama A and Reddy BD, New stable mixed finite element approximations for problems in elasticity. Computer Methods in Applied Mechanics and Engineering 256 (2013) 211-223.
  • Kajee Y, Pelteret J-P and Reddy BD, The biomechanics of the human tongue. International Journal for Numerical Methods in Biomedical Engineering 29 (2013) 4592-514. [link]
  • Lamichhane BP, McBride AT and Reddy BD, A finite element method for a three-field formulation based on biorthogonal systems. Computer Methods in Applied Mechanics and Engineering 258 (2013) 109-117.[link]
  • Reddy BD, Some theoretical and computational aspects of single-crystal strain-gradient plasticity. Zeit. angew. Math. Mech. (ZAMM) 93 (2013) 844-867.[link]
  • Yeoman MS, Reddy BD, Bezuidenhout D, Bowles HC, Zilla P and Franz T, Development of a fabric-reinforced porous graft for vascular tissue engineering using finite element methods and genetic algorithms. In Cardiovascular and Cardiac Therapeutic Devices (Franz T, ed.) Studies in Mechanobiology, Tissue Engineering and Biomaterials. Springer (2014) 29-62. [link]
  • Reddy BD, Variational formulations for single-crystal strain-gradient plasticity at large deformations. GAMM Mitteilungen 36 (2013) 149-160.[link]
  • Gurtin ME and Reddy BD, 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 68 (2014) 134-160. [link]
  • Povall TM, McBride AT and Reddy BD, Finite element simulation of large-strain single-crystal viscoplasticity: an investigation of various hardening relations. Computational Materials Science 81 (2014) 386-396.
  • Legner D, Skatulla S, MBewu J, Rama RR, Reddy BD, Sansour S, Davies NH and Franz T, 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 30 (2014) 416-429. [link]
  • Pelteret J-PV and Reddy BD, Development of a computational biomechanical model of the human upper-airway soft-tissues towards simulating obstructive sleep apnea. Clinical Anatomy 27 (2014) 182-200. [link]
  • Donev I and Reddy BD, Time dependent finite element simulations of a shear thinning viscoelastic fluid with application to blood flow. International Journal for Numerical Methods in Fluids 75 (2014) 668-686. [link]
  • Javili A, McBride, A, Steinmann P and Reddy BD, A unified computational framework for bulk and surface elasticity theory: A curvilinear-coordinate-based finite element methodology. Computational Mechanics 54 (2014) 745-764. [link]
  • Bargmann S, Reddy BD and Klusemann B, A computational study of a model of single-crystal strain-gradient viscoplasticity with a fully-interactive hardening relation. International Journal of Solids and Stuctures 51 (2014) 2754-2764. [link]
  • Chama A and Reddy BD, Stability and convergence of two three-field finite element formulations for elasticity. Computational Methods in Applied Mathematics 14 (2014) 305-316. [link]
  • Bogaers AEJ, Kok S, Reddy BD and Franz T, Quasi-Newton methods for implicit black-box FSI coupling. Computer Methods in Applied Mechanics and Engineering 279 (2014) 113-132. [link]
  • Bogaers AEJ, Kok S, Reddy BD and Franz T, Extending the robustness and efficiency of artificial compressibility for partitioned fluid-structure interactions. Computer Methods in Applied Mechanics and Engineering 283 (2015) 1278-1295. [link]
  • Anand L, Gurtin ME and Reddy BD, The stored energy of cold work, thermal annealing, and other thermodynamic issues in single crystal plasticity at small length scales. International Journal of Plasticity 64 (2015) 1-25. [link]
  • Reddy BD, Numerical approximation of variational inequalities arising in elastoplasticity. Proceedings of the International Congress of Mathematicians, Seoul, Korea (Sun Young Jang, Young Rock Kim, Daw-Woong Lee, Ikkwon Yie, eds), Kyung Moon SA, Seoul (2014) Volume IV, 1125-1144.
  • Anand L, Gurtin ME and Reddy BD, The stored energy of cold work, thermal annealing, and other thermodynamic issues in single crystal plasticity at small length scales. International Journal of Plasticity 64 (2015) 1-25 . [link]
  • McBride A, Bargmann S and Reddy BD, 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 55 (2015) 755-769 . [link]
  • Pauck RG and Reddy BD, Computational analysis of the radial mechanical performance of PLLA coronary stents. Medical Engineering and Physics 37 (2015) 7-12. [link]
  • Carstensen C, Reddy BD and Schedensack M, A natural nonconforming method for the Bingham flow problem is quasi-optimal. Numerische Mathematik 133 (2015) 37-66.[link]
  • 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. [link]
  • Gottschalk D, McBride A, Reddy BD, Javili A, Wriggers P and Hirschberger CB, Computational and theoretical aspects of a grain-boundary model that accounts for grain misorientation and grain-boundary orientation. Computational Materials Science 111 (2016) 443-459. [link]
  • Bayerschen E, McBride A, Reddy BD and Boehlke T, On slip transmission criteria in experiments and crystal plasticity models. Journal of Material Science 55 (2016) 2243-2258. [link]
  • 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 (2015) 53-68.
  • MacDevette M and Reddy BD, Can nanofluids improve solar collector efficiency? In Proceedings of the South African Solar Energy Conference (Pretoria, 2015) (Meyer JP, ed), University of Pretoria, ISBN 978-1-77592-109-7 (2015).
  • Reddy BD, Theoretical and Numerical Elastoplasticity‚Äč. In Advanced Finite Element Technologies (Wriggers P and Schröder J, edsCISM Course and Lecture Notes, Springer, Wien (2016) 177-194.
  • 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.
  • 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) 04015057.
  • 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.
  • De Lorenzis L, McBride, A and Reddy BD, Phase-field modeling of fracture in single crystal plasticity. GAMM Mitteilungen  39 (2016) 7-34.
  • 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.
  • Reddy BD, Mathematical foundations of elastoplastic deformations in solids. Encyclopedia of Computational Mechanics (Stein E, de Borst R and Hughes TJR, eds), John Wiley (2016) (in press).
  • 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.
  • Wakeni MF, Reddy BD and McBride AT, An unconditionally stable algorithm for generalised 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 (2016) 1 - 8
  • Wriggers P, Rust W and Reddy BD, A virtual element method for contact. Computational Mechanics (in press).
  • 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.
  • 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.
  • 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.
  • Griffiths E, Bargmann S and Reddy BD, Elastic behaviour at the nanoscale of innovative composites of nanoporous gold and polymer. Extreme Mechanics Letters (in press).
  • 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 (in press). Available at https://arxiv.org/abs/1704.07753
  • Musehane NM, Oxtoby OF and Reddy BD, Multi-scale simulation of droplet-droplet interaction and coalescence. Journal of Computational Physics 373 (2018) 924 - 939.
  • McBride AT, Reddy BD and Steinmann P, Dissipation-consistent modelling and classification of extended plasticity formulations. Journal of Mechanics and Physics of Solids 119 (2018) 118-139.
  • 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 (2018) (in press).
  • Reddy BD, Modelling, analysis and computation in plasticity. Acta Mathematica Sinica (2018) In press.
  • 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. In review.
  • 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. In review.
  • 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.
  • Reddy BD, Modelling, analysis and computation in plasticity. In review.
  • Shirzadi M, Appa H and Reddy BD, Development of a patient-specific finite element model of the Transcatheter Aortic Valve Implantation (TAVI) procedure. In review.
  • Wakeni MF and Reddy BD, Space-time Galerkin methods for simulation of laser heating using the generalized nonlinear model. In review
  • 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. Available at http://arxiv.org/abs/1901.08900.
  • Grieshaber BJ, Reddy BD and Rasolofoson F, Discontinuous Galerkin approximations for near-incompressible and near-inextensible transversely istropic bodies. Computers and Mathematics with Applications (2019) In press. Available at http://www.arxiv.org/abs/1810.13267.

TECHNICAL REPORTS AND OTHER PUBLICATIONS

  • (with GP Mitchell) The analysis of elastic-plastic trusses undergoing large deformations. AMRU TR14 (1981). 14 pp.
  • (with GA Duffett) The numerical solution of systems of nonlinear equations with many parameters. AMRU TR39 (1983). 29 pp.
  • (with GA Duffett, TB Griffin, JB Martin, CD Mercer and L Resende) NOSTRUM - A finite element program for nonlinear structural mechanics. AMRU TR18B (1983). 14 pp.
  • (with AC Bolt) The use of nonlocal nonlinear friction laws in the finite element analysis of contact problems in elasticity. AMRU Tech Rep 42 (1983). 26pp.
  • (with MJ Marais) A penalty approach to the rate problem in plasticity. AMRU TR49 (1984). 24pp.
  • (with CD Mercer and SD Pressinger) Finite element analysis of linear piezoelectric media: Part I - Statical analysis. AMRU TR51 (1984). 21pp.
  • (with TB Griffin and JB Martin) Finite element approximations for elastic-plastic continua using internal variable formulations. AMRU TR53 (1984). 32pp.
  • (with GA Duffett) Systems of nonlinear equations with many parameters. AMRU TR56 (1984). 32pp.
  • (with CD Mercer and RA Eve) The dynamic behaviour of piezoelectric media. AMRU TR73 (1985). 19pp.
  • (with GA Duffett) Numerical solution of bifurcation problems in nonlinear elasticity. AMRU TR74 (1985). 15pp.
  • Bifurcation and stability in structural mechanics. AMRU TR75 (1986). 9pp.
  • (with RA Eve) Conforming finite element methods for eigenvalue problems of thin elastic shells. AMRU TR88 (1987). 29pp.
  • (with RA Eve) Variational principles and finite element approximation of problems in finite strain plasticity. CERECAM TR133 (1989). 29pp.
  • (with K Arunakirinathar) A closed-form solution to the problem of an elastic bar of arbitrary but constant curvature and torsion. CERECAM TR184 (1992). 17 pp.
  • (with B-H Sun) Shell models based on additive decomposition of deformation gradient. CERECAM TR247 (1994). 15 pp.
  • (with SJ Childs) Finite element simulation of a rigid body in a fluid with free surface. CERECAM TR248 (1994). 14 pp.
  • (with AE Ozinsky and GA Ekama) Mathematical simulation of dynamic behaviour of secondary settling tanks. Research Report W85, Dept of Civil Engineering, UCT (1994).
  • (with MA Stülpner, GR Starke and A Spirakis) Constitutive models for scalar adaptive bone remodelling laws. CERECAM TR 264 (1996). 27 pp.
  • (with SKF Hattingh) A preliminary comparison between a finite element and a finite difference algorithm for modelling petroleum reservoirs. CERECAM TR284 (1997). 12 pp.
  • (with D Kleine) Development of a finite element 2D hydrodynamic model for secondary settling tanks. Research Report K5/835 (Water Research Commission) (2001). 45pp.
  • (with T Koch and T Franz) Stress Analysis of the Aortic Valve:  Comparison of Linear and Non-linear Constitutive Models for Aortic Valve Leaflets.  Proceedings of the SA Conference on Computational and Applied Mechanics, Johannesburg, 18 - 21 January 2005. 8pp.
  • (with R Adam, C de la Rey and KJ Naidoo) High performance computing in South Africa: Computing in support of African development. CT Watch Quarterly February 2006. Available online at http://www.ctwatch.org/quarterly/archives/february-2006
  • Penzhorn KEW, McBride AT and Reddy BD, Consistency and convergence of SPH derivative approximations (2011). [pdf]