My research contribution over the last 14 years has been centred on a number of topics of computational mechanics, namely: superplastic forming, human body impact analysis; particle based meshless methods; and membrane and shell structural analysis.

Superplastic forming

I have significantly contributed to the development of techniques for the numerical simulation and prediction of superplastic forming processes. In particular, my work in this field has been centred on the following areas:

• Finite element analysis of superplastic forming of thin sheet aerospace components including large strains, geometrical error estimators, adaptive mesh enrichment techniques, pressure control strategies and the simulation of sheet contact and diffusion bonding. This work generated 10 major international journal papers and three contracts with British Aerospace totalling over £250,000 and resulted in a software package SNAPFORM that is currently being used to efficiently design new superplastically formed aerospace components. As part of the developments, an entirely new ‘incremental flow formulation’ was devised in order to overcome the problems of previous non-Newtonian flow based techniques.  In addition, an energy based computational strategy to predict the forming pressure cycle that results in ideal forming conditions was developed and successfully implemented in an industrial context.
• Finite element analysis of the superplastic forming of thick aerospace components. This work included the design of a new hexahedral 3-D finite element and the required variational framework. This work was funded by British Aerospace (Airbus) and resulted in 6 articles in international journals. Further work involving 3-D error estimators and re-meshing is planned.
• Finite element analysis of superplastically formed dental prosthesis. This work is being carried out in collaboration with Guys & St. Thomas hospital in London and financially supported by an EPSRC project worth £338,000. The aim is to speed up and improve the manufacture of artificial palates by using numerical simulation.

Human body impact simulation

This area of research involves the finite element stress analysis of human body parts in impact conditions and was initially funded by BAe (Sowerby research Centre). Two very important contributions have been made in this field: the development of linear tetrahedral elements that do not exhibit volumetric locking; and the development of constitutive equations to model human flesh and soft tissue. In particular a new large strain viscoelastic formulation has been proposed which is capable of representing the often anisotropic characteristics of soft human tissue at large strains. Five papers in international journals have been published as a result of this research and excellent opportunities for further work and funding are envisaged by using the techniques developed in areas such as sports injuries, car crashes etc. A small research group of three students funded by a UWS cluster award of 2 PhD scholarships and one EPSRC scholarship are working in this area.

Membrane and shell structures

My contribution in this area has been centred on the following topics:

• Development of stress smoothing techniques and error estimators for the finite element analysis of facet shells. This work was partly funded by Chevron Oil and lead to 3 papers in international journals.
• Finite element analysis of membrane and tension structures including pneumatic and air supported membranes. New techniques have been developed to account for the additional stiffness resulting from trapped air inside pneumatic structures. In addition, a new formulation for the solution of form finding problems in membrane structures has been derived and successfully implemented. A small research group including a PhD student, a research visitor and two MSc students have been working in this area in collaboration with Tensys, a leading company in the design and analysis of such structures. The work to date has lead to a major paper in a high impact international journal and further publications are planned.

Particle based meshless methods

A significant part of my current and recent research effort involves the development of innovative computational strategies which do not require the use of finite element or finite difference grids. In particular, a new method, namely ‘Corrected Smooth Particle Hydrodynamics’ has been derived and implemented. This technique shares the advantages of existing particle methods such as Smooth Particle Hydrodynamics insofar as it can follow the particles of a continuum through a complex deformation process without the problems associated with mesh distortion or tangling. In addition, however, the new correction methods developed can match the accuracy of linear finite element formulations. A total of four major journal papers have been published in this field as well as numerous conference publications and presentations. Currently, there is a research group consisting of three research assistants and two research students developing these techniques further. It is hoped that the method developed can be applied to simulate highly complex phenomena such as turbulent free surface flows, mud flows, avalanches, large strain impact problems in ballistics, mould filling operations in pressure die casting, etc. This work has led to three major research contracts with EPSRC totalling nearly £400,000.

Error estimation in large strain problems

This is a very new area of research beig varied out in collaboration with Prof. Peraire of MIT (USA) and Prof. Huerta of UPC (Spain). We have developed new finite element techniques for the evaluations of strict upper and lower bounds of engineering outputs in large strain nonlinear problems in solid mechanics. An initial paper has been recently submitted to a prestigious international journal outlining the use of these techniques in hyperelasticity. With funding from Sandia Laboratories in New Mexico, USA, we are currently working on the extension of these methods for dynamic problems, especially in conjunction with the linear tetrahedral elements initially developed for human body impact applications. We are also exploring the extension of these techniques for plasticity, limit state analysis and shakedown problems.

Publications

Books

1. D. HENWOOD & J. BONET, Finite Elements - A Gentle Introduction, Macmillan Press, 1996,  [ISBN 0333646266]
2. J. BONET & R.D. WOOD, Nonlinear Continuum Mechanics for Finite Element Analysis, Cambridge University Press, 1997, [ISBN 052157272X]
3. J. BONET & R.D. WOOD, Nonlinear Continuum Mechanics for Finite Element Analysis, Cambridge University Press, second edition, to appear 2007.

Chapters in books

1. CERVERA, E. HINTON, J.BONET and N.BICANIC, ‘Nonlinear transient dynamic analysis of three dimensional structures - a finite element program for steel and reinforced concrete materials’, Chapter 7 in  Numerical Methods and Software for Dynamic Analysis of Plates and Shells, E.Hinton, (Swansea, Pineridge Press, 1988). [ISBN ]
2. J. MIQUEL and J.BONET, ‘Elements of matrix algebra’, Appendix1 in J.Miquel and A.H.Barbat Structural Response Computations in Earthquake Enginnering, (Swansea Pineridge Press, 1989) [ISBN 0906674557]
3. R.D. WOOD and J.BONET, ‘Finite element simulation of thin sheet superplastic forming processes’, chapter18 in P.Hartley, I.Pillinger and C.E.N.Sturgess (eds.), Numerical Modelling of Material Deformation Processes: Research, Development and Applications, (Springer-Verlag, 1992) [ISBN 354019584X]
4. J. BONET and R.D.WOOD, ‘Some recent developments in the numerical simulation of thin sheet superplastic forming’, in M.Cross, J.F.T.Pittman and R.D.Wood, (eds.), Mathematical Modelling for Material Processing, (Clarendon Press, Oxford, 1993) [ISBN 198536879]
5. J. BONET, P. BHARGAVA and R.D. WOOD, ‘The incremental flow formulation for the numerical analysis of 3-d forming processes’, in Recent Developments in Finite Element Analsis, A Book Dedicated to R.L. Taylor, ed. by T.J.R. Hughes, E. Onate and O.C. Zienkiewicz, (Barcelona CIMNE, 1994) [ISBN 8487867456]

Journal Articles

1. J. MIQUEL and J. BONET, ‘Estudio de estructuras sometidas a esfuerzos de impacto en régimen elastoplástico y con grandes deformaciones por el método de los elementos finitos, parte I: formulación teórica’, Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería vol 3(2), 1987. [ISSN 02131315]
2. J. MIQUEL and J. BONET, ‘Estudio de estructuras sometidas a esfuerzos de impacto en régimen elastoplástico y con grandes deformaciones por el método de los elementos finitos, parte II: algoritmo de contacto-impacto’, Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería vol. 3(3), 1987. [ISSN 02131315] 
3. J. BONET, A.H.S. WARGADIPURA and R.D.WOOD, ‘A pressure cycle control algorithm for superplastic forming’, Comm. in Appl. Num. Meth. vol. 5(2), 1989. [ISSN 07488025]
4. J. BONET, R.D. WOOD and A.H.S.WARGADIPURA, ‘Numerical simulation of the superplastic forming of thin sheet components using the finite element method’, Int. J. Num. Meth. Engrg. vol. 30, 1990. [ISSN 00295981]
5. J. BONET and J.PERAIRE, ‘An alternating digital tree (ADT) algorithm for geometric searching and intersection problems’, Int. J. Num. Meth. Eng. vol. 31, 1991. [ISSN 00295981]
6. J. BONET, A.PICA, J.PEIRO and R.D.WOOD, ‘Adaptive mesh refinement for facet shell elements’, Comm. in Appl. Num. Meth., vol. 8, 1992. [ISSN 07488025]
7. R.D. WOOD and J. BONET, ‘Superplastic forming simulation using the finite element method - A review’, Journal of Metals, Materials and Processes, special issue on  Metal Processing - Mechanical Properties Interrelationships, 1993.
8. J. BONET, ‘Error estimators and enrichment procedures for the finite element analysis of large thin sheet deformation processes’, Int. J. Num. Meth. Engrg., vol 37, 1994. [ISSN 00295981] (*)
9. J. BONET, ‘The incremental flow formulation for the numerical analysis of plane stress and thin sheet forming processes’, Comp. Meth. Appl. Mech. Engrg., vol 114, 1994. [ISSN 0045785](*)
10. J. BONET, R.D. WOOD and R.COLLINS, ‘Pressure control algorithms for the numerical simulation of superplastic forming’, Int. J. Mech. Sci., vol 36(4),1994. [ISSN 00207403]
11. J. BONET & R.D. WOOD, Incremental flow procedures for the finite element analysis of thin sheet superplastic forming processes, J. Mat. Proc. Technol. vol 42, 1994. [ISSN 09240136]
12. J. BONET, P. BHARGAVA and R.D. WOOD, ‘The incremental flow formulation for the finite element analysis of 3-d superplastic forming processes’, J. Mat. Proc. Technol. vol 45, 1994. [ISSN 09240136]
13. J. BONET and R.D. WOOD, Energy dissipation strategies for the prediction of pressure cycles in the numerical analysis of superplastic forming processes, Material Science Forum, 1994, Vol. 170-172, pp. 607-612, [ISSN 02555476].
14. J. BONET, P. BHARGAVA & R.D. WOOD, Superplastic forming simulation of three dimensional diffusion bonded components using the finite element method, Material Science Forum, 1994, Vol. 170-172, pp. 607-612, [ISSN 02555476].
15. J. BONET and P.BHARGAVA, ‘The incremental flow formulation for the analysis of 3-dimensional viscous deformation processes: continuum formulation and computational aspects’,  Comp. Meth. Appl. Mech. Engrg.  vol. 114, 103-122, 1995. [ISSN 0045785] (*)
16. A. PICA, R.D. WOOD, A.O. ADEKUNLE  and J. BONET, ‘Smoothing stress resultants in adaptive finite element shell analysis’,  Computers and Structures. vol. 54(5), 1995. [ISSN 00457949]
17. J. BONET and P.BHARGAVA, A uniform deformation gradient hexahedron element with hourglass control, Int. J. Num. Meth. Engrg  vol 38(16), 1995. (80%) [ISSN 00295981]
18. R.D. WOOD and J.BONET, A review of the numerical analysis of superplastic forming, J. Mat. Proc. Technol. vol 60, 1996. [ISSN 09240136]
19. J. BONET, P. BHARGAVA & R.D. WOOD, ‘Finite element analysis of the superplastic forming of thick sheet using the incremental flow formulation’, Int. J. Num. Meth. Engrg.  vol 40, 1997, [ISSN 00295981].
20. J. BONET, ‘Recent developments in the incremental flow formulation for forming applications’, Engineering Computations. 1998. [ISSN 02644401]
21. J. BONET and A. BURTON, ‘A simple average nodal pressure tetraheron for nearly incompresible large strain dynamic explicit computations’, Comm. in Appl. Num. Meth., 14, 1998, pp. 437-449, [ISSN 07488025]
22. J. BONET and A. BURTON, ‘A simple orthotropic transversely isotropic hyperelastic constitutive equation for large strain computations’, Comp. Meth. Appl. Mech. Engrg. 162, 1998, pp. 151-164, [ISSN 0045785].
23. J. BONET & T.-S. L. LOK, ‘ Variational and momentum preservation aspects of smooth particle hydrodynamics formulations’, Comp. Meth. Appl. Mech. Engrg.,180, 97-115, 1999. [ISSN 0045785].
24. J. BONET & S. KULASEGARAM, ‘Correction and stabilisation of smooth particle hydrodynamics with application in metal forming’  Int. J. Num. Meth. Engrg., 47, 2000, 1189-1214. [ISSN 00295981].
25. J. BONET, R.D. WOOD, J. MAHANEY, P. HEYWOOD, Finite element analysis of air supported membrane structures, Comp. Meth. Appl. Mech. Engrg., 190, pp 579-595, 2000. [ISSN 0045785]
26. J. BONET & S. KULASEGARAM, Finite increment gradient stabilisation of point integrated meshless methods for elliptic equations, Commun. Num. Meth. in Engrg. 16, pp. 475-483, 2000.
27. J. BONET, Large strain viscoelastic constitutive  models, Int. J. Solids & Structures 38(17), pp. 2953-2968, 2001.
28. J. BONET, H. MARRIOTT & O. HASSAN, Stability and comparison of different linear tetrahedral formulations for nearly incompressible explicit dynamic applications, Int. J. Num. Meth. Engrg., 50, pp. 119-133, 2001.
29. J. BONET, H. MARRIOTT & O. HASSAN, An average nodal deformation tetrahedron for large strain explicit dynamic applications, Commun. Num. Meth. in Engrg.,17, 2001, 551-561.
30. J. BONET & J. MAHANEY, Form finding of membrane structures by the updated reference configuration with minimum mesh distorsion, Int. J. Solids Struc., 38, 2001, 5469-5480.
31. J. BONET, S. KULASEGARAM, Remarks on tension instability of Eulerian and Lagrangian corrected smooth particle hydrodynamics (CSPH) methods,  Int. J. Num. Meth. Engrg., 52, (11),  2001, pp. 1203-1220 [ISSN 00295981]  
32. J. BONET & S. KULASEGARAM, A simple methods to enhance the performance of Smooth Particle Hydrodynamics (SPH)  techniques,  Appl. Math. & Computation, 126, 2002, pp. 133-155.
33. J. BONET, A. HUERTA, J. PERAIRE, The efficient computation of bounds for functionals of finite element solutions in large strain elasticity, Comp. Meth. Appl. Mech. Engrg., 191, 2002, pp 4807-4826.
34. J. BONET, S. KULASEGARAM & MX RODRIGUEZ-PAZ, Variational Formulation for the Smooth Particle Hydrodynamics (SPH) Simulation of Fluid and Solid Problems, to appear in Lecture Notes in Computational Science & Engineering, 2002
35. J. BONET & S. KULASEGARAM, Alternative total Llagrangian formulations for corrected smooth particle hydrodynamics (csph) methods in large strain dynamic problems, European Journal of Finite Elements, 11(7-8), 2002.
36. J. BONET, RD WOOD, R SAID, RV CURTIS, D GARRIGA_MAJOR, Numerical simulation of the superplastic forming of dental and medical prosthesis, Biomechanics and Modelling in Mechanobiology, 1(3), 2002 pp. 177-196.
37. MX RODRIGUEZ-PAX, J. BONET, A corrected smooth particle hydrodynamics method for the simulation of debris flows, in Numerical Meth. Partial Differential Eqns., 20-1, 140-163, 2003 (40%)
38. S. KULASEGARAM, J. BONET, RW. LEWIS & M. PROFIT, High pressure die casting simulation using a Lagrangian particle method, Communications in Num. Meth. Engrg. 19,-9, 2003. (30%)
39. D GARRIGA-MAJO, RJ PATERSON, RV CURTIS, R SAID, RD WOOD & J BONET, Optimisation of the superplastic forming of a dental implant for bone augmentation using finite element analysis, Dental Materials, 20-5, 2004, pp. 409-418.
40. J. BONET, S. KULASEGARAM, MX RODRIGUEZ & M. PROFIT, Variational formulation for the Smooth Particle Hydrodynamics simulation of fluid and solid problems, Comp. Meth. Appl. Mech. Engrg., 193, Issues 12-14, 2004, pp. 1245-1256. (40%)
41. J. BONET, S. KULASEGARAM, M. PROFIT AND R. W. LEWIS, A Particle based method for three-dimensional mould filling simulation in high pressure die casting, submitted to J. Mat. Proc. Technology, 2004.
42. RW LEWIS, RS RANSING, WKS PAO, K KULASEGARAM & J BONET, Alternative techniques for casting simulation, Int. j. Num. Meth. Heat & Fluid Flow, 14, 2004, pp. 145-166.
43. AM. SAUER-BUDGE, J. BONET, A. HUERTA, J. PERAIRE, Computing bounds of linear functional of exact solutions to Poisson’s equations, to appear in SIAM Journal on Numerical Analysis, 42, 2004, pp. 1610. (30%)
44. S. KULASEGARAM, J. BONET RW. LEWIS & M PROFIT, A variational formulation based contact algorithm for SPH applications, in Computational Mechanics, 33(4), pp. 316 - 325, 2004. (40%)
45. S.K. LAHIRI, J. BONET, J. PERAIRE, L. CASALS, A variationally consistent fractional time step integration method for Lagrangian dynamics, Int. J. Num. Meth. Engrg., 63-10, 2005, 1371-1395 (40%)
46. J. BONET & M. RODRIGUEZ-PAZ, Hamiltonian formulation for variable h Smooth Particle Hydrodynamics, Journal of Computational Physics, 209-2, 2005, pp.541-558.
47. S. FERNANDEZ, J. BONET & A. HUERTA, Continuous blending of SPH with finite elements, Computers & Structures, 17-18,  2005, pp. 1396-1410.
48. MX RODRIGUEZ-PAZ & J. BONET, A corrected smooth particle hydrodynamics formulation of the shallow water equations, Computers & Structures, special issue on Meshless Methods. 17-18, 2005, pp. 1396-1410.
49. J. BONET, A.J. GIL, RD WOOD, R SAID & RV CURTIS, Simulating superplastic forming, Computer Methods in Appl. Mech. Engrg.,195-48, 2006, pp. 6580-6603.
50. A.J. GIL & J. BONET, Finite element analysis of pre-stressed structural membranes, Finite Element Analysis & Design., 42-8, 2006, pp. 683-697.
51. N. PARES, J. BONET, A. HUERTA, J. PERAIRE, The computation of bounds for linear functional outputs of weak solutions to the two-dimensional elasticity equation, Computer Methods in Appl. Mech. Engrg.,195-4-6, 2006, pp. 406-429.
52. Y. VIDAL, J. BONET & A. HUERTA, Stabilized updated Lagrangian corrected SPH for explicit dynamics problems, to appear in Int. J. Num. Meth. Engrg., 2006.
53. J. FELDMAN & J. BONET, Dynamic refinement and boundary contact forces in SPH with applications in fluid flow problems, to appear in Int. J. Num. Meth. Engrg., 2006.
54. A.J. GIL & J. BONET, Finite element analysis of partly wrinkled reinforced prestressed membranes, to appear in Computational Mechanics, 2006.
55. H. CIRIA, J. PERAIRE & J. BONET, Computation of Upper and Lower Bounds in Limit Analysis using Second-order Cone Programming and Mesh Adaptivity, to appear in Int. J. Num. Meth. Engrg., 2006.
56. C. WOOD, A.J. GIL, O. HASSAN & J. BONET, A partitioned approach to for the solution of three-dimensional time-dependent incompressible fluid-structure interaction, to appear in Advances Engrg. Software, 2007.
57. C. WOOD, A.J. GIL, O. HASSAN & J. BONET, Partitioned three-dimensional time-dependent fluid-structure interaction with applications in biological membranes, to appear in Int. J. Num. Meth. Engrg., 2007.
58. C. WOOD, O. HASSAN, J. BONET, A.J. GIL, A partitioned coupling approach  for dynamic fluid-structure interactions with applications to biological membranes, submitted to Int. J. Num. Meth. Engrg., 2007.