Simulation of deformation behavior of porous Titanium using Modified Gurson yield function

Document Type: Research Paper


1 K. N. Toosi university of Technology

2 K.N. Toosi university of Technology


In this research the stress-strain curve of porous Titanium, as a common material for biomedical application, was predicted using the mechanical properties of fully solid Titanium experimental data. Modified Gurson model (Gurson-Tvergaard-Needleman (GTN) model) was used to predict the plastic response of porous Titanium in compaction. Different values of GTN parameters were used for different initial porosity. It was recognized that volume constancy assumption during plastic deformation of porous media cannot be satisfied due to both of changes in porosity and hydrostatic stress contribution on yielding. It was found that consideration of porosity variation is necessary during deformation for accurate modeling. Also, porous samples represented the same lateral expansion under less axial displacement relative to fully solid sample regarding the GTN model. The stress distribution of porous samples was different from solid sample considering the GTN model and this was predicted different shear banding. Evolution of porosity during deformation leads to linear like stress response in the plastic deformation regime.


 1. L.J. Gibson, Biomechanics of cellular solids, Journal of biomechanics, 38 (2005) 377–99.

2. G. Ryan, A. Pandit and D.P. Apatsidis, Fabrication methods of porous metals for use in orthopaedic applications, Biomaterials, 27 (2006) 651–70.

3. S.R. Nagaraja, S.G. Rakesh, J.K. Prasad, P.K. Barhai and G. Jagadeesh, Investigations on micro-blast wave assisted metal foil forming for biomedical applications, International Journal of Mechanical Sciences, 61 (2012) 1–7.

4. A. Merdji, B. Bachir Bouiadjra, T. Achour, B. Serier, B. Ould Chikh and Z.O. Feng, Stress analysis in dental prosthesis, Computational Materials Science, 49 (2010) 126–133.

5. J.D. Bobyn, R.M. Pilliar, H.U. Cameron and G.C. Weatherly, The optimum pore size for the fixation of porous-surfaced metal implants by the ingrowth of bone, Clinical Orthopaedics & Related Research, 150 (1980) 263– 270.


 6. H. Cameron, Six-year results with a microporous-coated metal hip prosthesis, Clinical Orthopaedics & Related Research, 208 (1986) 81–83.

7. J. Bobyn, E. Mortimer, A. Glassman, C. Engh, J. Miller and C. Brooks, Producing and avoiding stress shielding: laboratory and clinical observations of noncemented total hip arthroplasty. Clinical Orthopaedics & Related Research, Clinical Orthopaedics & Related Research, 274 (1992) 79–96.

8. M. Schneider and H. Yuan, Experimental and computational investigation of cyclic mechanical behavior of sintered iron, Computational Materials Science, 57 (2012) 48–58.

9. J. Kovacik, Correlation between Young’s modulus and porosity in porous materials, Journal of Materials Science Letters, 18 (1999) 1007–1010.

10. J. Tirosh and D. Iddan, Forming analysis of porous materials, International Journal of Mechanical Sciences, 31 (1990) 949–965.

11. H. Nakajima, Fabrication, properties and application of porous metals with directional pores, Progress in Materials Science, 52 (2007) 1091–1173.

12. L.J. Gibson and M.F. Ashby, CellularSolid: Structure and properties, Cambridge University Press (1988).

13. T. Imwinkelried, R. Biomaterials, S. Gmbh and C. Oberdorf, Mechanical properties of open-pore Titanium foam, Journal of Biomedical Materials Research Part A (2007).

14. R. Singh, P.D. Lee, T.C. Lindley, C. Kohlhauser, C. Hellmich, M. Bram, T. Imwinkelried and R.J. Dashwood, Characterization of the deformation behavior of intermediate porosity interconnected Ti foams using micro-computed tomography and direct finite element modeling, Acta biomaterialia, 6 (2010) 2342–51.

15. W. Niu, S. Gill, H. Dong and C. Bai, A two-scale model for predicting elastic properties of porous Titanium formed with space-holders, Computational Materials Science, 50 (2010) 172–178.

16. M.R. Karamooz Ravari, M. Kadkhodaei, M. Badrossamay and R. Rezaei, Numerical investigation on mechanical properties of cellular lattice structures fabricated by fused deposition modeling, International Journal of Mechanical Sciences, 88 (2014) 154–161.

17. C.C. Huang and J.H. Cheng, Forging simulation of sintered powder compacts under various frictional conditions, International Journal of Mechanical Sciences, 44 (2002) 489–507.

18. S.B. Biner and W.A. Spitzig, Densification of iron compacts with various initial porosities under hydrostatic pressure, Acta Metallurgica, 38 (1990) 603–610.

19. V. Tvergaard, Influence of voids on shear band instabilities under plane strain conditions, International Journal of Fracture, 17 (1981) 389–407.

20. V. Tvergaard and A. Needleman, Analysis of the cup-cone fracture in a round tensile bar, Acta Metallurgica, 32 (1984) 157–169.

21. R. Becker, A. Needleman, O. Richmond and V. Tvergaard, Void growth and failure in notched bars, Journal of the Mechanics and Physics of Solids, 36 (1988) 317–351.

22. M. Abbasi, M. Ketabchi, H. Izadkhah, D.H. Fatmehsaria and A.N. Aghbash, Identification of GTN model parameters by application of response surface methodology, Procedia Engineering, 10 (2011) 415–420.

23. W.A. Spitzig, R.E. Smelser and O. Richmond, The evolution of damage and fracture in iron compacts with various initial porosities, Acta Metallurgica, 36 (1988) 1201–1211.

24. J. Simo and T. Hughes, Computational Inelasticity, Springer, New York, (2013).

25. T. Belytschko, K. Wing and B. Moran, Nonlinear Finite Elements For Continua And Structures, John Wiley & Sons, (2014).