Abstract—The use of titanium foam (Ti-foam) as an implant material has gained a lot of interest recently due to its good biocompatibility as well as stable fixation between implant and human bone. A finite element model is required in order to effectively design appropriate implants. Accurate finite element analyses rely on accuracy and efficiency of the applied material models. Mechanical behaviour of the Ti-foam under loadings are different from the solid titanium therefore an appropriate metal foam constitutive model is needed. In this paper, the Deshpande and Fleck model which is available as the crushable foam model in the ABAQUS finite element software has been employed together with appropriate material parameters to describe the deformation behaviour of the Ti-foam with various porosity levels under compressive and bending loads. The simulation results have been compared against recently published data. Good comparisons have been seen. This validated Ti-foam material model has been employed to study stress distributions on the Ti-foam dental implant system. Index Terms—Dental Implants, Finite element Analysis, Material model, Titanium foam I. INTRODUCTION etal foams, a new class materials, have increasingly been employed for a range of applications such as structural components, automotive parts, sound and vibration absorbers, heat exchanger and biomedical implants [1]-[3]. This is due to their unique combination of properties such as low density, high specific stiffness, high specific strength and good energy absorption capability [4]. Among metal foams, titanium foams (Ti-foams) are preferred in many crucial applications including biomedical implants which biocompatibility is required. The main interests for using cellular metals come from the increase of the friction coefficient between the implant and the surrounding bone. It allows mechanical interlocking of bone with the implant by substantial bone in-growth and better long term stability. Additionally, stiffness of the implants can be tailored by varying porosity to reduce the stress shielding effect [5], [6]. One of promising biomedical application of Ti-foams is in dental implants. Finite element analysis has played an important role in designing of dental implants [7]-[11]. The success of the increasing use of the finite element method for analysing structures and components rests upon the accuracy and efficiency of the applied material models. Mechanical * Manuscript received Mar 04, 2011; revised April 1, 2011. Wiwat Tanwongwan is with the faculty of Engineering King Mongkut’s University of Technology North Bangkok. 1518 Piboolsongkram Rd Bangkok, Thailand (email: misterwiwat@yahoo.com) Julaluk Carmai* is with the faculty of Engineering King Mongkut’s University of Technology North Bangkok. 1518 Piboolsongkram Rd Bangkok, Thailand. (phone:662-9132500 ext 8208; fax 662-5870029; email: jcm@kmutnb.ac.th) behaviours of Ti-foam under loadings are different from the solid titanium. The Ti-foam is compressible material of which volume changes during the deformation while the solid titanium is incompressible material of which volume does not change. Hence, metal foams can yield under hydrostatic loading in addition to deviatoric loading. Furthermore, different levels of porosity in Ti-foam lead to different mechanical properties and failure mechanisms [11]- [13]. An appropriate metal foam constitutive model is required in simulation using the finite element technique. Constitutive models for metal foams [14]-[17]. have been developed for the past decade. Some of them have been built in commercial finite element packages such as LS-DYNA and ABAQUS. Most of them have been applied successfully in describing behaviour of aluminium foam. However, very few have been employed for Ti-foam under complex loading conditions. This paper, therefore, addresses an examination of applicability of the Deshpande and Fleck model, which is available in the ABAQUS finite element package as the crushable foam material model, on describing the Ti-foam behaviour. It will be employed to study the stress distribution on the Ti-foam dental implant which is subjected to the complex stress states. II. METAL FOAMS A. Mechanical Behaviours of Metal Foams The major difference between foam materials and solid materials is their microstructure. A large amount of cells or pores are present in metal foams can be imagined as sponge. A metal foam is, therefore, characterised microstructurally by its cell topology, relative density, cell size and cell shape [18]-[20]. The term, porosity, is a parameter used at the macroscopic scale to indicate the proportion of porous area in foams. The microstructure features of cellular metals are affecting their mechanical responses. The stress-strain curve for a metal foam in compression is characterised by three regimes a linear elastic regime, corresponding to cell bending or face stretching; a stress plateau regime, corresponding to progressive cell collapse by elastic buckling or plastic yielding; and densification regime, corresponding to collapse of the cell throughout the material and subsequent loading of cell edges and faces against one another. Low relative density metal foam can be deformed up to large strain before densification occurs [21]. For successful application as functional components, knowledge of the plastic yield surface and subsequent plastic flow behaviour of a metal foam is very important. In contrast to solid metals, metal foams can yield under hydrostatic loading in addition to deviatoric loading [4]. Therefore, the Finite Element Modelling of Titanium Foam Behaviour for Dental Application Wiwat Tanwongwan and Julaluk Carmai * , Member, IAENG M Proceedings of the World Congress on Engineering 2011 Vol III WCE 2011, July 6 - 8, 2011, London, U.K. ISBN: 978-988-19251-5-2 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online) WCE 2011