Analysis of stress-strain state of dental implants by the boundary integral equations method

The boundary integral equations method is applied for the computational analysis of the stresses and strain of dental implants. Isoparametric quadratic boundary elements are used for the numerical solution of the boundary integral equations. The numerical algorithm has been implemented in the form of computer software for solving problems of elasticity and thermoelasticity with mixed boundary conditions and conditions of non-ideal interface between sub-regions of a structure. The implants with a crown fixed by cement using various materials for the junction were considered. Computations were performed for the plane strain state of the structure and consisted of the two stages. The first stage was the analysis of the whole structure with a smoothed screw in the join between the implant and bone; the second one was the analysis of stress concentration in the screwed join at the contact zone between the implant and bone. The model of the first stage contained 7 sub-domains, which are conforming to various parts of the implant. The analysis of the stress concentration of the screw and bone joint is performed at the second stage of this research. It was assumed that those hollows in the spongy bone, which were formed in the bone after the implant’s penetration, are conformed to the screw thread on the implant. Also it was assumed that there is the formation of the full materials joint on the boundary line of the implant and bone. At the first stage of calculations of the implant structure with components made from various materials made it possible to determine, that the greatest stresses occur in implants with a predominant component of titanium. An estimate of the stress concentration in the screw turns of the thread and in the bone tissue was obtained at the second stage of calculating the screw joint of the implant and bone tissue. It was also established that the greatest stresses occur in the zone of the first turn of the thread of the implant screw.