The Elasto-plastic Response of the Bone Tissue Due to the Insertion of Dental Implants

Abstract

In this work, the elasto-plastic behaviour of the bone tissue, in the presence of dental implants, is numerically obtained using a discrete meshless method - the Natural Neighbour Radial Point Interpolation Method (NNRPIM). Within the NNRPIM the nodal connectivity is enforced using the Natural Neighbour concept. Additionally, using the same mathematical concept, it is possible to obtain the background integration mesh. The NNRPIM is a truly meshless method, because the construction of the nodal connectivity and the integration mesh depends uniquely on the nodal mesh discretizing the problem. No other spatial information is required. The integration mesh is used in the numerical integration of the integro-differential equations governing the physic phenomenon. The NNRPIM interpolation functions are constructed using the Radial Point Interpolators (RPIs). These functions are used as the trial functions of the Galerkin weak form, which permits to define the discrete system of equations. The obtained interpolation functions possess the delta Kronecker property, which simplify the imposition of the natural and essential boundary conditions. Since in this work it is performed an elasto-plastic analysis of the bone tissue, a non-linear solution algorithm must be adopted. In this work the Newton-Raphson initial stiffness method is considered. Additionally, the efficient “forward-Euler” procedure is used in order to return the stress to the yield surface. Experimental studies reveal that the bone tissue show a distinctive yielding followed by a constant nominal stress plateau for both uniaxial and confined compression, which can be represented with a classic “linear elastic – linear plastic” material behaviour. Thus, in this work, it is used the von-Mises yield surface to characterize the plastic behaviour of trabecular bone.