A level-set-based large sliding contact algorithm for easy analysis of implant positioning

Abstract

A finite element analysis of implant positioning inside a bone requires the creation of many meshes that model various implant orientations. This process can be very labour intensive and is difficult to automate. In order to facilitate this type of modelling, we present a large sliding contact algorithm that does not require the creation of a conforming discretization for the bone. The cavity inside the bone, necessary to accommodate the implant, is modelled with a Heaviside function calculated on the level set field, which is defined in terms of material coordinates of the bone. The algorithm is based on the minimization of the energy functional with a constraint term, formulated as in classical contact mechanics; however, instead of the distance function, we use the above-mentioned level set function. The presented numerical 2D and 3D examples validate the algorithm against the solutions obtained with commercial finite element software.

Keywords: contact; level set; finite element method; Lagrange multipliers: implant positioning