Advanced finite element analysis of L4–L5 implanted spine segment

In the paper finite element (FE) analysis of implanted lumbar spine segment is presented. The segment model consists of two lumbar vertebrae L4 and L5 and the prosthesis. The model of the intervertebral disc prosthesis consists of two metallic plates and a polyurethane core. Bone tissue is modelled as a linear viscoelastic material. The prosthesis core is made of a polyurethane nanocomposite. It is modelled as a non-linear viscoelastic material. The constitutive law of the core, derived in one of the previous papers, is implemented into the FE software Abaqus®. It was done by means of the User-supplied procedure UMAT. The metallic plates are elastic. The most important parts of the paper include: description of the prosthesis geometrical and numerical modelling, mathematical derivation of stiffness tensor and Kirchhoff stress and implementation of the constitutive model of the polyurethane core into Abaqus® software. Two load cases were considered, i.e. compression and stress relaxation under constant displacement. The goal of the paper is to numerically validate the constitutive law, which was previously formulated, and to perform advanced FE analyses of the implanted L4–L5 spine segment in which non-standard constitutive law for one of the model materials, i.e. the prosthesis core, is implemented.