Cortical Bone Tissue Viscoelastic Properties and its Constitutive Equation - Preliminary Studies

Abstract

Cortical Bone Tissue Viscoelastic Properties and its Constitutive Equation - Preliminary StudiesIn the paper, preliminary studies on formulation of a new constitutive equation of bone tissue are presented. A bone is modelled as a viscoelastic material. Thus, not only are elastic properties of the bone taken into account, but also both short-term and long-term viscoelastic properties are considered. A potential function is assumed for the bone, constant identification on the basis of experimental stress-strain curve fitting is completed and a preliminary constitutive equation is formulated. The experiments consisted of compressive tests performed on a cuboids-like bone sample of the following dimensions: 10×5×7.52 mm. The specimen was compressed along the highest dimension at the strain rates 0.016 s-1and 0.00016 s-1. In addition to this, stress relaxation test was performed to identify long-term viscoelastic constants of bone. In the experiments, only displacement in the load direction was measured. The bone sample was extracted from a bovine femur. The form of the proposed potential function is such that it models a bone as a transversely isotropic material. For the sake of simplicity, it is assumed that the bone is incompressible. After the material constant identification the strain energy function proved to be adequate to describe bone behaviour under compressive load. Due to the fact that the function is convex, the results of the studies can be utilised in modelling of bone tissue in finite element analyses of an implant-bone system. Such analyses are very helpful in the process of a new prosthesis design as one can preoperatively verify the construction of the new implant and optimise its shape.