Studies on constitutive equation that models bone tissue

A method for identifying viscoelastic constitutive equations for bone is developed. In the method, anisotropy, non-homogeneity and bone remodelling are taken into consideration. The equations correspond to monotropic rheological model of bone. In order to calculate the material parameters of elasticity and viscosity, a new algorithm is developed, in which the results of creep compression and shear tests are used. The way of determining the material constants of elasticity and viscoelasticity for bone in the areas that are crucial in strain and stress analysis is shown a well. The strength experiments (tests) and creep tests were performed on bone samples extracted from the femur of calf. The method of bone modelling in terms of rheology is the following: bone samples are properly prepared from biological material. For given bone samples, which have more or less the same density, three independent short-term creep tests are carried out. The results of the creep tests permit us to determine five elastic constants and viscoelastic constants of a monotropic material [1]. In order to describe rheological processes in terms of structural models, fractional exponential functions and normal exponential functions are used. The constitutive equations are formulated in the compliance form. The computer program that executes the algorithm of elastic and viscoelastic constant determination is used.