A numerical algorithm for stress integration of a fiber-fiber kinetics model with Coulomb friction for connective tissue

Complex behaviour of connective tissue can be modeled by a fiber-fiber kinetics material model introduced in Mijailovic (1991), Mijailovic et al. (1993). The model is based on the hypothesis of sliding of elastic fibers with Coulomb and viscous friction. The main characteristics of the model were verified experimentally in Mijailovic (1991), and a numerical procedure for one-dimensional tension was developed considering sliding as a contact problem between bodies. In this paper we propose a new and general numerical procedure for calculation of the stress-strain law of the fiber-fiber kinetics model in case of Coulomb friction. Instead of using a contact algorithm (Mijailovic 1991), which is numerically inefficient and never enough reliable, here the history of sliding along the sliding length is traced numerically through a number of segments along the fiber. The algorithm is simple, efficient and reliable and provides solutions for arbitrary cyclic loading, including tension, shear, and tension and shear simultaneously, giving hysteresis loops typical for soft tissue response. The model is built in the finite element technique, providing the possibility of its application to general and real problems. Solved examples illustrate the main characteristics of the model and of the developed numerical method, as well as its applicability to practical problems. Accuracy of some results, for the simple case of uniaxial loading, is verified by comparison with analytical solutions.