A numerical stress calculation procedure for a fiber-fiber kinetics model with Coulomb and viscous friction of connective tissue

A material model based on fiber-fiber Coulomb and viscous friction for connective tissue was introduced in references Mijailovic (1991) and Mijailovic et al. (1993). A numerical procedure was developed in reference Mijailovic (1991) by considering sliding of fibers as a contact problem between bodies, and results were verified by experiments. Another numerical approach, much more stable and efficient, for stress calculation in case of Coulomb friction only, was proposed in reference Kojic et al. (1998). This paper represents an extension of the numerical algorithm of reference Kojic et al. (1998) to include viscous friction between fibers. The complex history of sliding is traced by dividing the current sliding length between fibers on a number of segments. The computational procedure is simple, numerically reliable and provides stress calculation for arbitrary cyclic loading of connective tissue material in tension, shear, and tension and shear simultaneously. Typical hysteresis loops can be reproduced by using the proposed numerical algorithm. The model is implemented into a finite element program PAK (Kojic et al., 1996), with a possibility of solving real problems of connective tissue. Solved examples illustrate the main features of the fiber-fiber kinetics model and of the developed numerical procedure.