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 e t al. (1993). The model is based on the hypothesis of sliding of elast ic 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 consider ing sliding as a contact problem between bodies. In this paper we prop ose a new and general numerical procedure for calculation of the stres s-strain law of the fiber-fiber kinetics model in case of Coulomb fric tion. Instead of using a contact algorithm (Mijailovic 1991), which is numerically inefficient and never enough reliable, here the history o f sliding along the sliding length is traced numerically through a num ber of segments along the fiber. The algorithm is simple, efficient an d reliable and provides solutions for arbitrary cyclic loading, includ ing tension, shear, and tension and shear simultaneously, giving hyste resis loops typical for soft tissue response. The model is built in th e finite element technique, providing the possibility of its applicati on to general and real problems. Solved examples illustrate the main c haracteristics of the model and of the developed numerical method, as well as its applicability to practical problems. Accuracy of some resu lts, for the simple case of uniaxial loading, is verified by compariso n with analytical solutions.