Numerical investigation of elastoplastic and damage behavior of cortical bone by applying a new damage model

Due to the need for orthopedic surgeries, the mechanical behavior of cortical bone in cyclic loading and physiological strain rate has been investigated. The emphasis is on developing a structural law that can establish the behavior during loading, unloading and reloading observed in experiments. The created models have elastic, damage, and plastic modes. The formulations are based on two variables: internal damage and plastic strain. First, two one-dimensional models independent of the strain rate are formulated, one with one damage variable and the other with two separate damage variables in tension and compression, are examined, and using laboratory data, the coefficients of each model are obtained. By comparing the simulation results and laboratory data, the necessary modifications have been made to the models. Finally, by combining the Bresler-Pister anisotropic yield criterion and the one-dimensional model independent of the rate associated with the two damage variables, the corresponding three-dimensional model was obtained. This three-dimensional model was implemented in the form of an explicit finite element method and the result showed acceptable compatibility with the simulation results of the one-dimensional model and experimental data. This three-dimensional model will be suitable for simulating complex geometries. The coefficient of determination for one-dimensional models RI, ±RI, RI, and ±RI has been modified and the three-dimensional model has obtained values of 0.882174, 0.965665, 0.995508, 0.996279, and 0.984866, respectively