Modeling of Anisotropic Damage of Cortical bone and its Application to Simulations of Crash Aocident Injuries

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We proposed an inelastic constitutive model of cortical bone by taking account of anisotropic damage. The model is formulated by extending a one-dimensional theology model comprised of a viscoelastic and a viscoplastic element in series to a three-dimension model. The thermodynamic restrictive conditions are satisfied by using the framework of the constitutive model theory based on the irreversible thermodynamics. Damage properties of cortical bone are represented by a symmetric second-order tensor variable (damage variable),and the damage effects are incorporated into the constitutive model by assuming the hypothesis of total energy equivalence in the damage mechanics. The framework of evolution equation of the damage variable is determined by the representation theorem, and a concrete expression is formulated by examining experimental data in literatures.The applicability of the proposed model is discussed by simulating the experimental data of human cortical bones and by comparing the predicted results with the data. The results reveal that the proposed model can represent with a high degree of accuracy the strain rate dependency, the anisotropy, and the asymmetry of tension and compression, of elastic coefficients, yield stresses, strain hardening behavior, and bone fracture timing.The proposed model is implemented into the general-purpose dynamic finite element code LS-DYNA by use of the user-defined subroutine system. lb ascertain the adequacy of the implementation, finite element analyses using 1 element model are performed for uniaxial tension and compression, and the results are compared with those of direct calculation using the constitutive model. The two results agreed well.Then a human femur approximated by a circular cylindrical tube is analyzed under several basic loading conditions, and bone fracture patterns are predicted. Now we compare the results with the corresponding experimental data.