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

提出了一种考虑各向异性损伤的皮质骨非弹性本构模型。该模型是通过扩展的粘弹性和粘塑性元件串联组成的一维流变模型的三维模型。利用基于不可逆热力学的本构模型理论框架，满足热力学约束条件。皮质骨的损伤特性由一个对称的二阶张量变量（损伤变量）表示，损伤效应通过损伤力学中的总能量等效假设被纳入本构模型中。利用表示定理确定了损伤变量演化方程的框架，并通过对文献中实验数据的检验给出了具体表达式，通过对人体皮质骨的实验数据进行模拟，并将预测结果与实验数据进行比较，讨论了该模型的适用性.结果表明，该模型能很好地反映材料的应变率依赖性、各向异性、拉压不对称性、弹性系数、屈服应力、应变硬化行为和骨折发生时间，并通过用户自定义子程序系统在通用动力有限元程序LS-DYNA中实现。为了验证该方法的可行性，采用单单元模型对单轴拉伸和压缩进行了有限元分析，并与采用本构模型直接计算的结果进行了比较。在此基础上，对人体股骨在几种基本载荷条件下的骨折模式进行了分析和预测。现在我们将结果与相应的实验数据进行比较。

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.