The post-elastic mechanical behavior of cortical bone, which is represented by extensive microcracking once the elastic regime is exceeded, has been characterized by a nonlinear constitutive relationship for osteonal microcracking. The relationship/model is based on the formalism of Statistical Mechanics, allowing the degree of irreversibility to be calculated using the increase in entropy associated with the progression of microcracking. Specific tensile and bending tests were conducted to compare theoretical predictions of constitutive relationships to empirical curves. In addition, the tests were utilized to determine the model’s parameters, whose values were used to explicitly calculate the entropy increase. A large sample was used: 51 cortical bone coupons (dog-bone-shaped specimens) were extracted from the 4th ribs of numerous individuals and subjected to uniaxial tensile testing. Additionally, fifteen complete 4th ribs were used for bending tests. Displacement and strain fields were measured for both types of tests using digital image correlation or video recordings of the tests. All experimental specimen data were successfully fitted to the model, and all constitutive parameter values were found to be correlated with anthropometric variables. Explicit entropy calculations indicate that microcracking is minimal for low strain and, initially, stress is nearly proportional to strain. After a certain point, significant microcracking occurs, and the relationship between stress and strain becomes invalid. Several significant associations between constitutive parameters and age have also been identified.

皮质骨的后弹性机械行为，一旦超过弹性状态，就会出现广泛的微裂纹，其特点是骨微裂纹的非线性本构关系。该关系/模型基于统计力学的形式，允许使用与微裂纹进展相关的熵的增加来计算不可逆性程度。进行了特定的拉伸和弯曲测试，以将本构关系的理论预测与经验曲线进行比较。此外，测试还用于确定模型的参数，其值用于明确计算熵增加。使用大样本：从众多个体的第 4 肋骨中提取 51 个皮质骨试样（狗骨状标本）并进行单轴拉伸测试。此外，十五个完整的第四肋用于弯曲测试。使用数字图像相关或测试视频记录来测量两种类型测试的位移和应变场。所有实验样本数据均成功拟合到模型，并且发现所有构成参数值均与人体测量变量相关。显式熵计算表明，低应变时微裂纹最小，并且最初应力几乎与应变成正比。在某一点之后，出现显着的微裂纹，应力和应变之间的关系变得无效。还确定了构成参数和年龄之间的一些重要关联。